THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING THE INTEGRAL ISOBARIC HEAT OF VAPORIZATION OF MIXTURES Fred Po Stein A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The University of Michigan 1960 September, 1960 IP-456

ACKNOWLEDGEMENTS The author gratefully acknowledges and offers his sincere thanks for the valuable assistance, in the various forms described below, which he received from both organizations and individuals. The Department of Chemical and Metallurgical Engineering provided funds for the purchase of equipment and supplies used in the experimental worko Three predoctoral fellowships granted by the National Science Foundation afforded personal financial assistance. The duPont Fundamental Research in Chemical Engineering Fund provided a tuition grant for one semester. The Industry Program of the College of Engineering aided in the preparation and reproduction of the dissertation. Professor Joseph Jo Martin's guidance in the formulation of the thesis problem, his counsel and encouragement at various stages of the work, and his service as doctoral committee chairman were indispensable. The doctoral committee composed of Professors Lee Oo Case, Stuart W. Churchill, Donald L. Katz, and Go Brymer Williams gave of their time and counsel to the author. Professor Williams is to be singled out for his service as committee chairman during the period of Professor Martin's leaveo Frank Bo Drogosz and Cleatis Bolen of the departmental shop rendered competent assistance in the construction of parts of the apparatuso A number of fellow students offered helpful suggestions for and constructive criticism of the worko Finally, the moral and financial support of Monica B. Stein, Ethel Ho Stein, and Paul E. Stein, members of the author's immediate family, must be recognized. Without this support the author's undergraduate and graduate training would have been in serious jeopardy. ii

TABLE OF CONTENTS Page ACKNOWTLEGMENmTS...O*.O... o o.................. *......... ii LIST OF TABLESi.....*...................................... *vi LIST OF FIGURES......... *.o..........................v..... viii ABSTRACT........ o............................................... xi INTRODUCTION...... o..........a *.................. 1 THEORETICAL BACKGROUND........................................... 5 Enthalpy Change Accompanying a Liquid-Vapor Phase Change 3 Relationships Among the Heats of Vaporization of Mixtures................................9 METHODS OF PRIEDICTING HEATS OF VAPORIZATION OF MIXTURES....... 14 Summary...................................... 14 The Enthalpy-Temperature-Diagram Approach.............. 15 Application of Equilibrium-K Values................. 26 The Enthalpy-Concentration-Diagram Approach......... 33 Rigorous Application of Two-Phase, P-V-T-x Data......... 39 Clapeyron Equation for Mixtures........................ 41 Simpler Approximations......................... 44 EXPERIENCE OF PREV IOUS EXPERIMENTERS.......46 Earliest Investigations................................ 46 Recent Investigations.................................. 47 EXPERIMENTAL APPARATUS.................................... 51 Summary........................................... 51 The Flow System................... 51 Required Measurements..................... 56 Thermal Shielding..............................59 The Calorimeter......................................... 62 Auxiliary Equipment.................................... 67 Heaters and Electrical Circuits......................... 73 Analytical Equipment................................... 82 Materials.................................... 83 iii

TABLE OF CONTENTS CONT'D Page EXPERIMENTAL PROCEDURE................................ 84 Summary. +.............................................. 84 Preparation*.............................. 84 Cycling................................................. 87 Measurements............a............................ 88 Sampling and Analysis............................ 90 CALCUIATIONS o....................................................... 95 Summary....................................... 95 Uncorrected Latent Heat............................. 95 Corrections...................................... 96 Effects of Flow Rate................... 100 Estimate of Ac y.0o4 Estimate of Accuracy,................................. 104 EXPERIMENTAL DATA AND RESULTS*............................. 106 Summary.............*......................... 106 Calibration Data...*...1........................ 106 Integral-Isobaric-Heat-of-Vaporization Data........ 107 Vapor-Liquid Equilibrium Data.....*........4..,.. 114 Enthalpy-Concentration Diagrams..................... 129 Differential Heat of Condensation....,............ 137 CORRELATION OF OTHER INTEGRAL-ISOBARIC-IEAT-OF-VAPORIZATION DATA.. 139 CONCLUSIONS.............*...148 NOMENCLATURE, UNITS, AND CONVERSION FACTORS.................... 150 APPEND ICES APPENDIX A Unsteady State Operating Period of the Vaporizer........ 155 B I. Sample Calculation of Energy Consumption in the Vaporizer.............................. 159 II. Sample Calculation of Integral Isobaric Heat of Vaporization from Measured Quantities,.......... 161 C Sample Calculation of Integral Isobaric Heat of Vaporization from Data Available in the Literature,.......... 165 D Sample Calculation of Integral Isobaric Heat of Vaporization Using the Equilibrium-K-Value Equations,........ 167 iv

TABLE OF CONTENTS CONT'D APPEND.IX Page E Smoothed Data.....*................~. 171 Calibrations...................... 171 F Raw Data,.*.......*.....A......... O.*..... 178 BIBLIAOGRAP:HY* *.....*................. a......................... 182 ~

LIST OF TABLES Table Page I Mixtures for which Reliable, Experimentally Determined, Latent-Heat-of-Vaporization Data are Available........ 49 II Heat of Vaporization of the Pure Components............. 107 III Integral Isobaric Heat of Vaporization -Isopropyl Alcohol-Water......... * +.......................**..... 112 IV Integral Isobaric Heat of Vaporization- Acetone-Water.. 112 V Vapor-Liquid Equilibrium Data - Isopropyl Alcohol-Water. 115 VI Vapor-Liquid Equilibrium Data -Acetone-Water........... 120 VII Enthalpy of Isopropyl Alcohol-Water Mixtures........... 135 VIII Enthalpy of Acetone-Water Mixtures,....3...... 135 IX Calculated Heats of Mixing Compared to Experimental Values..................*.................. 156 X Differential Heat of Condensation - Isopropyl Alcohol-Water*..................*..+.. *.**............. 138 XI Differential Heat of Condensation - Acetone-Water....... 138 XII Summary of the Comparison Between Experimental and Calculated Integral Isobaric Heats of Vaporization...... 147 XIII Inventory of Vaporizer Contents...................... 156 XIV Sample Potential Measurements and Calculated Powers..., 160 XV Smoothed Integral Isobaric Heats of Vaporization at Even Compositions - Isopropyl Alcohol-WAter............ 172 XVI Smoothed Integral Isobaric Heats of Vaporization at Even Composition - Acetone-Water....................... 172 XVII Smoothed Vapor-Liquid Equilibria at Even Compositions - Isopropyl Alcohol-Water.....*......*...................... 173 XVIII Smoothed Vapor-Liquid Equilibria at Even Compositions - Acetone-Water,................... *............... 173 vi

LIST OF TABLES CONT'D Table Page XIX Smoothed Density-Composition Data at 25 ~C for Acetone-Water Mixtures.................................. 174 XX Raw Data from Isopropyl Alcohol-Water Runs,........... 179 XXI Raw Data from Acetone-Water Runs............. 181 vii

LIST OF FIGURES Figure Page 1 Pressure-Temperature Diagram for a Hypothetical Mixture, *................. * * * *...... 4 2 Enthalpy-Temperature Diagram for a Hypothetical Mixture*......................... * *.. *.................. 16 3 Integral Heat of Mixing for Acetone-Water............... 27 4 Enthalpy-Concentration Diagram for a Hypothetical Mixture............ *..* 0*****............. ***..... **... *...... *........ * 3 5 Schematic Diagram of the Flow System................ 52 6 Photograph of the Apparatus............................ 53 7 The Calorimeter3*....,..... 6 8 The Preheater*....................... 68 9 Circuit Diagram for the Vaporizer Heater.............. 75 10 Circuit Diagram for the Preheater..................... 78 11 Potential-Measuring Circuit and Thermocouple Circuit.... 81 12 Heat of Vaporization of Water as a Function of the Reciprocal of the Flow Rate Through the System,........ 102 13 Heat of Vaporization of Water as a Function of the Reciprocal Flow Rate to the Third Power................ 102 14 Integral Isobaric Heat of Vaporization of Isopropyl Alcohol-Water Mixtures on a Mas is.B............ 108 15 Integral Isobaric Heat of Vaporization of Isopropyl Alcohol-Water Mixtures on a Mole Basis...............,.. 109 16 Integral Isobaric Heat of Vaporization of Acetone-Water Mixtures on a Mass Bis.................... 110 17 Integral Isobaric Heat of Vaporization of Acetone-Water Mixtures on a Mole Basis*............................ 111 18 Temperature-Composition Diagram for Isopropyl Alcohol-Water......................................... 116 viii

LIST OF FIGURES CONT'D Figure Page 19 y - Equilibrium Diagram for Isopropyl AlcoholWater*...,....................................... 117 20 Temperature-Composition Diagram for Acetone-Water,...... 118 21 y - x Equilibrium Diagram for Acetone-Water,............ 119 22 Log of the Ratio of Activity Coefficients Versus Concentration for Isopropyl Alcohol-Water................. 124 23 Individual Activity Coefficients Versus Concentration for Isopropyl Alcohol-Water............................. 125 24 Log of the Ratio of Activity Coefficients Versus Concentration for Acetone-Water.................... 126 25 Individual Activity qoefficients Versus Concentration for Acetone-Water.......................... 127 26 Enthalpy-Concentration Diagram for Isopropyl Alcohol-Water* e..vv....e................................. 133 27 Enthalpy-Concentration Diagram for Acetone-Water....... 134 28 Calculated and Experimental Integral Isobaric Heat of Vaporization for Methyl Alcohol-Benzene Mixtures..... 140 29 Calculated and Experimental Integral Isobaric Heat of Vaporization for Acetone-Benzene Mixtures............ 141 30 Calculated and Experimental Integral Isobaric Heat of Vaporization for Methyl Alcohol-Water Mixtures....... 142 31 Calculated and Experimental Integral Isobaric Heat of Vaporization for Ethyl Alcohol-Water Mixtures...... 143 32 Calculated and Experimental Integral Isobaric Heat of Vaporization for n-Propyl Alcohol-Water Mixtures........ 144 33 Calculated and Experimental Integral Isobaric Heat of Vaporization for Nitrogen-Oxygen Mixtures.............. 145 34 Sample Power-Time Curve.............................. 162 ix

LIST OF FIGURES CONT'D Figure Page 35 Heat of Vaporization of Isopropyl Alcohol as a Function of the Reciprocal Flow Rate to the Third Power,........*. *... *................... * 175 36 Heat of Vaporization of Acetone as a Function of the Reciprocal Flow Rate to the Third Power............., 175 37 Thermocouple Calibration,.......................176 38 Graph Relating Mole Per Cent to Mass Per Cent.......,*.. 177

ABSTRACT The integral isobaric heats of vaporization of the isopropyl alcohol-water system and the acetone-water system have been measured in an essentially adiabatic flow calorimeter at atmospheric pressure. The integral isobaric heat of vaporization is defined to be the enthalpy change which occurs when a mixture is totally vaporized under isobaric conditions - the initial state being saturated liquid at the bubble point and the final state being saturated vapor at the dew point. The data obtained have been used to construct accurate enthalpy-concentration diagrams for the systems studied and to serve as the criteria for evaluating methods of predicting integral isobaric heats of vaporization, In addition to the enthalpy data the vapor-liquid equilibria for the two binaries were determined, simultaneously in the same apparatus, and compared to similar data published in the literature. The flow calorimeter consisted primarily of a small, thermally insulated vaporizer in which vaporization was effected by the consumption of electrical energy in a submerged heater. A constant liquid level was maintained in the vaporizer by the gravitational flow of liquid from a large, constant-head preheatero The vapors which escaped from the vaporizer passed through externally heated lines to a condenser and returned to the preheater as liquid. The rate of cycling from the preheater, to the vaporizer, through the condenser, and back to the preheater was controlled by the amount of power supplied to the heater located in the vaporizer. The principal measurements which were required for determining the integral isobaric heat of vaporization were the power supplied to the heater and the amount of material vaporized in a given interval of timeo xi

The analyses for both systems were determined by density measurements in calibrated pycnometers. Analyses of the condensate (vapor) and the preheater liquid, which were identical, provided the composition of the mixture for which the enthalpy data were taken. A sample of the liquid contents of the vaporizer, in conjunction with the condensate (vapor) sample and the temperature and pressure in the vaporizer during the run, provided the necessary data to determine the vapor-liquid equilibria for the mixture. Heat transfer between the vaporizer and the surroundings was minimized by a reduction of both the heat-transfer coefficients and the temperature difference. The coefficients were reduced by conventional means. The elimination of the temperature difference was effected by carrying out, in a chamber which surrounded the vaporizer, a vaporization process identical to the one in the vaporizer. The integral isobaric heats of vaporization obtained for the two binaries studied in this investigation are estimated to be reliable within plus or minus 03 per cent. The data were correlated by an equation of the form P = zj Lj,Tl + zk L,T1 + (Zj Cp,j + zk Cpk)(T2 - T1) where Xp is the integral isobaric heat of vaporization; zj and zk are the mole fractions of j and k, respectively; T1 and T2 are the bubblepoint and dew-point temperatures of the mixture, respectively; Lj,T1 and Lk T1 are the heats of vaporization of pure j and pure k, respectively, taken at the bubble-point temperature of the mixture; and Cp j and Cp k xii

are the ideal-gas specific heats of pure j and pure k, respectively, taken at the average temperature between the bubble point and dew point. This equation is quite simple to use. The average difference, without regard to sign, between the experimental data and the heats of vaporization calculated from the above equation was 0.8 per cent for isopropyl alcoholwater mixtures and 0.3 per cent for acetone-water mixtures. Application of the above equation to experimental data for methyl alcohol-benzene, acetone-benzene, methyl alcohol-water, ethyl alcohol-water, n-propyl alcohol-water andT nitrogen-oxygen mixtures also produced satisfactory resultso xiii

INTRODUCTI ON The heat of vaporization of mixtures is a particular subject which is encompassed by the broader classification of enthalpy of mixtureso Most studies or calculations involving the enthalpy of mixtures soon lead to questions concerning the heat effects which accompany a liquid-vapor phase change. Any chemical processing step which involves either vaporization or condensation of mixtures, such as distillation and liquefaction operations, requires knowledge of the enthalpy difference between the two phases. The emphasis of this investigation was on the integral isobaric heat of vaporization, which is the most important type of vaporization from a practical viewpoint; however, this emphasis is not restrictive because the various heats of vaporization are interrelated. The experimental objectives involved the design, construction, and operation of an adiabatic flow calorimeter for the precise measurement of the integral isobaric heat of vaporization. Heat leaks, which are the bane of all calorimetric measurements, received special attention in the design of the apparatus with the forethought to operation of the calorimeter with mixtures which have a large temperature difference between the bubble point and the dew point. The integral isobaric heat of vaporization was measured at atmospheric pressure for the acetonewater binary, which has large temperature differences between the bubble point and dew point over most of the concentration range, and for the isopropyl alcohol-water binary, which in addition to large bubble-point - dew-point temperature differences at some concentrations also contains -1

-2a minimum boiling azeotrope. A secondary experimental objective was to determine, simultaneously with the heat-of-vaporization data and in the same apparatus, the vapor-liquid equilibria- for the mixtures and to compare these data with those published in the literature. The experimental data were used to prepare enthalpy-concentration diagrams for both binaries. The theoretical objectives concerned the development of new methods for predicting integral isobaric heat of vaporization and the evaluation of existing methods. The experimental data served as criteria for evaluation of the reliability of these predictive methods.

THEORETICAL BACKGROUND Enthalpy Change Accompanying a Liquid-Vapor Phase Change In reference to a pure material the term "heat of vaporization" defines a single phenomenon. The liquid-vapor phase change is both isothermal and isobaric, and the amount of heat required to change a unit quantity of the material from its saturated-liquid state to its saturated-vapor state is the heat of vaporization. The heat of vaporization of a mixture, unlike that of a pure compound, is not unique. A mixture can be vaporized in a number of ways, and the heat of vaporization depends on the method chosen. Consider the pressure-temperature diagram of a hypothetical mixture shown in Figure 1 on page 4. Point 1 represents the mixture in its saturatedliquid state at a pressure of P1-2 and a temperature of T1_3. A unit quantity of the mixture in the state represented by point 1 could be completely vaporized by adding heat to it while holding the pressure constant. This vaporization would proceed along a line of constant pressure and increasing temperature from point 1 to point 2, At point 2 the mixture would be in a saturated-vapor state at a pressure of P1-2 and a temperature of T2_4. The amount of heat required to effect this type of phase change is known as the integral isobaric heat of vaporization. The word "integral" is included because the mixture is completely vaporized. From point 1 the vaporization could also proceed along an isothermal line. That is, heat could be added to the mixture along a line of constant temperature and decreasing pressure from point 1 to point 35 -53

- 4CRITICAL I~~/ \POINT P,-2 - -2 —------------- -- -- 2 / I I w I I 3-4 --—'4 T.-3 Ta-.4 TEMPERATURE Figure 1. Pressure-Temperature Diagram for a Hypothetical Mixture. (Constant Composition)

-5At point 3 the entire mixture would be in a saturated-vapor state at a pressure of P3-4 and a temperature of T1_3. The amount of heat required to effect this type of phase change for a unit quantity of the mixture is known as the integral isothermal heat of vaporization, Still another type of vaporization could begin with a mixture in the state represented by point lo A differential amount of material could be vaporized from this saturated-liquid mixture at both constant pressure and constant temperature. In order for the vapor formed to be in a saturated state at a pressure of P12 and a temperature of T13, the vapor must be of different composition than the liquid, and in particular this composition must be that of the vapor in equilibrium with the liquid. The amount of heat required to effect this type of physical change is known as the differential heat of vaporization. An entirely equivalent procedure would be to begin with an essentially infinite quantity of the mixture in the condition described by point 1 and to vaporize from that a unity quantity of vapor in equilibrium with the liquid. It is difficult to accurately determine the differential heat of vaporization experimentally; for, the task of producing a small amount of equilibrium vapor from an amount of liquid so large that its composition is effectively unchanged does not lend itself to precise experimental technique. Each of the three types of vaporization described above began with a common saturated liquid denoted by point 1, but each terminated with a saturated vapor under the different conditions denoted by point 2, by point 3, and by the vapor in equilibrium with the point-i liquid.

-6The heat required for the integral vaporizations is the difference in enthalpy between the initial and final states; therefore, the integral heats of vaporization are definitely of different magnitude. The differential heat of vaporization, since it involves a vapor of different composition from the liquid, is not in general equal in magnitude to either of the integral heats of vaporization~ Both types of integral heat of vaporization have corresponding integral heats of condensation of exactly the same magnitude but of opposite signo No such corresponding heat of condensation exists for the differential heat of vaporization because of the differences in the composition and the amount of material involved in each phase. However, a differential heat of condensation can be defined analogously to the differential heat of vaporizationo It is the amount of heat which must be removed from an infinite amount of a saturated vapor in order to condense a unit quantity of liquid in equilibrium with the vapor Whereas the difference in enthalpies involved with the two integral heats of vaporization is obvious, for example Xp = Hsat~v~ HSat.l. the difference in enthalpies involved with the differential heat of vaporization is not obvious. The enthalpy of the final state is simply that of a unit quantity of the equilibrium vapor, but the enthalpy of this material in its initial state is not immediately apparent. It is not the enthalpy of a unit quantity of the infinite amount of liquid, because this liquid is of a different composition than the vaporo Hence, some of the less volatile material in a unit quantity of the liquid would

not be vaporized while some of the more volatile material that was actually vaporized would have to be drawn from outside of the original unit quantity of liquid. Further insight into the enthalpies involved can be gained from the consideration of heat and mass balances around a hypothetical, perfectly insulated, flow calorimetero Consider a binary mixture in a saturated-liquid state which flows to the calorimeter at a rapid rate, sat 1 F. This stream has a composition, x, and an enthalpy, H ~ t A small amount of heat at a rate, Ah, is assumed to be released in the calorimeter. The release of heat energy produces a saturated vapor at a small rate, AFo The vapor, which is in equilibrium with the liquid, is of composition y and has an enthalpy of Hat o.v The liquid flows from -y the calorimeter at a rate of F - AF. This exit liquid has a composition of x + Ax and an enthalpy of Hsat~l~ + AH1, Thus, there is one stream which enters the calorimeter, but two streams which leave. The enthalpy input to the calorimeter is given by FHsat.~l + 4h. The enthalpy output in the vapor stream is AF H at~~ and in the liquid -y stream is (F - AF)(Hsat.l. + AH1)o -x Equating the input and output yields F Hsat.l. + Ah = AF Hsat.v + (F - AF)(Hat.lI + lH1) (1) -x -y -- Multiplying, collecting terms, and dividing through by AF yields aH1 h = H sat.vo Hsat.l. + F - H1 (2) AF y -Y-x AF - As Ah approaches zero, as required by the definition of the differential heat of vaporization, the process proceeds at both constant temperature

-8and pressure, and AH1 and AF also approach zero. Equation (2) then becomes dh sat oVo satolo FH1. — ~ a p H - H + F( (3) dF X1^ — y -x 6F Equation (3) is undesirable because it is dependent on the flow rate, FO However, a mass balance around the hypothetical. calorimeter produces another equation which permits the elimination of Fo Equating the rate of influx. of one component, Fx2, to the rate of efflux in the vapor stream, AFyy, plus the liquid stream, (F-AF) (x + x), yields Fx = AFy + (F - F)(x + Ax) (4) Multiplying, collecting terms, and dividing through by AF yields x y = F -A (5) AF In the limit as Ah approaches zero, Ax and AF also approach zero and Equation (5) becomes x -y - F dx (6) dF A slight rearrangement of Equation (3) yields Hsat.v. satl. + F() F( (P) XT-P -y - Hx + F pF X. pT Substitution of Equation (6) into the last term of Equation (7) yields the final result for a binary X =Hsatv' - H sat ~ + (x = Y)(a - )m (8) y, -- -x y) )TP

-9Equation (8) shows exactly which enthalpy terms are involved in the differential latent heat. The derivative is to be evaluated at the saturation point at composition x, An analogous expression can be derived for the differential heat of condensationo If a unit quantity of the equilibrium liquid of composition x is considered to be condensed from a large quantity of saturated vapor of composition y, then the differential heat of condensation is given by tat. _ at.v + (y x)(v (9 Hv Here, the derivative is to be evaluated at the saturated-vapor point at composition yo Relationships Among the Heats of Vaporization of Mixtures Of the three heats of vaporization of a mixture described in the previous section, the integral isobaric heat of vaporization is of primary interest. In practice most vaporization processes are conducted at constant pressure and on non-differential quantities of material. Furthermore, the method adopted for this investigation makes the integral isobaric heat of vaporization the easiest of the three to accurately determine experimentally. However, the heats of vaporization are related, so that if data for one exist over the range of conditions of interest then the others may be calculated. The relationship between the two integral heats of vaporization is easily explained in terms of the pressure-temperature diagram shown in Figure 1 on page 4. As previously defined, the integral

-10isothermal heat of vaporization is the enthalpy difference between the mixture in a state defined by poinnt 3 and the same mixture in a state defined by point 1o Because enthalpy is a state function, the path traversed in going from point 1 to point 3 is inconsequential, Thus, the sum of the enthalpy changes in t-raversing the route 1-2-4-3 is identically the integral isothermal:heat of vaporizationo By defini.tion the enthalpy difference between poi.nt 2 and point 1 is the integral isobaric heat of vaporization0 The path from point 2 to point 4 represents the isothermal expansion at T2,,4 of the vapor from a sa.turation pressure of P1l2 to a pressure P3-4o This enthalpy difference is given by P3 4 6 v AH_ [V -T(-)]dP (i) P1-2 The path from point 4 to point 3 represents an isobaric cooling at P3-4 of the vapor from a temperature of T2-4 to a. saturation tempera.ture of Tl-3o This enthalpy difference is given by T1-3 AHr fT cv dT (11) -Cool T24 Pm The summation of the above enthalpy terms gives the rel.atilonsbh.i.p between the two integral heats of vaporization T = XP + oo (12) It i.s doubtful if the second and third terms on the right-hand side of Equation (1.2) can be evaluated rigorously for any mixt-urxe because of

-11the lack of the required data. Fortunately, however, the first term is quite large in comparison to the latter two, and as a result,suitable estimates of the latter terms permit calculation of the integral isothermal heat of vaporization with very nearly the same degree of accuracy as is embodied in the first term, the integral isobaric heat of vaporization. The enthalpy change resulting from the expansion step can be evaluated - if, indeed, it is significant at all - with sufficient accuracy by use of generalized charts and the pseudo-critical concept for mixtures. The specific heat for the vapor mixture can be obtained by averaging the specific heats of the pure components for the pressure P3-4 pursuant to the concentration of each component in the mixture. The specific heats for the vapor are additive in this manner except at extreme conditions where the heat of mixing in the vapor phase becomes significant. If it is not desirable to average the pure-component specific heats or if none are available for a pressure of P3_4, then the enthalpy change for the step which involved the isothermal expansion would have to be evaluated for an expansion to zero pressure, where the specific heat of the mixture can be determined rigorously by a molal average of the ideal-gas specific heats. This procedure, of course, would require the additional evaluation of the enthalpy change for the isothermal compression of the vapor from zero pressure to the final pressure of P3-4' The relationship between the integral isobaric heat of vaporization and the differential heat of condensation is simpler, and in practice it is easier to apply, than the relationship which involves the

X12differential heat of vaporization.O If the composition of the mixture shown on Figure 1. on page 4 is denoted by x, then in order to produce by differential condensation a unitv qu.antity of x in. the saturatedliqui.d state described by point 1, one must start with. an infinite amount of saturated vapor which has a composition y, a. temperatvure of T_13 and a pressure of Pl-2 An entirely equivalert procedare'which would produce thne same end result is as follows, (1) separate from the large amount of vapor of co:mposition y a unit qu.antity of vapor of composition x at a constant temperature of T1-3 and a constant pressure of P1-2, (2) isobaricly heat the unit quantity of vapor of composition x from T1i3 to T2_4 (3) totally condense the unit quantit, of vapor of composition x under isobaric conditions o Tih.e enthalpy change accompanying step 1 is the same magnitude as the vapor-phase differential V heat of mixing, M o for a unit quantity of composition x in an infinite quantity of composition y; however, the sign on the differenti.al' heat of mixing is reversedo It is doubtful. if such data exist for any mi.:xture, but, fortunately, the heat effects accompanying th.e i. xing of vapors are quite small and can safely be neglected except alt ext reme conditionso This term will be neglected in further: discussion.So The enthalpy change accompanying step 2 is given byv T2 4. heatt C m dT 15) T3 where Cp is the specific heat of the vapor of composition x at a pressure of P1-2o It is doubtful if this piece of data is available for mixtures, but a molal average of the specific iheats of the pure

-13components will give a reliable answer for all conditions where the vapor-phase heat of mixing is small. Step 3 by definition is the negative of the integral isobaric heat of vaporization. The sum of the enthalpy changes involved in the three steps is the differential heat of condensation. AT-p- = H= + eat - Xp (14) Since the integral isobaric heat of vaporization has been related to both of the other heats of vaporization by Equations (12) and (14), a combination of these equations yields the relationship between the differential heat of condensation and the integral isothermal heat of vaporization. It is A,p - LHM+ + eat - + cool +(15) Since the terms OHeat and HIcool refer to heating and cooling the same material over the same temperature range, one is the negative of the other; hence, they cancel, and Equation (15) becomes ATp XT + AHxp AH (16)

METHODS OF PREDICTING HEATS OF VAPORIZATION OF MIXTURES Summary The subsequent sections in this chapter deal'with -relationshi'ps between the heats of vaporization of mixtures and other propert".ies of both the mixtures and the pure components, The data availabl.e in the literature for these "other properties" are much more abundant than heat of vaporization data.; therefore', the available data in conjunc'tion with the relationships developed hereinafter serve as a means of predicting heats of vaporization of mixtureso The emphasiis is on relationships involving the integral. isobaric heat of vaporizatti.on; however, this emphasis is not restrictive because, as shown in the previous chap-, ter, the heats of vaporization are interrelatedo The possible predictions range in complexity from the assumption of a constant molal. heat of vaporization for an entrire range of compositions to the ri.gorous application of two-p-hase, PVI-T-x data:fo~r the evaluation of t;he heat of vaporization of a single mi-x:ture Eact. method has its own merits; co:nsequently, for a specific. case the most rigorous method which is consistent with both the data and the t:.me available should be choseno Predictive methods which require, as a fundamental part, data on the behavior of mixtures (with the exception of data on vaporlliquid equilibria) are more lim.ited in application than -methods which require only data on pure materials, because the available data on mixtures are scarce relative to those for t:le pure components. Integral heat of mi.xi,ng in the liquid phase at temperatures above ambient temperatures and the specific heat of liquid mixtures as -14

-15a function of temperature are examples of frequently needed mixture data which are quite scarce. In addition, long, tedious calculations to adjust available data to fit the requirements of a predictive technique tend to cast suspicion on the reliability of the adjusted data and, thereafter, the results of the prediction. In the section entitled "The Enthalpy-Temperature-Diagram Approach" particular emphasis is given to the development of an equation for the prediction of the integral isobaric heat of vaporization. This equation permits prediction of the integral isobaric heat of vaporization by much shorter and much less tedious computations than those required for construction of an enthalpy-concentration diagram, which seems to be the most used and most frequently recommended method. In addition, the aforementioned equation requires less data on mixture behavior than the enthalpy-concentration diagram; consequently, the results, which are a function of the reliability of the data used, can reasonably be expected to be more accurate, or at least of equal accuracy to those obtained from the diagram. The Enthalpy-Temperature-Diagram Approach Figure 2 on page 16 is an enthalpy-temperature diagram for a hypothetical mixture. The diagram is for a constant composition; every composition would have its own envelope on the H-T plane. The isobar, P1-2, represents the enthalpy-temperature relationship for the addition of heat to the mixture at constant pressure, beginning in the subcooledliquid region and extending through the two-phase region into the superheated-vapor region. The straight isobar through the two-phase

-16T2._?,~_ _ _2 CRITICAL POINTf X II~~ ///f~~~~~~~ I I W. I ---—,u^r~~ ~~. —---------— 1 -(jl'SXiH TEMPERATURE Figure 2. Enthalpy-Temperature Diagram for a Hypothetical Mixture. (Constant Composition xi = y-= zi)

-17envelope is simply a connection of points 1 and 2 and is not intended to construe that an isobaric vaporization must or does proceed along that path. The straight isobars in the superheated-vapor region and the subcooled-liquid region imply that the specific heats of the vapor and the liquid are independent of temperature, an assumption which is valid only for small temperature ranges. From the definitions of the heats of vaporization and with the aid of the isobar, P1-2, it is easy to identify the distances, Xp and XT, to be the integral isobaric heat of vaporization and the integral isothermal heat of vaporization, respectively. Reference is made in subsequent paragraphs of this section to the quantities shown on the figure, during the process of developing an equation for the prediction of the integral isobaric heat of vaporization. From the definition of integral isobaric heat of vaporization and the properties of partial enthalpies one can write - 1-2. Yi 2 - Xi Hi11 (17) In Equation (17) the mole fractions, xi and yi, are equal; the H's are partial molal enthalpies; subscripts 1 and 2 refer to points 1 and 2, respectively; and the superscripts, 1 and v, refer to the liquid and vapor phases, respectively. The definition of a new term, H T equal to the enthalpy of component i in the ideal-gas state at temperature T permits one to write Equation (17) in the form Xp ~ - Yii + XiYi,2,1, X i z,1i + ( 1i8, Y - Z xi. (18)

-18The newly defined term was inserted by simply adding and subtracting both yH 2 and Z x.H0 to the right-hand side of the equation. i i-i9 i i- l Here again xi = yio Rearranging Equation (18) yields Xp -- Z y,( 2,2) + Z x(i,- Hi,1) + H Zi,(H2 - H, (19) i i where xi = i = zi~ The definition of three more new terms for the =v 0 -v -1 0 bracketed terms, AHi2 = i2 - Hi2, i Hil and H = H- 1 permits one to write Equation (19) in the shorter form X Z x ( l_) + H zzi( ) - yi( v2) (20) Equation (20) is the basic equation to be considered in this development; it is rigorous, and its various terms are illustrated on the H-T plane. The terms are considered individually for evaluation. The last term, Z yi(Hi,2), is the enthalpy change for the isothermal expansion at the dew-point temperature, T2, of the vapor from the saturation pressure, P1-2, to zero pressureo For ideal gases the enthalpy change is zero, and even for a non-ideal gas at moderate pressures it is quite small in comparison to the other enthalpy terms. It can be estimated from the generalized charts in conjunction with the pseudo-critical concept, if it can not be safely neglected. However, for the purposes at hand it will be assumed that Yi (0i,2) o (21) Equation (21) is tantamount to making points 2 and 2' on the figure coincide,

-19The term Z zi (HO) represents the enthalpy change on heating i1 the ideal-gas mixture from the bubble-point temperature, T1, to the dewpoint temperature, T2. It is given by T0 _32 dT= T2 0 Z z(A) C dT = yC dT (22) T1 i T1 where Cpi is the heat capacity of component i in the ideal-gas state. xi(AHi,l) is the enthalpy change accompanying the vaporization of the mixture at constant temperature T1 and the isothermal expansion of the resulting vapor to zero pressure. The evaluation of this term is not accomplished as directly as the others. The thermodynamic equation which gives the temperature variation of the fugacity function is H0 T = R,T(n ) Hij T - HijT = RT ( aT P;N (23) This equation is derived in many thermodynamic texts, for example Hougen and Watson.(30) It represents the partial molal enthalpy difference for component i in a mixture which undergoes a change from any initial state to a final state of zero pressure and the same temperature as the original state. The restrictions on the derivative are constant total pressure P and constant total composition N. Since the entire H-T diagram is for constant total composition, the subscript N will be dropped henceforth. fi is the fugacity of species i in the mixture in its original state. In the notation of this development Equation (23) becomes -1 xi(Al) = RT Z xi( ) (24) 6T Pl-2

-20-1 The fugacity, fi, is given by = Yi Xi Pi (25) where 7i is the activity coefficient, which is a corrective factor for the non-ideality of the liquid mixture; xi is the mole fraction of species i; and pi is the vapor pressure of i at the temperature of interest. If one takes logarithms of both sides of Equation (25) and substitutes the result for lnfi into Equation (24) the result is Z xi(Ii1,1) = RI? Z xi[( ln i) + (xln i ) aT P1-2 T P12 T P1-2 where all derivatives are to be evaluated at T1. Consider the term, Z xi ( i), in Equation (26). If this term is written out for a i - T P1-2 binary, and if it is observed that dxj + dxk = 0 for a binary the result is 6 1nXSln x- 6nn x 6ln x( P i ( n x i P2 + xk( T k) xj ( ) +Xk 1 (k) jj 6T Pl-2 xk 6T P1-2 - (-i) - (A) =o (27) aT P1-2 aT P1-2 thus, Equation (26) becomes Zx.(n i ) -T pln ) ) ="RT?1i.i [( ln Pi-2 1-2

-21The combination of Equations (21), (22), and (28) according to the basic Equation (20) yields XP= z xi( i) + Zi( ) Z y( (20) Hj ) i i (2 2 ln pi)ln T2 RT2 Z xi[(n ) + ( i) ] + z y,dT (29) i x T Pl-2 6T P"l2 T1 1 Equation (29) written out for a binary becomes p = xj R ( )ln p + Xk RT1 (ln Pk) 1T P1i2 aT P1i 2 + RT2 1 [xj + k( k) T Pl-2 x T P1-2 T2 0T2 0 y c j dT + Yk C,k dT (50) T1 1 where all the derivatives are to be evaluated at T1. The terms in Equation (30) will be examined further in pairs. The term, RT1 (nP_),p is the Clausius-Clapeyron equation for the heat of vaporization, Lj,T1, of component j at temperature T1. The restriction of constant total pressure on the derivative has no significance here. The substitution of the heat of vaporization for the Clausius- Clapeyron equation involves the assumption that the ratio RT1/P1 2 q is essentially equal to unity. With this substitution the first two terms of Equation (30) become xjLj,T1 + XkLk T1 (31) Each mixture of j and k has a different bubble point, T1; therefore the L's, as well as the x's, will be different for every composition.

-22The limits on the integrals of the last pair of terms in Equation (50) are the bubble-point and the dew-point temperatures. If these temperatures are not widely separated, the ideal-gas specific heat, Cp,j, at the average temperature should be a good approximation. Thus, the last two terms in Equation (30) can be reduced to (yj + k k)(T2 - T) (2) The middle pair of terms of Equation (30) can not be reduced as straightforwardly as the others. Rearrangement and collection of terms for this pair yields RT [Xj( ln ) + Xk( ln 7k) RT1 2 T P1.2 k T P1-2 =ao -T 6n 7J 6X. 6(ln Zk\ ) X =RT_ [xj( —1) (-+ xk( ) ( ) ] 1 J P1j 2 aT 1-2 aj p,-2 aT p1-2 T2' 6x, 61n7hln 7kY) 6,k, = RT2 (j) [xj ( i 7) + xk( ] 0 (33) 1 T Pl-2 6xj P1-2 6xj P1-2 The terms in the brackets are almost equivalent to the Duhem(15) relationship; however, in the Duhem relationship the derivatives carry the additional restriction of constant temperature. In spite of the lack of rigor the Duhem equation has been used extensively under isobaric and varying-temperature conditions, and it has been found satisfactory in many cases under these conditions (see for example Dodge(l3)). Therefore, the bracketed terms are set equal to zero by the Duhem equation; hence, the entire expression becomes zero. Additional discussion of these relationships appears in subsequent paragraphs of this section.

-23Rewriting Equation (30) according to Statements (31) and (32) and Equation (33) and recalling that throughout the development x; = yj = zj (The different letters were used merely to avoid confusion as to which phase was under consideration at the time.) yields the final working equation for the prediction of the integral isobaric heat of vaporization of a binary Xp = zj LT1 + Zk Lk,T1 + (Zj Cpj + Zk Cp,k)(T2 - T1) (34) Throughout the development of this equation the composition terms had to be in mole fractions and the temperatures in absolute degrees in order to use a unique value for the gas constant, R, However, R does not appear in the final working equation so that any consistent set of units, such as mass fractions, calories per gram, and degrees centigrade may be used successfully. The following data are required for the prediction of integral isobaric heats of vaporization from Equation (34): (1) isobaric vapor-liquid equilibria, (2) the heat of vaporization of the pure components as a function of temperature in the temperature range covered by the bubble points of the mixtures, (3) the ideal-gas specific heat of the pure components as a function of temperature in the temperature range covered by the bubble points and dew points of the mixture. The computations required by this equation are both simple and short. The inherent assumptions involved in the derivation of Equation (34) are not restrictive, but they are noted here in case estimates of the magnitude of their effect are desired. The assumptions are (1) the mixture under isobaric and varying-temperature conditions obeys the Duhem equation, (2) the ratio RT1/P1.2AV is essentially equal to unity for both

pure components, (3) the pressure effect on the enthalpy of the vapor between P1.2 and zero pressure is negligible* An investigation of the terms in Equation (33) with respect to their relationship to the Duhem equation adds additional information to the properties of the mixtures. First, however, it should be pointed out that direct evaluation of Equation (33) is tedious and not likely to produce satisfactory results. Graphical differentiation of the activity-coefficient data is apt to introduce larger errors than the assumption of applicability of the Duhem equation. Differentiation of most of the correlating equations for activity coefficients, including the Redlich-Kister(55) equations, produces identically zero results because the Duhem equation is inherent in their derivations. Ibl and Dodge(32) have shown that the rigorous Duhem equation for isobaric and varying-temperature conditions is given by aln 7 aln Yk 1 )T -ln] [- n (-) (35) on xj p ln(l-Xj) p xj p or in the form used herein l(bl) lln 7) 1 ) (56) xj(T 7 + xk (-) - ~JT2. j.(c.) (36) P ) P where ~ is the integral heat of mixing at the bubble point. Substitution of this relationship for the bracketed terms in Equation (33) yields R(a) (xj( Z)n p12-) + xk( )p PLa 2 ( )P12+ ( )p - 1 (3 bP 2r - E x: P1X2 x 7)

-25Thus, Equation (34) might be written Xp s= jLjT ZkLkT + (zj pj + Zk Opk)(T2 - T1) - h * (58) Whereas the addition of this new ths eerm enhances the knowledge about the original assumption of zero for the expression involving the Duhem equation, it does not greatly enhance the ability to predict integral isobaric heats of vaporization, because integral heat of mixing data at temperatures near the bubble point of the mixture are practically nonexistent. It would be unrealistic to assume that heat of mixing data taken at temperatures well below the bubble points would be applicable at the bubble point. If, however, sufficient specific heat data for the liquid mixture as a function of temperature up to the bubble point are available, the integral heat of mixing data might be adjusted to the bubble point temperature. It should be added, however, that such specific heat information for mixtures is not readily available in the literature. The definition of the integral heat of mixing at temperature T is AHM,T = nm,T - xj jT - xk Ck,T (39) Differentiation of Equation (39) with respect to temperature at constant pressure and composition and observation of the definition of specific heat yields the variation of the integral heat of mixing with temperature. [6MA T/ \ )H. 6[tm. T] = Xi(;Jm - xj( )paxj ) xk 6T' P aT P,xj 6T xj XTT k pj = Cpm - xj Cpj - Xk CP,k (40)

-26The integral heat of mixing in, say, the liquid phase at any temperature in relation to the integral heat of mixing at some base temperature, say 25 ~C is obtained by integrating Equation (40). 1 1 T 1 1 MI T = HM,25 + 2 (CPm -x Cpj xk C,k) dT (41) 25 Data on the specific heat of the mixture are necessary because, as can be seen in Equation (41), an assumption that a molal average of the specific heats of the pure components can be used for the specific heat of the mixture is equivalent to assuming that the integral heat of mixing is the same at all temperatures, Figure 3 on page 27 shows the comparison of the integral heat of mixing of the acetone-water binary at the bubble-point temperatures and at the constant temperature of 25~C. The 25~C data are those of Kister and Waldmano(36) Specific-heat data for the mixtures(56) and both pure components(55346,64) were used in Equation (41) in conjunction with bubble-point data(49) for the computation of the integral heats of mixing at the bubble-point temperatures. It can easily be seen on the figure that it is unrealistic to assume a constant integral heat of mixing for this system. The heats of mixing, without regard to sign, are on the whole much smaller at the elevated temperatures and can be safely neglected in the prediction of integral isobaric heats of vaporization from Equation (38)o Application of Equilibrium-K Values Edmister(16) derived an equation for the calculation of integral isobaric heat of vaporization by reasoning from an enthalpy-temperature

o 6 D ATA FOR 250C REF.36 ij.. DATA ADJUSTED TO O -4 -- BUBBLE-POINT TEMP. 4 z - 2_ LL j -2 0 10 20 30 40 50 60 70 80 90 100 MASBUBBLEPOINT T PER CENT ACETONE Figure 3. Integral Heat of Mixing for Acetone-Water. — 6 -8~- - - - - 0 10 20 30 40 50 60 70 80 90 100 MASS PER CENT ACETONE Figure 3. Integral Heat of Mixing for Acetone-Water.

diagram similar to the one shown in Figure 2 on page 16 of the previous section. His final equation requires knowledge of equilibrium-ratioK values and the ideal-gas specific heats of the pure components. The equation is p RT1T2 zi in K + Z i (42) T2-Tl i K i i where R is the gas constant; T1 and T2 are the bubble-point and dewpoint temperatures, respectively, zi is the mole fraction of component i in the mixture of interest; K, 2 is to be evaluated at T2 and is defined as yi,2/x, 2, where Yi,2 is the concentration of i in the mixture of interest in the vapor phase (numerically equal to zi) and x' is the concentration of i in the liquid mixture which would be in equilibrium with a vapor of composition, y at temperature T2; Ki 1 is to be evaluated at TI and is defined as Yi*l/xI, where xi, is the concentration of i in the mixture of interest in the liquid phase (numerically equal to zi) and y* is the concentration of i in the vapor mixture which would be in equilibrium with a liquid of composition xi 1 at temperatlre T1; AH, is the difference in the ideal-gas enthalpies between T1 and T2. The derivation embodies the assumption of the applicability of the Duh.em equation to the mixture of interests and the assumption that the terms Yi Hi,T and Z xi 1,T shown in Figure 2 on page 16 are constant over the range T1 to T2 and equal to Z y1 AH5 2 and z x; HI i,ly respectively over that temperature range. A modified version of Edmister's equation is developed in the subsequent paragraphso The view point taken and the method of approach

are similar to those of Edmister; however, additional terms are included -1 to more adequately define the variation of Z xi AHi T over the temperature interval between T1 and T2. The final result is an equation which contains the two terms already present in Edmister's equation plus one additional term. Equations (20) and (23) have been given previously on pages 18 and 19 where the salient features of each have been discussed. Xp = Ex(l ( ) + - 7 yiJ ) ) (20) i' i -- i AHiT = HT T -H = RT2 ( i) (23) 1T P In order to substitute a difference form of Equation (23), instead of its present differential form, into Equation (20) for the quantities IAH 2 and L4i1, Edmister integrated Equation (23) over the range from _v _1 T1 to T2 under the assumption that AHiT and A'i T were constant and equal to AHi,2 and AHr1,' respectively, for any point between T1 and T.2 This assumption is followed here, exactly, for the integration involving the vapor phase. The immediate result is -V _v RT1T2 f 1 Mi.2 l In lnv (43) T2-T1 fi,2 For the integration involving the liquid phase a deviation from the course taken by Edmister is made. The term AHi T for any point between T1 and T2 can be expressed by T -1 0 -,1 -1 Ci Mi,T - HT - Hi,l - Aa (P) - f Cp,i dT (44) Oom,i,l T1

-30where H1 is the partial molal enthalpy of i in the liquid mixture at the bubble point; AH1 CP), is the partial molal enthalpy difference involved in the isothermal compression at T1 of the liquid from P12 to P (here (P) serves as a reminder that this expression is a function of the terminal pressure, P, which in turn is a function of the terminal temperature, T); the term containing the integral sign is the partial molal enthalpy change involved in the isobaric heating of the liquid from T1 to T at a pressure of P. HO in Equation (44) is the ideal-gas enthalpy at temperature T and is given by =i,T -i,l T2 - T1 -i if the ideal-gas heat capacity is assumed to be independent of temperature for the Tl-to-T2 temperature range. Substituting H T from Equation (45) into Equation (44) yields T 4-l0 T - T1 0 -1 - iT = i,l+ (T2- - 1 - A o I C dT (46) Neglecting the effect of pressure on the enthalpy of the liquid phase and -1 assuming that Cp,i the partial molal specific heat of i in the liquid phase, is independent of temperature between T1 and T2, Equation (46) becomes,I 0.0 _10 -7),T = H,1 + Cp i(T - T1) - Hi,1 -,i(T - T1) (47) since AHO/(T2 - T1) is equal to Cp i according to the assumption given following Equation (45). Collecting terms yields,T jtl - (T - Tj)(C^pi - Cp,i) (48)

-31Substituting Ai, T from Equation (48) into Equation (25) and integrating between T1 and T2 yields -1 T2 T2 f i,2 T2 2dT O (T ) dT R d ln (49) T2 - cpi T{T2 dT = 1 ii -1i i T1T2 - (Cp i - Cp i ) [n 2 -+ T1 5 ^1, T1 T2recalling that for the constant-composition system x = Yi = zi yields 1T2 1 2 fiY2 - RT1T2 fi, -i 0 T1 T2 T2 T2-T fi,2 T2-T1 T1 From this point the development is the same as that used by T2-T1 ln i T:Pi Pi i (52) Edmister. Substintions for K3) and K are given on page 28 following Equation (20) and (42).recalling that for the efonstant-composition with the fact that at equilibrium,elds )v — 1 = iT' yied the following expression for the equilibrium-ratio 1 ~ =RT1T2 2zi [2n in ] Ki, 2/i,2 (5)i,2 + (- in T1) Zi c~ + z5 iT2-T1 i= i -( (42). These definitions in conucton with the fact that at equilibr K's. f,',2/x2i, Kil. = v(53

-32Substituting these K's into the first term on the right-hand side of Equation (52) yields -RT K zi [ln Ki2 L; l/yi,l in 1 i _,/, (55) T2-T1 i [ X(55 21 i f1,2/ i,.2 i,2/xi.2 Collecting terms and rearranging yields RTT 2 KiT2 - L — 1 i T2-T i K 1 i,1/ J i, 1 2. T2 T1 ZZi [ln 2 F ln v + in ~v -, ] + (56) i 1(1,1 i.i i12 The latter two terms inside the brackets of Statement (56) can be eliminated by application of the Duhem equation; one form of which is Z Zi d In fi = 0 (57) i Observing that Z zi = 1 and writing the Duhem relationship in difference form rather than in differential form yields Z zi A In (i/zi) - 0 (58) The term A In (fi/zi) can be expressed as A In (fi/zi) = in (fi/zi)' - In (Ti/zi)' - In (59 where the prime and double prime indicate two different compositions for the same phase, temperature, and pressure. This equation is applicable to either the vapor or liquid phaseo Thus, substituting Equation (59) into Equation (58) yields Zi ln ( L ~0 (60) i~~(r/iI

-33Application of Equation (60) to the latter two terms inside the brackets of Statement (56) eliminates them. Under these restrictions Equation (52) becomes RT1T2 KZ i 2 0 5ip =' — E z i In' + zi HO T2-T1 i Kil i _ + (TT2 In - T1) zi (Cpi - Cp i) (61) T2 - T1 T1 1 This equation differs from that given by Edmister, Equation (42), only by the inclusion of the last term. The Enthalpy-Concentration-Diagram Approach Figure 4 on page 34 is an enthalpy-concentration diagram for a hypothetical binary mixture. The conditions on the H-x plane are constant pressure and varying temperature. The integral isobaric heat of vaporization for any composition is the vertical distance between the saturated-liquid line and the saturated-vapor line at that composition. The saturated-vapor and saturated-liquid lines, as shown in the figure, are in general not straight. The frequently used McCabe-Thiele type of distillation calculation, for example see Brown,(3) embodies the assumption of constant molal heat of vaporization; that is, it is assumed that on a molal basis the heat of vaporization of both pure components and the integral isobaric heat of vaporization of all mixtures thereof are equal. The McCabe-Thiele assumption is tantamount to the assumption that on the enthalpy-concentration diagram the saturated-liquid and saturated-vapor lines are not only straight, but also parallel. If these lines are assumed to be straight, but not parallel, then the integral isobaric heat of vaporization of any mixture of the pure components

-34sat. v B Of( H - ------- _-0RATE y b Hv I V l bY )TF _, -—',, I X ~CNz MOL, PFAI (Constan Ps 0~ O ItI~ ~~ I's I/ I WX TI CONCENTRATION,MOLE FRACTION Figure., Enthalpy-Concentration Diagram for a Hypothetical Mixture. (Constant Pressure)

-35is given by a molal average of the heats of vaporization of the pure components, each taken at the pressure of interest. The method of construction of an enthalpy-concentration diagram when the integral isobaric heat of vaporization data are not available has been given by several authors, for example Dodge.(l) It is reviewed here quite briefly. A datum level for the enthalpies, usually the pure materials in their normal state at 0~C and the pressure of interest, is chosen first. The end points of the saturatedvapor line are fixed by marking on the ordinate of each pure component its saturated-vapor enthalpy. The remainder of the saturated-vapor line is then established as follows: (1) on both pure-component ordinates the vapor enthalpies are marked for various temperatures above the saturation temperature - and in the case of the less volatile component are also marked at temperatures below saturation, neglecting pressure...effects on the enthalpy, (2) straight isotherms are then drawn connecting the pure-component ordinates, (3) the dew-point temperatures for a number of mixtures are determined from vapor-liquid equilibrium data and are located on the H-x plane by interpolation between the isotherms, (4) these saturated-vapor values and the previously determined end points are joined by a smooth curve, which is the saturated-vapor line. The use of straight isotherms in the vapor region assumes zero heat of mixing in that phase, which is a reasonable assumption. It is not likely that the isotherms in the liquid region will be straight. The temperature at which the integral heat of mixing data in the liquid phase are available serves as the starting point for the constructions. The enthalpies of both pure liquids at this temperature

-36are marked off on the respective ordinates to fix the end points of the isothermo The end points are joined temporarily by a straight lineo The integral heats of mixing for a number of compositions are then represented by their proper distances above or below the temporary line, according to sign. These points are joined by a smooth curve, which is the base isotherm. Other isotherms are established at higher temperatures by determining the enthalpy change accompanying an isobaric heating of the liquid mixture. The bubble-point temperatures for a number of mixtures are determined from vapor-liquid equilibrium datag the sensibleheat terms are then calculated up to these temperatures and marked on the H-x plane. A smooth curve through these points establishes the satturatedliquid lineo The foregoing graphical construction yields the entire enthalpyconcentration diagramo However, if only a few integral isobaric heats of vaporization are needed, it would be convenient to have the construction features described in equationso These equations are tbp, i DP,m Tsatovo - 7 Zi L J t p i iHsat.v, z, ^ fZ C dt + Lp + Cv dt] + (62) 0 P,9 i iIP ~ 25,t'BP,m Hsatl z zi [ CP, dt +, 25 J CP dt (6 The ntegral isobaric h o25 apo the he integral isobar eat of vaporzations he dfeence b Equations (62) and (653) p - Hsatv - Hsat0l (64) The assumptions involved in writing Equations (62) and (65), none of which affect the rigor of the equations but which do involve the number of terms

-37used and some of the limits on the integrals, are as follows: (1) both pure components are liquids at the reference temperature (0~C), (2) the integral heat of mixing data are available at only one temperature, that being 25~C. If the heat of mixing in the vapor phase is neglected, the following data are required for the calculation of the integral isobaric heat of vaporization by using the enthalpy-concentration-diagram approach: (1) isobaric vapor-liquid equilibria, (2) specific heat of the pure components in the liquid phase as a function of temperature from 0~C to the boiling point, (3) the heat of vaporization of the pure components at the pressure of interest, (4) the specific heat of the pure components in the vapor phase as a function of temperature in the vicinity of the boiling point, (5) the integral heat of mixing in the liquid phase, (6) the specific heat of the mixture in the liquid phase as a function of temperature up to the bubble point. The calculations involved are simple, but tedious. The relationships between the saturated-liquid and saturatedvapor enthalpies and both the differential heat of vaporization and the differential heat of condensation, which were described with equations in the chapter entitled "Theoretical Background", can be illustrated graphically on Figure 4 on page 34 with the aid of an equilibrium tie line and the isotherms. The tie line joins a saturated liquid of composition x with a saturated vapor of composition y. Isotherms in both the liquid and vapor regions terminate at these saturation points. Equation (9) from the previous chapter gives the differential heat of

-38condensation as satolo satov~ Hv (9)^ P - g- Hy + (y x) (f (9) The distance -(Hsatv - H satol,! is easily located on the figure. The -1~ -x. I derivative is given by the slope of the vapor-phase isotherm at point Bj however, since these isotherms are straight, simply an. extension of the T1 isotherm beyond the saturation point for a horizontal distance aHV of (y - x) yields a vertical rise of (y - x) (~)h pO Thus, the differential heat of condensation from a vapor of composition y is represented by the distance A - Co A similar procedure applies for the differential heat of vaporization, which as given by Equation (8) in. the previous chapter is XT. Hsat oVo _ at ol + (x y) (l ( hTP Z" _x T P The difference between the saturated enthalpies is the same- however, the liquid-phase isotherm is not straight so, consequentl.y, a tangentmust'be drawn to it at point Ao If the tangent is extended beyond the saturation point for a horizontal, distance of -(x - y) the resultant vertcal rise of ( x TP) ( vertical rise of -(Xx - y) T ) shows -that th.e di.starnce B D- repre-~ sents the differential heat of vaporizationo It can be seen from these illustrations that the essential data for making enthalpy balances for distillation calculations are not differential heats of vaporization or condensation. as suggested occasionally in the literature, but are saturated-liquid and saturated-vapor enthalpies, whi.ch are most readily obtained from integral-isobaric-heat-of-vapori.zati.on data.

-39Approximately 17 enthalpy-concentration diagrams have been published in the literature for various liquid-vapor systems. Most are on large enough graphs to be useful or are supported by tabular values. A literature survey by Lemlich et al539) lists references to the original diagrams. Rigorous Application of Two-Phase, P-V-T-x Data The integral isothermal heat of vaporization can be computed from a rigorous application of the two-phase, P-V-T-x data for a mixture. A combination of the first and second laws of thermodynamics in conjunction with the definition of enthalpy produces the general expression dH = TdS + VdP (65) At constant temperature the entropy term, dS, can be expressed in terms of pressure, volume, and temperature by use of the Maxwell relationship ()T (6}V (66) Substitution of this expression into Equation (65) for dS yields dHT = (PT ) dV + VdP (67) Equation (67) can be integrated from the bubble point to the dew point along a reversible isothermal path. D.P. YDP PDP XT = I dH = T f (T) dV + f V dP (68) B.P. T BP V - BP - In order to carry out the indicated integrations a large amount of precise P-V-T-x data for the two-phase region are required. The computations

-4oare tedious, and precision is required because the data must first be differentiated, then cross plotted, and finally integrated. Although this method is outlined several. places in the literature, for example Hobson and Weber,(29) it has rarely been carried out because of the scarcity of the data required and the computational difficulties involvedo Bahlke and Kay(2) performed this type of calculation, for a commercial gasoline and a narrow-boiling-range naphthao They began the computation by plotting the pressure-volume isotherms for the two phase region. The volumes involved are, of course, the combined volumes of the equilibrium vapor-liquid mixtures which. would be present during a reversible, isothermal vaporization. From these pressure-volume isotherms a number of the corresponding pressures and temperatures were read off for a series of different vollumeso The pressures and temperatures so obtained were plotted as log pressure versus reciprocal, temperature with the different volumes as parameters. The slopes, (dlo' ) were taken at the temperature of the er e evaporization from each of the constant-volume curves in the serieso The slopes in this form - (d log ) - could then be easily transformed to (-P) and plotted d l/T V.. V against the corresponding volumeso The area under the resulting (6P) -V 6T" v curve between the saturated-liquid volume and the saturated-vapor volume is the value of the first integral on the right-hand side of Equation (65). In comparison to the above computation the second integral on the right-hand side is simple to evaluate. Only the area under the pressure-volume curve, which was previously plotted, for the temperature of interest between the bubble-point pressure and the dew-point pressure need be determined,

-41Strickland-Constable(66) has carried out the evaluation of two-phase, P-V-T-x data for the prediction of the heat of vaporization of an equimolecular mixture of propylene and carbon dioxide at 0~C, Equation (65) is not adaptable to the prediction of the integral isobaric heat of vaporization because the restriction of constant pressure eliminates the second term on the right-hand side and reduces the equation to an identity. Clapeyron Equation for Mixtures The Clapeyron equation, which is often used to predict the latent heat of vaporization of pure materials, can be applied to mixtures to relate the differential heat of vaporization or condensation to the vapor pressure and specific volumes of the mixture. The differential processes occur both isothermally and isobaricly - conditions which are requisites for the applicability of the Clapeyron equation. This equation has been outlined in the literature, for example Hobson and Weber,(29) as a possible method of predicting heats of vaporization of mixtures, but in practice it is seldom used because of the scarcity of the required data on mixture behavior. The Clapeyron equation for the differential heat of vaporization for the removal of a vapor of composition y from an infinite amount of liquid of composition x is given by XTP = T A (a x (69) The terms look identical to those appearing in the Clapeyron equation for a pure material; however, a closer examination in view of the actual

-42phase change being considered reveals that they are slightly more complicated, T is simply the absolute temperature of the differential vaporization, A V is not the difference between the volulme of t;he saturated vapor y and the volume of the saturated liquid x because the molecules constituting a mole of the vapor y did not occupy in t.he liquid phase the same volume as was occupied by a mole of the liquid x The exact expression for the volume difference can be derived in a manner analogous to that used on pages 7 through 9, Equations (1) through (8), to der.ve the relationship for the enthalpies involved in the differential heat of vaporization. If one merely uses t;he appropriate volume terms in place of the enthalpies in that development, the equation for the volume difference is obtainedo Thus, for a binary A V vsatoV. v, atl. + (x.y) ( ) (70) - Y -y x x,T P The last term, (P-) in the Clapeyron equation is the slope of the pressure, x temperature curve for the bubble points of a mixt.ure of composit ion x taken at the temperature, T, of the vaporization. The analogous equation for the differential heat of condensation for the removal of a liquid of composition x from an infinite amount of vapor of composition y is given by ATp - TA V ( ) (71) where T is the absolute temperature; (SP) is the slope of the pressure — y temperature curve for the dew points of a mixture of composition y taken at T. and A V is given b-y A - vsat-l- - sat- x) ( - ) (- 72) - -x a-y TP

-43Stiehl et al.(65) Hobson and Weber,(28) and Weber,(75) used Equations (71) and (72) to calculate the differential heat of condensation of a number of hydrocarbon binaries at pressures ranging from 100 to 600 psia. They used precise dew-point-pressure-temperature, volumetric, and equilibrium data in conjunction with an equation of state for the vapor-phase mixtures to make the calculations. The derivative in Equation (72) was determined from a graph of Vv versus y at constant pressure. The Vv - y isotherms for the superheated-vapor region on this graph were determined from an equation of state for mixtures, and the saturated-vapor envelope was established with the aid of vapor-liquid equilibrium data. From the Vv - y graph the slope of the isotherm taken at the saturation point for the temperature of interest furnished the avv ( —) term. Experimental data and a graphical differentiation of the by T,P dew-point - pressure-temperature data yielded the other information required by Equations (71) and (72). The usual assumptions can be made to reduce the Clapeyron equation to the simpler Clausius-Clapeyron equation. That is, if one assumes that only the volume of the vapor in Equations (70) and (72) is significant and that, furthermore, the vapor volume can be expressed with sufficient accuracy by the ideal-gas law, then the equation for the differential heat of vaporization becomes - B~ T = (-IF —) <(73) A similar equation applies to the differential heat of condensation, The evaluation of Equation (73) requires only the pressure-temperature relationship for the bubble points of the mixture. Equation (73) also

-44presents a simple relationship whereby vapor pressures of mixtures could be computed, if differential heat of vaporization data were available over a wide range of conditionso The latter, however, are not prevelant enough to make the technique of much practical valueo Simpler Approximations A number of simple approximations, which are relatively easy to apply, have been. used to estimate heats of vaporization for mixtureso Most methods have been directed toward the estimation of the integral isobaric heat of vaporization, because it is this quantity which is most often required in design calculationso Hydrocarbon mixtures have received the bulk of the attention of those attempting to establish rapid approximate techniques The most common approximation is the use of a mass average or a molal average of the pure-component latent heats taken at the pressure of interest. Another common. approximation is based on the fact that on a molal basis the latent heats of a number of pure materials are roughly equal. On this premise it has been customary to assume constant molal heat of vaporization for many types of mixtures. That is, an arithmetic average of the pure-component latent heats is assumed to be a satisfactory representation of the heat of vaporization for all mixtures there-, of. Hougen and Watson(31) have published a chart for the heat of vaporization of hydrocarbons and petroleum fractions which uses the molalaverage boiling point in degrees Fahrenheit and the molecular weight or the AoPo.I gravity as correlating variableso The chart gives the heat of vaporization at atmospheric pressure in Btu5s per poundo

-45Hydrocarbon mixtures sometimes have been characterized as being equivalent to a hypothetical pure component for which the heat of vaporization can be established, Edmister(l7) refined this technique somewhat for the integral isothermal heat of vaporization. He proposed that the calculation be made in two parts. The heat of vaporization of the equivalent pure component at atmospheric pressure is first estimated from Meissner's generalized chart(42) using the pseudo-critical concept to determine the reduced properties. A pressure correction calculated for isothermal conditions is then added to the hypothetical purecomponent latent heat to determine the integral isothermal heat of vaporization for the mixture.

EXPERIENCE OF PREVIOUS EXPERIMENTERS Earliest Investigations The first attempts to measure latent heats of vaporization of mixtures were reported in the early nineteen hundredso(2059) These early investigations were concerned wi.th the vaporization of liquid airo The investigators failed to recognize that the heat of vaporization of a mixture is not a unique phenomenon. However, Shearer(59) noted, "There seemed to be a distinct increase in the heat of vaporization as the liquid boiled away," At the time these experiments were conducted. the heat of vaporization of one of the pure components, oxygen, had not been determined. These first investigations suffered from three important deficiencies Firstly, the experiments were not disciplined'by a guiding definition of the heat of vaporization which was to be measured. Secondly, the experiments suffered inherently from attempts to use the same calorimetric equipment which was then used for latent heat measurements on pure materials Thirdly, the heat leaks were large In the early 1910:s Tyrer(70971,72) and Fletcher and Tyrer(22) published heat of vaporization data for several mixtures, The integral isothermal heat of vaporization was adequately defined (Tyrer called it_ vaporization at constant composition.), and Fletcher and Tyrer(22) designed an experiment to measure the defined quantity, Attempts were made to develop a formula relating the so-called "vaporization at constant composition" to a so-called "vaporization at constant pressure," an ills defined term somewhat like the differential heat of vaporization. The calorimetric equipment and procedures employed by these investigators -46

-47did not lend themselves to highly accurate measurements; consequently their data are not sufficiently reliable for present use, Recent Investigations In 1925 Dana(8) published an excellent paper on the heat of vaporization of liquid nitrogen-oxygen mixtures. In this work Dana measured the integral isobaric heat of vaporization. Large steps were taken toward the correction of the aforementioned deficiencies of the pioneering investigators. Adequate thermodynamic definitions of the latent heats of interest were used as a guide for designing calorimetric equipment suitable for the measurement of these quantities, Cognizance of the heat leaks to the low temperature system was taken, and efforts were made to reduce them. The basic features of Danats flow calorimeter have been used in more recent calorimeters constructed by other investigators. Recently, Tallmadge et al. (6768) and Plewes et alo(52,53,54) used modified versions of Dana's calorimetric equipment for the measurement of the integral isobaric heat of vaporization of mixtures which have boiling points above room temperature. The systems studied by these investigators are listed in Table I. Tallmadge et al.(67'68) gave considerable attention to heat leaks in their apparatus. Calibrated heaters external to the unsilvered, vacuum-jacketed calorimeter prevented conductive heat losses from the system. A temperature difference between the calorimeter and its immediate surroundings, the magnitude of which was governed essentially by the difference between the bubble point and the dew point of a given mixture,

-48was an inherent liability of their apparatuso Radiative heat losses from the calorimeter to the surroundings resulting from this temperature difference, were estimated, and the necessary corrections were applied to the latent heats In two of the systems studied(67 the maximum temperature difference probably did not exceed six centigrade degrees, thus rendering the corrective terms for the radiative heatlosses rather small percentages of the latent heats0 However, in the other system studied(68) the temperature difference between the calorimeter and its surroundings was probably as high as seventeen centigrade degreeso The high precision of their latent heat data attests to the accuracy with which they were able to estimate the radiative heat leako Plewes et alo(52953554) did not discuss the possibility of heat leaks in their apparatus Their apparatus was similar to that of Tallmadge et al. in that a dew-point - bubble-point temperature difference between the calorimeter and the surroundings was an inherent featureo They had to deal, with heat losses similar to those of T&all:madge et alo,'but probably to a somewhat lesser degree because the silvered, vacuum-jacketed calorimeter they used provided a smaller emilssi.ve coeffi`cient for radiative heat transfer than that experienced by Tallmadge et al. in their unsilvered calorimetero In their initial paper Plewes et al.(53) reported studies of systems which produced maximum. temperature differences between the calorimeter and its immediate surroundings of about fifteen centigrade degreesO However, the important measurement of the amount of power delivered to the calorimeter was made with only moderate precision; consequently, the heat-leak effects were

-49probably masked by the uncertainties in the power measurements. In subsequent studies(52,54) their technique of power measurement attained a high precision. However, the systems studied never produced an inherent temperature difference between the calorimeter and its surroundings of greater than about three centigrade degrees. These small temperature differences would, of course, have produced only small heat leaks. The high precision of the latent heat data presented in their latter papers probably vindicates ignoring the heat leaks for those systems. Stallaid and Amis(63) have published differential latent heat measurements for the system dioxane-water. As was mentioned in a previous section, the differential latent heat of vaporization is the most difficult to deal with experimentally. Wrewsky(82) measured the differential heat of vaporization of one sulfuric acid-water mixture. Table I lists the systems studied and reported in the literature referred tol hereinbefore. TABLE I MIXTURES FOR WHICH RELIABLE, EXPERIMENTALLY DETERMINED, LATENT-HEAT-OF-VAPORIZATION DATA ARE AVAILABLE Mixture Type of Data Reference Remarks Water-Formic Acid Int. Isobaric (54) 760mm Hg Water-Acetic Acid Int. Isobaric (52) 760mm Hg Methanol-Benzene Int. Isobaric (68) 735mm Hg (avgo) Acetone-Chloroform Int. Isobaric (67) 738mm Hg Acetone-Benzene Int. Isobaric (67) 738mm Hg Methanol-Water Int. Isobaric (53) 300 & 760mm Hg Ethanol-Water Int. Isobaric (53) 300 & 760mm Hg n-Propanol-Water Int. Isobaric (53) 300 & 760mm Hg Water-Dioxane Differential (63) 760mm Hg Sulfuric Acid-Water Differential (82) Only one conc. Nitrogen-Oxygen Int. Isobaric (8) Avg. atm. press.

-50Other investigators have made enthalpy measurements on petroleum, fractions and other mixtures. (19 935414376) In most of these investigations the emphasis was on measurements of moderate accuracy over wide ranges of temperature and pressure, including measurements in the superheated-vapor region and in the subcooled-liquid region., as well, as in the two-phase region.

EXPERIMENTAL APPARATUS Summary A thermally insulated flow calorimeter which operated at a steady state was used for the precise measurement of the integral isobaric heat of vaporization. A continuous flow of the liquid mixture to the calorimeter was vaporized by the consumption of electrical energy in the heatero The vapor which escaped was condensed and collected for an accurately timed intervalo The mass of vapor collected and the energy consumed by the heater during the timed interval were the principal measurements required for the determination of the latent heats. The Flow System A modified version of a flow system, which was used in cryogenic work by Dana and originally reported by him in the literature (8) was constructed for this investigation. The apparatus was designed for operation at atmospheric pressure on mixtures with bubble points above ambient temperatures. Steady-state operation of the apparatus is considered first. A discussion of the approach to the steady-state condition is taken up in the latter part of this section. Figure 5 on page 52 is a schematic diagram of the calorimetric apparatus, showing the items in the same relative positions as in the photograph, Figure 6 on page 53. Only the functions and purposes of the components are discussed herein. Details of the individual commponents are given in subsequent sections. -51

VAPOR LINES S.C.I S.C.2 VAPOR -LINE HEATERS CONDENSER I CONDENSER 2 RECEIVER I IRECEIVER 2 PREHEATER CONDENSERS - - REFLUX CONDENSER THERMOMETER VAPOR -LINE S.C.3 S.C.4 | VAPOR-LINE -- - HEATERS TR E /- THERMOREGULATOR T.C.17 m VAPORIZER T.C. 14 T.C.13 VAC. JACKET — VAPORIZER HEATER SHIELD MAIN CAPILLARY -T.C.1 SHIELD HEATER I E DRAIN HEATER A B PREHEATER LIQUID LINE PREH SAMPLING D CALORIMETER VALVE Figure 5. Schematic Diagram of the Flow System.

-53. li~i':ij~ i'~:~j il~'~j:Di~:~j:~R~i:,:j'::I~::::I~:1~;::::-.............. K;::itil J/*......'~ ~~~~~ " I::~~~~~~~~~~~~~~~X Sk.i. Calorimeter h. Vapor tines 2. Preheater 5. Receivers 5j. Li~quid. Lines 6. Standard Resistors Figure 6. Photograph of the Apparatus............ \::~.. ~:~:I~i:~::::a:-:~:: Y.'::::............-...........:..........~~~~S 3~r ". f~~ i~...:.:: ~ 1: ~~~. I. Calorimeter Vapor Lines~~~~~~~~~~~~~~~~~~: 2. Preheatr e ei er Liquid Lines Standard Resistors: Iii~ ~c i:;' Fiue6 htgahofteAp.r;'s

-54Consider the steady-state flow of a mixture9 as i:t passed through the apparatus, beginning at the preheatero The function of the preheater was to maintain a relatively large, liquid inventory of constant; compositi on at a temperature only slightly below the bubble point of the mixture0 To accomplish this mission the preneater was equipped with, a thermoregulator, heater, thermometer,9 and stirrera The liquid mixture, near its bubble point, flowed by gravity 1to the calorimeter through the heavily insulated liquid.liner, Near the calorimeter the liquid line split into two branches. One branch fed'the vaporizerj the other fed the shieldO Consider, first, the branch which led to the vaporizero The liquid feed entered the vaporizer through a capillary tube in the bottom. The capillary served to prevent any sporadic "kick back" of the vaporizer contents into the liquid line -whi.ch mi.ght have been caused by boiling action in the vaporizero The liquid feed, upon entering t';he vaporizer9 immediately mixed with the vigorously boiling cont-ents9; w-as vaporized, and escaped from the vaporizer via the vapor line at the topo Heat for vaporization of the feed was supplied by consumption of elect;rical enerxgy in the vaporizer heatero An identical vaporization process was carried out:i. the shieldo The purpose of the shield was to thermally i.sulat/ the vaporizer from heat exchange with its surroundings. This aspect is discu.ssed i n more detail in a subsequent section entitled " Thermal Shieldingo" In order to accomplish its mission the shield performed the sa-me junctions as the vaporizer; that is, it provided a place for vapor-izati.on

-55to take place, housed the heater, and provided a volume for the necessary liquid holdup. When in subsequent discussions, a given condition is said to apply to the vaporizer, it should be recalled that the same condition also must apply to the shield because identical processes occurred in each, The vapor which left both the vaporizer and the shield passed through externally heated vapor lines to the preheater condensers. External heat to the vapor lines was required to prevent the above-ambienttemperature vapor from condensing on cold lines and falling back into the containers. The vapor was then totally condensed in the preheater condensers and returned to the preheater, thus completing the cycle. In summary, the steady-state cycle was as follows: (1) liquid at its bubble point flowed by gravity from the preheater to the vaporizer, (2) in the vaporizer it mixed with the contents, was vaporized, and escaped via the vapor line, (3) the vapor was condensed and returned to the preheater. Control of the flow system rested with the vaporizer heater. The power supplied to this heater determined the rate of vaporization, which in turn set the rate of liquid flow by gravity to the vaporizer. A most important feature of the calorimeter was that under steady-state operating conditions the composition of the liquid mixture which entered the vaporizer was identical to the composition of the vapor which -left it. This condition can, of course, be confirmed by an elementary material balance around the vaporizer, which at steady state had a constant liquid level with only one entering stream, the liquid, and

-56only one exiting stream, the vapor. Yet, this condition may seem paradoxical in view of the fact that vapor which rises from a boiling, binary mixture is richer in the more-volatile component, than is the liquid. Both statements are correct, because during the approach to steadstate from the initial state, where liquid of the same composition pervaded the preheater, liquid line, and vaporizer, the liquid holdup in the vaporizer became progressively richer in the less-volat.ile componer:nt. Finally, a composition was reached in the vaporizer such that the vapor which rose from the boiling contents was of identical composition to the incoming liquid. The liquid contents of the vaporizer had thus attained a composition exactly eqal, or at least very nearly equal, to that of the equilibrium composition. For a more detailed discussion of the unsteady-state operating period, the reader is referred to Appendix A. where an intuitive illustration and a time-varying material balance around the vaporizer are presented. A steady-state operation of the type described above is not unfamiliar to chemical engineers. The similar performance of the re'oiler of an equilibrium distillation column which is operating at It-otal reflux, a hypothetical situation - but a much studied one, is familiar to most. The popular Othmer still(47) used for the determination of vapor-lic.q.uld equilibrium data operates in a similar fashion. Required Measurements The flow system described in the previous section was ideally suited for calorimetric determinations of the integral isobaric heat of vaporization for a number of reasons. Firstly, it permitted an almost

-57direct measurement of the latent heat, as defined. Secondly, it permitted operation at a steady-state condition which eliminated the problem of having to cope with time-varying temperatures and compositions. Thirdly, it permitted simultaneous determination of isobaric, vaporliquid equilibrium data for the mixtures under study with only a small expenditure of additional effort. A considerable cycling period was required to bring the apparatus to its steady-state operating condition, Once this condition had been reached, the inlet and outlet conditions of the vaporizer corresponded almost exactly to the defined initial and final states involved in the integral isobaric heat of vaporization - the initial state was defined to be liquid of a given composition at its bubble point under a given pressure, and the final state was defined to be vapor of the same composition at its dew point under the same pressure. The liquid feed, however, was not delivered to the vaporizer exactly at its bubble-point temperature, but usually a few degrees lower. Thus, the electrical energy consumed by the vaporizer heater, while used almost entirely for the heat of vaporization, had to make up this small amount of sensible heat. Equation (74) indicates the important measurements which were required for arriving at the integral isobaric heat of vaporizationo Integral Isobaric (Power) (Time) Sensible Heat Heat of Vaporization (Mass of Condensate) Correction t74) Reference is again made to Figure 5 on page 52. The flow system was brought to a steady-state condition and operated in. that manner

558for a period of time priorL to aking the latent-heat. measurements, The actual. measurepmients were begunr. y s::rltaneousLy star tirng a timer and turni!ng stopcock n-wubenr 2 so as to d:i.vert the cycling vapor i.nto condenser nm be;r' 2 and it s atr tached tared recei vero Dur ing The ti med inter - val, of t;he deterirnation sev-eral accuratte current and voltage readings wer-e made on th.e vapor. zer:-,eater circuit.o.Ee inlet temperature at point TC 12 was measured several, tLes during ethis interval. as we-re the other temperatuures a+, points marked TC 13^ TC 1.4^ TC If and TC 17. The measuzr:emren,,,:ts were t;ermiL.nated b-y simult;aneously stopl.n.g +he tim.er and turnring sto*,,pcock.nuirzmber 2 +to a strai.ght-t+hrough position0 A similar, check de'termi. nation was immediately made with the use of +bhe nulmber 1 stopcock, condenser, and +tared receivero These measurements const+,ituted all thbat w-ere requi..ed for' applicati.on of Equation (74). Du)ring the uns'teady-state operating period the temperaaet ures at all poin.;s were recorded at i jntervalso Several co:.secuti+..ve^ unvar'-. ing temperature readings i.ndi.cated that the apparatus had rea.c.ed s-tead-y state. Temperatures, ho'wever, served only as an. indicatl.ion. in.all. cases the steady-state condi.ti.on was've:rified by analysis of samples taken f-rom the liq.uid feed and'the conde:.sa'e. It has been pointed ou.t i.n ti.e preced.ing sect4ion t"J'.at the liquid conterInts of'th vapori..zer attaie.:-r.d a comopositio;:on aticnh. was in. equilibrium wi.th.- th,.e departJ..ng vapor. The temperature of t-h.e vap;ori.zer and the vapor com.posi+tion. were determin-ed during the latenr.4t+-heat measurements as a matter of course In order to obtain the vapor-li.qui d eq Cuilibrium data only the composi.tion of the li.qui.d contents of the vapori,zer remained'to be determinedo At tlhe conclusion of each determi.'nat, i on

-59a sample of this liquid was removed for analysis. Proper technique and manipulation of valves A, B, C, and D permitted independent sampling of any of the liquid contents of the system. Thermal Shielding In order to make precise calorimetric determinations of latent heat, it is imperative that the measurements be made in a thermodynamic system which is adiabatic, or in one in which the heat exchange with the surroundings is accurately known. In the ideal calorimeter accurate measurements of energy, mass, and time are made with no heat exchange occuring between the calorimeter and its surroundings. For adiabatic operation the ideal calorimeter must have either zero heat transfer coefficients or zero temperature difference between it and the surroundings. A variety of methods have been reported in the literature for maintaining thermal shields at the same temperature as their associated calorimeters. These methods have all been applied to calorimeters used to determine the latent heats of pure substances, but many of the methods would be applicable, probably with more difficulty, to calorimeters used for mixtures. Several investigators(44'45) have used shields which were heated externally by small electrical heaters attached to the surface. Temperature sensing devices detected differences in temperature between the calorimeter and the shieldo These differences were then corrected, either manually or automatically by adjustment of the shield heaters. Manual adjustment would demand a considerable portion of the operator's time and attention and distract himn from other

-6oessential tasks. As a consequence, a number of complex, automatic temperature -regulating-and-recording shields have been developed 7' 978 81,85) Other investigators (21,40,41,43,46,58,74) have used constant-temperature baths of boiling liquids, condensing vapors, or heated liquids of suitable viscosity and vapor pressure to establish shield temperatures. All previous calorimeters used by other investigators for the determination of integral isobaric heats of vaporization and reported in the literature(8,55368) operated with an inherent temperature difference between the calorimeter proper and its surroundings The magnitude of the difference was essentially that of the dew-point - bubble-point temperature difference for a given mixture, For many mixtures this difference is rather small,^ but for the acetone-water and isopropy.1l al coholwater mixtures studied in this investigation the temperature differences would have been large and would have caused large heat leaks:n calorimeters of the previous design. Thus in the calorimeter designed for this investigation, the temperature difference between the calorimeter proper (vaporizer) and its surroundings had to be eliminated, and in addition9 the conductive, convective and radiative coefficients for heat' transfer had to be made as small as practicable~ Figure 7 on page 63 is a cross-section. of the calorimeter used in this investigation. In this calorimeter a temperature difference between the vaporizer and its surroundings was eliminated'by setting up, in the shield, a steady-state vaporization process identical to the one which was occurring in the vaporizer, This method was well. suited for caloretric work with mixtures ad especially for the th e teof flow apparatus used in this investi.gatiorn, in that;, the correct shield temperature

-61was easily and automatically guaranteed regardless of the exact, final, steady-state composition, Furthermore, no complex, automatically controlled apparatus was required to maintain the temperature, and only a minimum of the operator's attention was required to achieve excellent results. Heat transfer by all modes was practically eliminated by this technique In addition to the aforementioned precaution for temperature control, the heat-transfer coefficients were reduced to a minimum by conventional methods. The jacket immediately adjacent to the vaporizer was evacuated to reduce the convective coefficient, and both the outer surface of the vaporizer and the inner surface of the jacket were silvered in order to reduce the radiative coefficient. The electrical leads and the lines carrying material to and from the vaporizer provided a means by which conductive heat transfer occurred. The associated conductive coefficients were reduced by the use of electrical leads as small as possible, consistent with the limits of electrical resistance tolerable in them, and by construction of the lines from thin material of low thermal conductivity, The heat leak along the liquid-feed capillary at the bottom of the vaporizer which resulted from a higher temperature at the vaporizer end of the capillary than at the inlet end of the capillary was reduced by the rapid flow of the liquid feed through the capillary in the opposite direction. In addition, the low thermal conductivity of the glass and its thin wall, were favorable to the reduction of this heat leak to a small quantity.

-62A quantitative discussion of the effect of the very small, but ever present, heat leaks on the results is taken up in a subsequent section entitled "Effects of Flow Rate," The Calorimeter The word calorimeter is used here to refer to all of the apparatus, except the flow lines, shown on the left-hand portion of the schematic flow diagram, Figure 5 on page 52~ The calorimeter consisted of two main components Tb.e vaporizer and its vacuum jacket formed the heart of the calorimeter the shield constituted the other main component. Figure 7 on page 63 is a cross section of the calorimeter The vaporizer and its vacuum jacket constituted a single unit constructed of standard-wall Pyrex glass The outside surface of the vaporizer and the inside surface of the jacket were silvered. the jacket was then evacuated to a very low pressure by a mercury diffusion pump and sealed off0 Both the vaporizer and the vacuum jacket were cylindrical in shape, The vapor outlet tube at the top wAas 14mm in inside diameter and extended approximately 3/4 inch beyond the top of the jacket. The outside surface of this tube was tapered toward the topo A spiralwound capillary tube extended from the bottom of the vaporizer through the evacuated space to the bottom of the jacket where it joined the inlet tube. This capillary was thin walled with an inside diameter of 1l3mm and a passage length of approximately 6 inches The inlet tube was 6mm in outside diameter and extended approximately 2-1/2 inches below the jacket,

-656" 1/4" NPT FOR CONAX BEGINNING OF GLAND MTG- 20-2S SHIELD VAPOR TO SEAL TC17 SHIELD VAPOR TC1 - - ~z / LINE /8is L-^ --— 5m -- -VAPORIZER CAPILLARY INLET INCLAMP TUBE GD - RING z 1 — T2 A4 H LSLEEVES 0/V^ ^-T.C17O-RING GROOVE POSlITION 4.500" I.D.x4.84POSO Figure 7. The Calor.x.123" SIGHT GLASS FITTING 60mim. — ACUUM JACKET --- 5mm. ----- VAPORIZER I II Mid m, Su, TC13 S OSITION S" TC 16 *J F/O-._BW? ^ilf ^ wV —- POSITION yTEFLON TAB I/4" NPT FOR CONAX LAPILLARY INEET NYLON INLET TUBE GLAND TG-24-4S TO SEAL ~LINE ~ NUT / IITC-16 AND HEATER LEADS TEFLON WEDGE W TC-12 POSITION Figure 7. The Calorimeter.

_64The shiel.d was constructed for the most part from'brass and consisted primarily of a cylinder with two removable ends A brass flange was silver-soldered to each end of the cylinder, and a groove was machined into each annulus to accommodate a Teflon O-ring which formed the seal, between the flange and the t;op or bottomo The flanges each contained eight tapped holes f or, the accommodation of the machine screws which secured the top and bottorm o A sight glass was installed on one side of the cy.li.ndero Two, 1/2-iLnch, brass pipe fittings, which were milled to f.t t.e wal.l, curvature, were silver-soldered to the wall. over 3/4-inch holes. Standard brass fittings for 5/8-inch gauge glass and the glass, it;self, were installed~ The pipe threads were sealed with soft soldero The stem packings in the fittings were replaced with packings cut from Teflon sheet, and the gauge-glass pack-ings were re-, placed with modified Teflon V-rings (nominal size 1/.2 incih by 1 inch)o The top of the shield contained the openings for the beginning of both vapor lines and an outlet for thermocouple wireso A l/2-inch copper tube which extended from 1/2 inch. below th.e botr tom of the plate, where it met the outlet tulbe of the vaporizer, to 5/'8 inch above the top was silver-soldered into the center of'the plat;e The top of the copper tube was tapped to accomrmodate a l/4-inch. brass nipple to which was attached a 1/4-inch brass cross The left side of the cross was fitted with a gland (Conax MTG-20-2S Teflon sealant) which sealed thermocouples number 13 and 14o The right side was fitted with a gland (Conax TG-24-A4 Teflon sealant) which sealed the vaporizer heater leads0 The top of the cross accomodated a brass compression fitting which contamned a short length of 35/8-inch copper tubing for the beginning of

-65the vapor line. All threads and joints were adequately sealed with soft solder. The vapor line from the shield originated directly behind the line from the vaporizer as one looks at Figure 7; however, the shield line was purposely misplaced to the right on the figure for illustrative purposeso The top of the shield was tapped for the accomodation of a brass compression fitting which contained a short length of 3/8-inch copper tubing for the beginning of the shield vapor line. The bottom of the shield provided openings for the capillary inlet line to the shield and the vaporizer inlet tube, as well as, an outlet for thermocouple wires and the shield-heater leads. In addition, it furnished support for the shield heater and the vacuum-jacketed vaporizer. A coil of 1/8-inch copper tubing with a passage length of 8 inches was silver-soldered into an inlet hole to one side of the bottom. Five, 1/8-inch brass nuts were soft-soldered in an upright position to the inside of the bottom of the shield in a pentagonal configuration to form the base for the shield heater supports. Brass machine screws held Teflon tabs (approximately 1/4 inch by 1/2 inch by 1/8 inch) to the nuts. Slots cut into the top of the Teflon tabs firmly secured the bare wire of the shield heater. A recessed space, which permitted liquid to flow through the inlet tube to the vaporizer unaffected by the temperature of the shield contents, was formed by a one-inch brass tube extending 1/2 inch into the shield. This tube was silver-soldered to the bottom of the shield, and it supported, at its top, a circular piece of copper 1-1/2 inches in diameter which. had t.,he same contour as the bottom of the vacuum jacket. This dished piece ) which contained a 5/8-inch hole at its center, was silver-soldered to

-66the top of the tube. A 1/4-inch, brass, flared tubing connector was cut in half, drilled out to 21/64 inch, and silver-soldered over the hole in the copper piece Connection between the top of the shield and the vaporizer outlet tube was effected by a specially formed Teflon sleeveo This thin-walled sleeve was one inch long and had an inside diameter of 1/2 inch in its upper half, The lower half had the same contour as the tapered outside surface of the vaporizer outlet tube, An epoxyresin adhesive (Armstrong Products Company type C-l) was applied between the glass and the sleeve to make certain that any small irregularities in the glass or sleeve did not lead to leaks between the shield and the vaporizer. The strength of the bond with the Teflon sleeve need not be of concern here, because in the assembled calorimeter this bond was not under stress. It was observed, however, that the bond was of sufficient strength to support the weight of the glass unit, In its quite limited exposure the resin was adequately resistant to attack by the vapor. The top of the Teflon sleeve was secured tightly to the copper outlet tube by forcing it over the tube, In addition, a brass tubing clamp was installed to make certain of the seal. In assembling the calorimeter the bottom of the shield was secured to the upright cylinder, and the vacuum-jacketed vaporizer, which was joined to the top of the shield by the Teflon sleeve, was carefully lowered into position inside the shield, The bottom of the vacuum jacket was cushioned on the copper support by a coil of 24-guage Teflong spaghetti, A check for perfect alignment of the parts, which

-67was necessary to prevent damage to the glass, was made before the top of the shield was secured to the cylinder. A specially constructed Teflon ring with a wedge-shaped cross section was forced over the outside of the inlet tube in a position such that it could make the seal between the tube and the modified fittings A nylon nut, manufactured for connectors used in conjunction with 1/4-inch polyethylene tubing, was slipped over the inlet tube and tightened to complete the seal at the bottom. The entire calorimeter was insulated on its outer surfaces with about one inch of Fiberglas and then covered with a cloth jacket. The exposed parts of the sight-glass fittings were covered with molded asbestos. The calorimeter was supported on the underside of the top flange by Flexaframe rods, which facilitated adjustment of the elevation of the calorimeter during preliminary experiments. Auxiliary Equipment The auxiliary equipment consisted of all the apparatus associated with the calorimeter in the flow system, except the electrical equipment. It can be broken down into three main categories - the preheater, the flow lines, and the collection system. Figure 8 on page 68 is a sketch of the preheatero It consisted primarily of a shell constructed from a modified stainless-steel beaker and a brass top fabricated to accommodate and support a variety of apparatus. The top of a 5800-ml, stainless-steel beaker was cut off at a height of 7-5/4 inches to form the shell, A brass flange was

— STIRRER GLAND CONAX PG-4,1/4" THERMOMETER GLAND BIMETALLIC CONAX PG-2,1/4" THERMOREGULATOR ^1 |y~. ~ ^~ J r]~ ~ AMINCO (4-235) 3/8 L I"'- 4CONDENSER 0NDENSER O-RING GROOVE 8 l l I I LINE LINE /9.00. x 9...340"O.D.x0.123" 0 - RING, NOMINAL,,~ —-~~~~ -|SIZE: I"x9 I" ___ _ -- 8" 4 SIGHT GLASS FITTING nE 0 UI.I DRA wI N Figurr 8. ThePrehea.o 0 2 z 0 o~~~~~~~~~~~r ~SHELL w /ILW 4 4 w ~1! BEGINNING OF LIQUID LINE I DRAIN Figure 8. The Preheater.

-69silver-soldered to the top of the shell, and a groove was machined into the annulus to accommodate a Teflon. Orring whic.h formed the seal between the flange and the2 topo The flange ccntai.ned 12 tapped holes for the accommodati.on of the machine serews -'which. secured the topO A sight glass similar to the one previously described for the calorimeter was installed on th-e shell.o Thin, brass baffles, approximately one inch by two inches, were attached to small tabs, silv-er-soldered to the inside of the shell in an irregular conmfiguration, in order to facilitate better mixing of the contents0 The liquid outlet from the shell. was located opposite the. sight glass about 3/4 inch above the bottomo At this point a l/4 inch.9 brass pipe fitting 9 milled to fit the wall curvature, was silver-soldered to the shello This fitting accomodated the main, liquid-line valve (Hoke 306M) A drain. valve was attached to the bottom of the shell in a similar manner0 The top of:the preheater contained three lines from various condensers, a packing gland for the thermometer, two heater terminals, a thermoregulator, and the packing gland for the stirrero The lines from the three condensers all terminated in s:hort lengths of 3/88-lnch copper tubing which were sil.ver-soldered into rh.oles in the top of the preheatero The thermometer (Cenco 1924k5-C),'which was sealed in the top, had a range of 0 to 100~C with 0ol~' subdivisioso Accurate readings were not required of this thermometer, hence its calibration was unnecessaryo The active section of the copper-sheathed heater was bent into an almost circular shape with a diameter a little less than that of the shell. The "cold" section of the heater extended throug the vapor spac,

-70rd t;he terminals were sealed in the top. These seals were effected by a Teflon gasket between the bottom nut of each. of the electrically insulated terminals and the bottom of the plate~ A Teflon gasket somewhat larger in inside diameter than the collar of the thermoregulator provided the seal between its flange and the top of the preheater, The center of the top of the preheater was tapped to accombdate the packing gland for the stirrer0 Teflon V-rings (nominal size. 1/4 inch by 5/8 inch) were used as packing0 The stirrer was powered by a Sargent-Cone-Drive stirring motor adjusted for an operation that gave adequate agitation without excessive splashing. The 1/4-inch, stainless-steel shaft was equipped with two propellers approximately 1-1/2 inches long, The lower propeller was positioned 1-3/4 inches from the bottom of the shell, and the other was located 53-3/8 inches above the bottom, The entire preheater was insulated on its outer surfaces in the same manner as the calorimeter, The preheater, like the calorimeter, was supported on the under side of the flange by Flexaframe rods bwhch permitted adjustment of the liqjui.d levels. The liquid line, as shown in Figure 5 on page 52, began at the main, liquid-line valve, which was attached to the preheater, and extended to the calorimeter where it divided into two branches. T.e lines consisted of 1/4-inch copper tubing and brass compression fittings. Because of their short lengths the lines seemed to be more fittings than tubing. At the point where the lines divided, the bottom port of the 1/4-inch brass cross was fitted with a valve (Hoke 306M) to which. the

-71sampling apparatus was attached. The vaporizer branch contained a valve (Hoke 306M) and a 1/8-inch brass tee which accomodated a gland (Conax MTG-20-2S) used to seal the wires of thermocouple number 120 The end of the vaporizer line was joined to the glass inlet tube with a short length. of thin-walled Teflon tubing which was forced over the glass and secured to the copper tubing by a tubing clampo The shield branch contained only a valve (Hoke 304) and the necessary fittingso Teflon was used for the steam packing in all valves. All pipe threads were sealed with soft solder. The lines were wrapped with Fiberglas insulation to a diameter of about two inches and then enclosed in a cloth jacketo The vapor lines as shown in Figure 5 on page 52, extended from the calorimeter to the preheatero The lines were constructed of 10-mm, Pyrex glass tubingo They were joined to the short pieces of copper tubing, which protruded from both the calorimeter and the preheater, by short lengths of thin-walled Teflon tubing forced over the glass and secured to the copper tubing by tubing clamps. Three-way stopcocks with 4-mm bores were placed in the lines as showno West-type, Pyrex glass condensers, 12 inches long with drip tips and 24/40-groundglass joints, were installed in the vapor lineso Connections to the condensers were made with the aid of bushing-type adapters and neckeddown 24/40-ground-glass joints. All ground-glass joints were lubricated with Dow Corning Silicone Lubricant0 The lines were wrapped with heating tapes from the points of origin at the calorimeter to the tops of the condensers. One layer of Fiberglas insulation on top of the heaters helped to contain the heat and even-out the temperature distribution0

-72Two9, Allihn-type condensers, each nine inches long and attached in series to the preheater, were open to the at.osphere and served to prevent liquid loss from the preheater, which su L bCse qJ.enrtI wocud have changed the composition. In addition, the top condenserprovided a convenient opening through which h mater:lal was charged to the preheater without removing the topo The collectionr system consisted of two condensers', two receivers, and a timer0 The receivers were modifieds 125-m1,i Erlernmeyer flasks with 24/40-ground-glass joints They can be seen i.n The p:hoto graph on page 55 on. top o:f the small platform below the condensers0 Duri.ng operation. of the apparatus, each, receiver rested in a beaker of crushed ice and was elevated so as to attach directly to the bottom 24/40-Cground-glass joint of its condenser0 No grease was used on this joint o In the attached position the modified flask was open to the atmosphere via a coil. of 4-mm glass tubingo The passage through the cofrl began in the flask wall jubst below the grcb.:nd-agas4 joint and extended externally almost to t.he bottom of the flask. A; that- point the coil tuarned upward in a straight tube which terminated in a small. opening at a height approximately equivalent to the cen"ter of the grouind-glass joint This circulitous passage through the -t i ce-illed 1beaker prevented losses by evaporation, from the receivero Ligt-weight tops from wTeighing bo.ttles neatly stoppered the r'eceivers wh, en they were not atttached to tthe condensers The length of time for which the condensate wras collected was recorded on a stop wat ch which had O0l-second divisionso -The stop watch. was checked several times wi.th the Michigan Bell. Telephone Company

-73time signal and with an electric timer over a 20-minute intervalo The differences were never more than 032 second, and they were neither consistently fast nor consistently slows consequently, the differences must be attributed to the operation of the stop-start buttono Heaters and Electrical Circuits Four electrical heaters and the associated circuits constituted integral parts of the apparatus. They were (1) the vaporizer heater, (2) the shield heater, (3) the preheater heater, and (4) the vapor line heaterso In addition, the thermocouple and potentiometer circuits formed equally important componentso The vaporizer heater was constructed from 40 inches of 36-guage platinum wire. The wire was coiled on a 3/32-inch arbor, and for support in service it was slipped over a sealed, glass, melting-point tube formed into a helix of about 3/8-inch inside diameter. The room temperature resistance of the heater was approximately 8-1/2 ohms. Twentyfour-gauge copper leads were soldered to each end of the platinum. Approximately 1-1/2 inches above the heater coil, a position which corresponded approximately to the average liquid level in the vaporizer, potential leads of 24-gauge copper wire were soldered to the current leadso This arrangement permitted the very small potential drop in the leads to be included in the measurement of the potential drop across the heater All leads were insulated with 24-gauge Teflon spaghettil The four, relatively short leads were adequate support for the heater coil..

-74Figure 9 on page 75 shows the circuit for the vaporizer heaterO The circuit consisted of two parts - the A.Co section which was used during the long cycling period in order to conserve the batteries, and the DoCo section which was used while the actual measuremen'ts were taken. The AaCo power was controlled by a variable transformer~ The AoCo ammeter and voltmeter aided in the power adjust.ment+O The DoCo power was supplied by three, 12-volt,? lead storage batteries These batteries were frequently recharged in order to keep the specific gravity in the range from about 1225 to 1o235. Any one or any combination of the batteries could be switched into the circuit, as desired0 The power consumed by the vaporizer heater was controlled by a combination of the number of batteries in the circuit and the adjustment of the water cooled, 55-ohmn and 5-ohm variable resistors which were in series with the heatero The 35-ohm resistor afforded coarse control, and the 5-ohm resistor was used for fine controlo The DoCo ammeter and voltmeter were used only for the adjustment of the power delivered to the heater; the voltmeter was switched out of the circuit after the adjustment had been made. An accurate calculation of the power consumed by the heater was made from determinations of its current and potential dropo The potential drop was determined from the measurement of the potential across the 100-ohm standard resistor, which was part of the 100-ohm - 1.000-oohm combination connected in parallel with. the heatero The current which passed through the heater was determined from the measurement of the potential across the Ol.-ohm standard resistor, which was in series witch the heater0 A correction was applied for the small

-7512-VOLT STORAGE BATTERIES + 0+ + 0 --- o.lQ STO. RESISTOR (NO. 1327633) i; I POTENTIOMETER - 8.5 HT A VAPORIZER HEATER IooOs STD. I IOOSSTD. RESISTOR (N0.1339328 ) RESISTOR VARIABLE (NO.1508856) TO TRANSFORMER POTENTIOMETER 115-VOLT A.C. LINE Figure 9. Circuit Diagram for the Vaporizer Heater.

-76amount of current which was shunted through the 100-ohm - 10,000-ohm circuit. The equation used to calculate the power from the two potential measurements is given in Appendix Bo The Leeds and Northrup, 100-ohm and 10,000-ohm standard resistors were of the National Bureau of Standards type and possessed recent certificates from the National Bureau of Standards which verified the actual resistances as 100o000 absolute ohms plus or minus 0.005 per cent and 10,000o5 absolute ohms plus or minus 0.005 per cent, The resistance of the leads and switch between these resistors and the heater was measured as approximately 0.2 ohm, which is less than the stated uncertainty in the 10,000-ohm resistor. The Leeds and Northrup, Ool-ohm, standard resistor of the Reichsanstalt type also possessed a recent National Bureau of Standards certificate which verified its actual resistance as 0.099995 absolute ohm plus or minus Oo01 per cent. All three of the resistors were immersed in an oil bath to a level. almost even with the top of the 0.1-ohm resistoro The shield heater was constructed from approximately 7-1/2 feet of 28-gauge, Chromel-C wireo Its room temperature resistance was approximately 32 ohms. The wire was coiled on a 1/8-inch arboro The strength of the wire coil made the support given it by the five Teflon tabs attached to the bottom of the shield more than adequate. The circuit for the shield heater was quite simpleo The heater was connected through a fuse and an ammeter to the output side of a variable transformer, which was used to control its power consumption,

-77The preheater circuit is shown in Figure 10 on page 78 o The circuit provided a simple on-off control for the thermostated liquid bath. The temperature was quite easily controlled to within plus or minus 00050~C The full 500 watts of the heater were utilized during the early stages of an operation in order to rapidly bring the liquid contents of the preheater to the desired temperature. Once the operating temperature was reached, the variable transformer which controlled the voltage applied to the heater was adjusted so that the correct temperature could be maintained with only a minimum number of interruptions of the power supply by the control circuit. The presence of the variable transformer in the circuit required a modification of the Trimount Electronic Level Control, which had the function of connecting terminals 2 and 3 when heat was requi-red, to prevent burning of its relay contacts, A 100-ohm resistor and a one-microfarad condenser connected in series between terminals number 2 and 3 served this purpose, The four commercial heating tapes (60 ohms, two of 80 ohms, and 100 ohms) wrapped on the vapor lines were connected in parallel through a fuse and an ammeter to a variable transformer which was used to control their power consumption0 Copper-constantan thermocouples with bare junctions were used to measure temperatures at the points indicated on Figure 5 on page 52 The thermocouples were joined with soft solder, but not twisted, at the junctionso One thermocouple was used for the ice-point reference junction, and the remainder were soldered to the terminals inside the switcho This entire unit was then used in the calibration of the

------- ~ ----- o~~~0000-0- 0 ------- — ^ 115- VOLTTRIMOUNT A.C. LINE ELECTRONIC ELECTRONIC LEVEL VARIABLE CONTROL TRANSFORME PLOT STIRRER LHT MOTOR STIRRER BIMETALLIC 500 - WATT, COPPER - THERMOREGULATOR SHEATHED HEATER (AMINCO 4-235) (AMINCO 3-404) Figure 10. Circuit Diagram for the Preheater.

-79thermocouples in the controlled-temperature mediumn of a stirred-liquid batho The calibration curves for the ther.ocouples used are given in Fig ure 57 of Appendix, E o Th.e wires were covered with a high temperature insulating enamelo In addition, cerarmic insulators were used on numbers 16 and 17; the remai.nder were insu.lated with. Teflon spaghettio Thermocouple number 12 was constructed from 30-gauge wires and was used to measure the l1iquid inlet temperature to the capillary'o The junction was 1-mm in cross section and was located exactly at, the entrance of the 1o3-mm capillary. Thus, the average inlet temperature was determined with one position of the thermocoupleO Thermocouples number 13 and 14 were also constructed from 50-gauge -wires and were located inside the vaporizer. Number 13 was submerged in the liquid about 1/2 inch above the heater. Number 14 was located in the vapor stream at the top of the vaporizero Its size and environment were favorable for accurate temperature measurement That is, it had a small junction, was located in the rapidly movingr; vapor stream, and "saw" silvered walls which were at the same temperature as the vapor itself. Numbers 13 and 14 were both attached to the insulated heater leads to insure their location at'the desired position.'.Thermocouples number 1.6 and 17 were constructed from 24-gaAge wires and were located inside the shield, Number 1.6 was located 1-5/8 inches below the top of the shield in the vapor spaceo Niuber 17 was used for measuring the liquid temperatures and was located 1-1/4 rinches above the bot+tom of the shield, The ceramic insulators used on both 1.6 and 17 also served as support for the wireso

-80The potential-measuring circuit and the thermocouple connections are shown in Figure 11 on page 81 The potential measurements were made with a Leeds and Northrup, K-2-type potentiometer and suitable auxiliary equipment Two Eppley standard cells (Noso 132182 and 610144) were used during the worko At 25 C their emf's were 101867 and 101881 absolute volts respectively, as determined with a Weston cell (No0 15559) of the unsaturated type which possessed a recent certificate from the National Bureau of Standards. A Leeds and Northrup, type-2500-C galvanometer was used to detect unbalances in the potentiometer circuit0 A 330-ohm damping resistance was installed between the galvanometer and the potentiometer. The unbalances were indicated on the etched ground glass of a Leeds and Northrup, type-2100 lamp and scale located at a distance of one meter from the galvanometer mirroro Four, 105-volt dry cells in a series-parallel connection supplied the working current for'the potentiometer. A pinch-type, DPDT switch was the hub of the potentiometer circuito Its center terminals were connected to both the emf terminals of the potentiometer and the inner contact rings of the multipoint thermocouple switch. With the thermocouple switch in an open position the potential across either the 100-ohm or the Ool-ohm standard resistor could be applied to the emf terminals of the potentiometer by throwing the pinch switch0 With the pinch switch in an open position any of the thermocouples could be connected directly to the potentiometero The thermocouples were attached to the ten-point, double-pole switch as shown in the figure

TO POTENTIOMETER 0 IZ 1~~ -2(JU INSULATIONCIOPINCH TYPE SWITCH COPPER BRUSHES ROTARY SWITCH Figure 11. Potential-Measuring Circuit and Thermocouple Circuit.

-82Analytical Equipment Analyses of the mixtures were determined from the measurements of the density of the liquids in calibrated pycnometerso Hot liquid samples were withdrawn from the system through the sampling valve, D, (Figure 5 on page 52 ) and were cooled in the detachable sample cooler before delivery to the pycnometers. The condensate samples were taken directly from the receivers. The volumes of six pycnometers of various sizes (nominally: one 5-ml^ four 10-ml, and one 25-ml) with ground-glass joints and caps, which contained capillary perforations, were determined by calibration, The calibrations were made at 250C and 35~C with double-distilled water in the constant-temperature medium of a well agitated, thermostatically controlled water bath. The temperature, which was easily controlled to plus or minus 0.05 ~C, was observed on a mercury-in-glass thermometer (Prince No. 460641) which possessed a recent certificate from the National Bureau of Standards. The pycnometers were submerged to a depth. approximately 1/2 inch below the top of the caps by custom-fitted suspensions fashioned from 1/8-inch copper tubing and attached to the side of the bath. The weights of the pycnometers were determined quickly and easily on a Christian Becker Projectomatic Balance (Model AB-l)o The detachable sample cooler consisted primarily of a coil of 1./4-inch copper tubing soft-soldered into a number-2-1/2 tin can. In service the can contained crushed ice which surrouned the coil. Both ends of the coil protruded through the side of the can, A short length of polyethylene tubing was installed for flexibility between the top

-83of the protruding coil and the fittings used to attach the cooler to the sampling valve. The bottom end of the coil delivered the sample directly to the pycnome'tero Materials Reagent-grade isopropyl alcohol of 99o91. per cent purity marketed by the Jo To Baker Chemical Company was used without further purification Reagent-grade acetone of 99~60 per cent purity marketed by Merk and Company, Inco'was used without further purificationo Double-distilled water from the University Chemistry Store was used for all dilutions and calibrations

EXPERIMENTAL PROCEDURE Summary The culmination of the experimental procedure -was reached during a timed interval. in which t:he actual data used for the determination of the integral isobaric heat of vaporization were taken. During this interval measurements of mass, power, and temperature were made on the calorimetero Less engaging, but of no less importance to the final results, were the prerequisite procedures of preparation. for the run and of cycling the mixture in the apparatus, The post-requisites of sampling and analysis were likewise indispensable~ Preparation The preparation period was considered to have begun with the routine laboratory tasks and to have extended to the time at which, the first vapor escaped from the shieldo A liquid mixture approximately of the composition of interest was charged to the preheater through the openilng i.n the- top of the reflux condenser The liquid was allowed to run into -the shield and vaporizer until it reached a level. of 3-1/2 inches from the bottom of the shield, as shown in the sight glass. At that time the valves in the shield and vaporizer branches of the liquid line Twere closed, and the liquid level in the preheater was brought to 4-1/2 inches from the bottom, as shown. in its sight glasso Experience gained from preliminary experiments with'various adjustments of the Flexafra:me supports indicated that these levels were desl.rable and easil.y maintainedo

-85The entire composition range was covered by beginning with a rich mixture of the more volatile component, either isopropyl alcohol or acetone. Thus, the more frequently used charging process consisted of the dilution of the rich mixture already in the preheater with doubles distilled water, However, after a number of dilutions the preheater was drained and refilled with a completely fresh mi.xture as previously described. After many runs, which began with the same liquid composition everywhere in the system, had been made with the observation that a steady state was attained as described in a previous section entitled "The Flow System," it was decided to shorten the lengthy cycling period by assisting in the approach to steady state. The final contents of the shield and vaporizer were always leaner in the more volatile component (isopropyl alcohol. or acetone) than were the initial contentso (An exception to the foregoing statement occurred for compositions of the isopropyl alcohol-water binary between the mininum-b oiling azeotrope and pure isopropyl alcohol; however, this case is not relevant to the discussion here because all runs in this composition range happened to have been made with the original procedure of beginning with the same composition throughout the apparatus.) Therefore, a mixture with a higher concentration of water than the mixture in the preheater was charged to the shield and vaporizer through the sampling valve However, this special, shield-vaporizer charge always contained less water than the final contents of the shield and vaporizer in order to guarantee that steady state was at all times approached from the same direction0

-86That is to say, to guarantee that the concentration of water in the shield and vaporizer always increased with ti.me and never decreasedo In order to insure this condition for the vaporizer, it was necessary, because of the relative volumes of the apparatus involved, to drain from the vaporizer and ilts liquid line a volume of the special mixture equivalent to the line volume and to then allow the line to refill with the mixture from the preheatero After the correct mixture was charged to the apparatus and a number of routine tasks, such as turning on cooling water, were completed, the preheater was readied Stirri.ng and heating were'begun, and the thermoregulator was adjusted to control the temperature at approximately two centigrade degrees lower than the bubble pointo As the temperature of the contents approached the control temperatur e, the voltage applied to the heater was reduced to a level, usually between 27 and 60 volts, which experience:had shown was satisfactory for mainta:ining a constant temperature with a minimum of interruptions of the power by the controllero Simultaneously with the preparation of the preheater a predetermined amount of power was supplied to the shield heater and the vapor-line:heaterso Experience gained from preliminary experiments indi.cated that power at a level. 2-1/2 times that consumed by the \apori zer heater should be supplied to the shield heater for smooth operation and a reasonable rate of cycling of material through. the shieldo Observations during preliminary experiments showed that, for "the complete range of mixtures, from 72 to 118 watts were required by the vapor-line

-87heaters in order to prevent, condensation in the lines~ A period of approximately 1-1/2 hours was requi.red to warm-up the apparatus and to get a significant flow of vapor from. the shiel.d When a s.ig.n:ficant flow was establish+ed he valve in the s. lhield branch of the li.quid line was opened and adjusted to maintain a liqu.id level. of 3-1/2 to 3-5/8 inches i.n the shield, Operating conditions and the relative densities of the preheatler and shield contents affected the levels9 consequently, tlhe operator s experie:nce was valiuab;l.e in the adjustment of the valveo As the m.xture began to cycle in the shield the valve in the vaporizer branch of the liqui.d line was opened, and al ternating current was supplied to t:be vaporizer heater in an amomLnt sufficient to establish the desired flovw rate. Vaporization in thi.s container began almost immediately because the surroundings had been conditioned by the shield; thus, all of th.e heat was immediately availlable to t:he liquid, Cycling The cycling period was considered to have begun with, the mix-, ture circulat-]ing through the: apparat,us and to have extended to the beginning of the actual determinationo The average cycling period lasted aboout 2-1/2 hourso Duriang this time temperature readings were taken at intervals at all points A number of consecutive, unvarying temperatures in'the vapor..zer and shield indicated that the apparatus had reached steady state0 This period also provided time for necessary, routine tasks, such as atStach.ing the receivers with their ice-filled beakers'to the condensers and

-88insulating the liquid-line valve handles after the final adjustmen.-ts had been madeo When temperature observations indicated that a steady state had been reached and about 20 minutes'before the actual determnar.ton was begun, the vaporizer heater'was switched from alternating current to direct current Prior to the switch the sliding-corntact, watercooled resistors in the DoCo circuit were positioned so as to make th.e initial battery-supplied power approximately the saame as the AoCo powero Experience in positioning the resistors made the instantaneous switch from AQCO power to battery power, and the subsequent fine adjustment of the current to the vaporizer heater, a process which required only a few secondso After the final adjus+tm.ent of power had been made, t;he DoCo voltmeter, which would [have drawn a small amount of current9 was switched out of the circuit, The steady-state cycling was continued for about 20 minutes during which time the potentials across the standard resistors and the emf's of all. the thermocouples were measured and recordedo Measurements Two successive determinations were always carried out on0 t+he same mixture, at the same flow rate consequent;ly, the measurement period extended from. the start of the timer at the beginnifng of the first determination to the stop of the timer at the end of the second determinationO The average length, of the first determination was approxi.mately 22 minutes the second averaged approximately 17 minutes0 Measurements were taken for each particular mixture at: flow rates of

_89approximately 1-1/2 grams per minute and one gram per minute0 Data were taken for each of the pure components at foLr flow rates between O0703 and la733 grams per minute v With the material cyclLng smoothly in the apparatus, a determinati.on was begun by simultaneously starting the timer and turning stopcock number 2 to divert the vapor into its condenser and tared receivero A 60ominute stop clock was then started in order to give the approximate time of the determination at a glanceo Two sets of measurements of the potentials across the standard resistors were taken and recorded along with the time of each measurement0 The emf's of thermocouple numbers 19, 14, 16 and 17 were measured twice and compared with the measurements obtained during the cycling periodo If they were not in agreement the determination, was halted and discarded, and the cycling period was continuedo The emf of thermocouple number 12 was measured several. times during the interval. This temperature was not perfectly constant with time; however, i4t rarely varied more than plus or minus 0o5~C and usually varied considerabl.y lesso An arithmetic average of the readings taken was used for calculations After the thermocouple emfis had'beer measured one more set of measurements of the potentials across the standard resistors was made. Stopcock number 2 was then turned to a straight-through position simultaneously'with the stopping of the timer in order to end the determinationo Duxring the determination., readings of all the meters and gauges attached to the apparatus, as well. as the barometric pressure and amibient temperature, were recordedo

_90Immediately after the end of the first determination, a second was begun using stopcock number 1 and its condenser and tared receiver. The procedure followed was identical to the one described in the previous paragraph, except that one of the two early sets of potential measurements was eliminateda At this point in the procedure two alternatives were availablee The vaporizer heater coul.d be switched to A.Co power at a lower level in order to begin the cycling period for the deter:mnations at a slower flow rate, or the sampling and analysis could be started immediately in which case the apparatus would be shut down and the slower-rate run made at a later date, The former procedure practically eliminated another preparation period and considerably shortened the cycling period. Usually, the slow-rate determination could be commenced as soon as the sampling and analysis which was associated with the faster rate and which could not be delayed had been. completed. From these standpoints the former procedure was preferred. however, the time required for the single run was quite length y, and an increase of l/3 tto 1/2 was not always possible~ In practice the ruIns were split approximately equally between the alternative procedures~ Sampling and Analysis The period for sampling and analysis began.immediately after. the final determination. The amount of condensate in each receiver was determined^ and samples of the condensate, preheater contents, vaporizer contents, and shield contents were analyzed by density measurements o

-91The receivers were detached from the condensers stoppered, removed from the ice-filled beakers and driedo The receivers, -which had tares of approximately 1.05 grams, were then, weighed on a threekilogram, chain-type, Seko balance with'weights calibrated with a set of class S weights which possessed a National Bu:reau of Standards Certi-, ficate verifying their accuracyo In spite of the fact that the condensers were cleaned thoroughly with chromic-acid cleaning solution and rinsed with d:isti.lled water before use, a few, small droplets of condensate clung to thee inside of the condenser tubes at the end of determinations on mixt;ures which contained high concentrations of waterO The droplets which remained in the tubes and which could not be "coaxed7' down. the tubes into the receivers by gentle tapping were swabbed out quantitativelyo Two identical swabs, approximately 5/4 inch by 1-1/2 inches, cu.t from the same piece of filter paper were usedo One piece was attached to a. wire and used to absorb the droplets on the inside of one of the condensers after which it was put into a tared weighing bottle Thi.Ch was weig;ed on an analytical balance; the other piece was -used as tare o:nr the.Teigh+ht pan. of the balance. The net weight of the additional material9 thus collected and measured, was added to the weight of the receiver contentso The maximum amount of material recovered in this fashion was o0 78 gram, which is approximately 0o2 per cent of the average amount of condensate of 33 gramsO The average difference in. weight in ten. preliminary attempts to cut identical swabs amounted to only 0O002 grama

-92= After the receivers had been weighed, they were retur:ed t:o the ice-filled beakers to again. cool the condensateo Samples of the cold condensate were then transferred directly from the receivers to the 10-=-ml pycnometers The apparatus had to be parti ally shut down prior to *taking the l.iqud samplesO The vaporizer h.eater was turned off simul.aneousl> wivth the closing of tbh.e valve in the vaporizer branch. of the liquid line, as were the shield heater and the valve in the shiteld branchb. It was necessary to contin.ie the power to the vapor-line heaters urtil after the samples were taken in order to prevent the.rich. vapo:r from condensing an.d falling back into the containers, and- t.:ereby changirng the composition of the conten. ts' Thqe main lliuid-.li.re va ive was then. closed-, and one of the ice-filled sample coolers was at. ached to the open sampling valve About 25 mls of the preheater liqu.id were drained through the sample cooler before the actual sample wa8s takerT. J:, 25-ml. pycnometer This sample coole3 was'then -removed- a-;nd t.heb second. was attachedo AboLut 20 mnls of liqliid were d-rained from tT-he shield line and the shield through +the cooler before the actual ssmple was taken in one of the 10-ml pyc-nometerso Aft;er the coil of tAhe sample cooler was drained r a similar pr.ocedure was follved In. takin.g th.e vapo>rizer sample, except that only about 15 mi.s rere wasted before t;wo suc,cessive samples were transferred to 10-nt rl and. the 5-, m pyc:.o.metersa The full pycnometers were suspended In the consttan't-te;pemstu.re medlium of a well agitated-vwater bath. for approximately seven minu:t;esa It was founrd. ir:. prel.imi-nary tests with a pycnometer which cn.r:Xafnedl a,

-93thermometer that only about five minutes were required for the contents to attain the same temperature as the batho The temperat+lire in -the water bath was always higher than ambient tempe:rature and. was eas:,l.ycontrolled to plus or minus Oo05~Co The therm.o+rmetr could ~be read to plus or minus 0o02~C with the aid of a magnifying reader As the pycnometers were removed from the water bath., each. was touched quickly in ice water to contract the Iliquid in the capillary-perforated top and then wiped dry with absorbent9 lintless paper. The pycr.no'meters were weighed rapidly on a projectomatic-type analytical alla.ance Evaporation losses were quite small because of the contraction of the l.:iquid down the capillary and away from the atmosphere and because of the rapi.d handling which was greatly facili.tated by the rapidi.ty with wh.ich approx.mately known weights could be determined on -the projectomatic-type balance o Density of the isopropyl alcohol-water mixtures was nr. mea.sured at 35500O~C Analysis was effected by use of the precise densitycomposition data at 35500~C of Langdon and Keyeso(38) Preniminary'mreasurements of the density of nine carefully prepared mixtures of krnownn composition, which were randomly distributed over the ent:ire compositrion range of 0 to 1.00 per cent, showed an average deviation rwithout% regard to sign of only 0o08 mass per cent from the smoothed data presenr.lted by Langdon and Keyes Density of the acetone-water mixtures was measured at 25o00~Co Preliminary measurements of the density of carefully prepared mrxtures of known composition at 25o000C did not produce agreement with anyr single set of published density-composition data (2562,6 9) over the

-94entire range of composition. Agreement within 0.1 mass per cent with the data of Thomas and McAllister(69) was observed in the composition ranges of 0 to 52 and 92 to 100 mass per cent acetone. However, these investigators covered the entire range of composition with only seven density points, which made interpolation for accurate analytical purposes quite impractical and uncertain. No set of the aforementioned, published data agrees over the entire range of composition with any of the other sets to closer than plus or minus 0.5 mass per cent. Although the density-composition measurements taken in this investigation were not completely in agreement with any published set, they were quite self-consistent and reproducible to less than plus or minus 0.2 mass per cent. Therefore, a density-composition curve at 25.00~C was produced for analytical purposes by measuring the density of 24 carefully prepared mixtures of known composition over the entire range of 0 to 100 per cent. The smoothed values of density at even values of composition are shown in Table XIX of Appendix E.

CALCULATIONS Summary The essence of all the calculations is contained in the equation Integral Isobaric (Power) (Time) Corrective Heat of Vaporization (Mass of Condensate) Terms (75) The first term on the right-hand side is referred to as the uncorrected latent heat. Of a number of possible corrective terms only the sensibleheat correction was found to be significant, and it averaged only 1.5 per cent of the uncorrected latent heat. A sample calculation which demonstrates the use of Equation (75) is presented in Appendix B. Tabular values of the important measured quantities used in the calculations for each mixture are shown in Appendix F. The vapor-liquid equilibrium data were obtained directly from the corrected temperature measurements and from density measurements used in conjunction with density-composition data. Uncorrected Latent Heat The calculation of the uncorrected latent heat, the first term on the right-hand side of Equation (75), was carried out in three distinct steps. Firstly, the measurements of potential across the standard resistors, taken at various times during the determination, were used to calculate the instantaneous power consumption of the vaporizer heater. Secondly, these values of power were plotted versus time and the area under the power-time curve was calculated to determine -95

-96the total heat evolved by the vaporizer heatero Sample calculations which illustrate the first two steps are shown in Appendix Bo Thirdly, the total heat evolved was divided by the mass of condensate collected during the determination and was -mul.tiplied by the proper' conversion factor to arrive at the desired set of units. Corrections Of a number of possible corrective terms only the correction for the small. amount of sensible heat supplied to the liquid was significant. The others were either eliminated by the design of the apparatus or were insignificant from the beginningo The sensible-heat correction was required because the liquid was not delivered to the vaporizer exactly at its bubble-point temperature, but usually a few degrees lowero The corrective term was calculated from the equation Sensible-Heat Correction = 0o981 l (tBp - ti) (76) The factor 0O981 is a constant; its significance and origin is explained in a subsequent paragrapha Cp m is the average specific heat of the liquid mixture between the temperatures, tBp and tIno Data on the specific heats of liquid mixtures near their bubble points are scarce, and for the mixtures studied in this investigation these data are nonexistento Consequently, the available data for acetone-water mixtures at 25 and 40C(36) were adjusted for use in Equation (76) in accordance with the temperature variance of the specific heats of the pure components(35 j4664 ) and with the observed temperature dependence of the

-97mixtures in the 25-40~C interval; the available data for isopropyl alcohol-water mixtures(14Y56) were treated similarly with the aid of the pure-component; data (24,46) Fortunately, the average corrective term amounted to only 1.5 per cent of the uncorrected latent heat, so that an error as large as five per cent' in the estimation. of the specific heat of the mixt-ure would introduce an error of onl.y o0.75 per cent in the integral isobaric heat of vaporization~ In Equation (76) tBp is the bubble-point temperature of the mixtureo This temperature was read from the bubble-point line on a temperaturecomposition diagram, which was o.btained from the vapor-liqauid equilibrium data taken over the entire composition range during this investigationo The inlet temperature, tIny is an, experimental quantity which was measured during each determination0 During the timed interval of a determination material was withdrawn from the system into a receiver, thus causing a drop in t;he liquid level of all containers This drop in level -was quite small because of the large surface area and volume of the preheatero During the average fast-rate determination 33 grams, or approximately 4Jx-ml.s9 of material were withdrawno The resulting drop in level was approximately Ool.. cmo In spite of the small magnitude of the drop an uinvestigation of its significance is in order. The drop in level means that during the timed interval of a determination slightly less liquid flowed into the vaporizer than was collected as condensate in the receiver0 Thus,'the sensible-heat corrective term should include the ratio of the mass of liqu.id Which

-98flowed into the vaporizer during the interval. to the mass of condensate collected during that time, because the vaporizer heater was not required to make up the full amount of sensible heat. This ratio of masses is actually dependent only upon the relative cross-sectional areas of the apparatus and is independent of the amount of material collected in a receiver during a determination. The essential items for the calculation of this ratio are shown in Equation (77)~ Liquid Entering Vaporizer Area. of Vaporizer Mass of Condensate 1 Area of Entire Apparatus 1 706 cm2 = o981 (77) 366.7cm2 This factor appears in the sensible-heat correction, Equation (76). When the liquid level fell. in the vaporizer this volume, previously occupied by liquid, was filled by material which was vaporized but which was not accounted for in the condensate at the end of the determination. This correctiop to the mass of condensate involves the ratio of the density of the vapor to the density of the liqluid as well as the relative cross-sectional areas of the apparatuso The proper combination of these factors leads to a corrective term,, which indicates that the measured mass of condensate should be increased by approx,mately 0,001 per cent. This amount, of course, is insignificanto It was also possible that a falling liquid level could upset the steady-state operating condition. However, the fall of level actually involved was too slight to produce any significant effects, The constancy of the composition of the condensate, collected during conr secutive determinations, experimentall.y verified this conclusiono

-99Evaporation of material from the receivers prior to the time at which they were weighed could involve a correction of th.e measuraed mass of condensate~ The design of the receivers cut tAhis loss to an insignificant fraction. Preliminary tests with 50 grams of acetone in each, stoppered receiver showed the evaporation rate to be approximrately 0Oo004 gram per hour at room temperature over a period of approximately one dayo In actual practice the receivers were set in ice-filled beakers which. further reduced the evaporation rateo The receivers we:re al'ways weighed within 15 minutes after the termination of a runr T.n.us. th.e correction involved was insignificant~ The experimental. runs were not conducted at a controlled pressure, but were conducted at the ambient pressure on a given. day, The barometer readings were recorded several. times during eacbh run. The ambient pressure encountered during the entire series of runs ranged from 72359 to 745 0 mm of mercury with approximately 90 per ce.n't o:f n-h.e runs falling between 733 and 743 mm of mercurya The pressrire var.a~tion of the heat of vaporization over this range is less than the experi.mental accuracyj however, the measured temperatures used in thle vaporliquid equilibrium data had to be corrected for the pressure differences0 Interpolation of the precise data of -the National Bureau. of Standards on the heat of vaporization of water(46) at the pressures extremes of 72359 and 745.0 mm of mercury shows a difference of only 0o499 calorie per gram, or approximately 0O09 per cent of the heat; of vaporization. The difference between the heat of vaporization of water at 760 mm of mercury and at the average pressure of 73657 rm of xercury

-100is Ool per cent, which indicates that the data presented herein can be used at a pressure of 760 mm of mercury within the experimental. accuracy It was desirable to correct the measured temperatures used in the vapor-sliquid equilibrium data to a common pressureo A linear relationship between the logarithm of the pressure and reciprocal temperature was assumed for the small pressure range involvedo The required slope for each mixture was obtained from a molal average of the slopes for the pure components, which were taken to be -2200 for water, -2300 for isopropyl alcohol, and -1630 for acetone. The units used were mm of mercury and ~Ko All measured temperatures were corrected to a pressure of 760 mm of mercury, The average correction amounted to approximately 008~C. Effects of Flow Rate Operation of the apparatus at a number of flow rates aided in the evaluation of the effectiveness of the thermal shielding and of the design of the vaporizer and its heater. The few, remaining, small heat leaks, which. were not eliminated by design, were detected by a variation in flow rat;e With a given material in the apparatus heat leaks would be essentially constant with time and roughly independent of flow rate Therefo re approximately the same quantity of heat would be lost in any given time interval, regardless of the flow rateo As a result, the greater the through-put (or flow rate), the less effect these heat leaks would have on the magnitude of the resulting heat of vaporizationo At an infinite flow rate the effect would be i.nfini.tesimalo

-101The heats of vaporization of the three pure components were measured over approximately a 2o5-fold range of flow rates, and the results were plotted as a function of reciprocal flowr rate~ Th e cu:rve obtained for water is shown in Figure 12 on. page 102o An extrapolation of the data to the ordinate, 1/F - 0, 9which corresponds to an infinite:flow rate, results in an answer whlch is devoid of heat leak:s The unguided extrapolation. of a curve is dependent on judgement and prejudice; therefore, the latent heats were plotted as a function of reciprocal flow rate to the third power, as shown in Figure 13 on page 102, which permitted a straight-line extrapolation. The equation of the line was determined by a least-squares fit of the datao Similar graphs for isopropyl alcohol and acetone are shown in Appendix E. The fact that the observed heats of vaporization should'be higher than the extrapolated one is rather easy to explain qualitatively0 Consider the first term on the right-hand side of Equation (75) "Power" and "Time" are measured quantities unaffected by heat leaks, so'+t,at attenti.on must be focused on the "Mass of Condensate" If the direction of heat flow is from the calorimeter toward the surroundings, as was the case in this investigatiron because all the pure component;s and mixtures had boiling points above ambient temperatures, t:hen, any sma.ll amount of heat which leaks out is unavailable for vaporizing ma.feria. o As a result, the condensate which is actually collected and weighed i.s less than the amount which would be observed in the perfectc91ly adi.abatic system. The "Mass of Condensate" appears in the denominator of t1he equationj therefore, this less-than-true-value quantity produces a high latent heat

-102546 Z 0 544 0 0. <> 542. R 540 --- rdIJ - = 538 LJ 536 0.2.4.6.8 1.0 1.2 1.4 1.6 I/FLOW RATE (min./gr.) Figure 12. Heat of Vaporization of Water as a Function of the Reciprocal of the Flow Rate through the System. 546 544 542 1 O ^. — 4 <*> 540 538 Z 536 --- 0.4.8 1.2 1.6 2.0 2.4 2B 3.2 I/FLOW RATEs (min./gr.)$ Figure 15. Heat of Vaporization of Water as a Function of the Reciprocal Flow Rate to the Third Power.

-103The foregoing discussions were developed on the basis that the heat leaks were constant with time and independent of flow rate. Actually, the design of the equipment was such that an even more favorable situation was encountered in practice; in that, one of the individual heat leaks was reduced by faster flow rateso The flow of the liquid through the capillary at the bottom of the vaporizer was in the opposite direction to the heat flow along the capillary0 As a result the faster flow rates tended to lessen this individual heat leak, as well as reduce the overall effect of heat leaks. The difference between the heat of vaporization at rates greater than 1.5 grams per minute and the extrapolated values was small enough so that data taken in the range of 1.5 grams per minute were adequate. It was, therefore, unnecessary to determine the entire curve for every composition; however, a run was made as a check at a slower rate, approximately 1.0 grams per minute, for nearly every compositiono A flow rate of approximately 1.5 grams per minute happens to correspond to the 120-ml-per-hour rate recommended by Canjar and Lonergan(5 for use in obtaining vapor-liquid equilibria in circulating - type stills. The variation in flow rate also helped establish the absence of entrainment or of mechanical ejection of liquid by any mode from the vaporizer. Observations during preliminary experiments with a number of vaporizer heaters, used under a variety of conditions, showed that the bare-wire heater of the design used in this investigation could be used to vaporize liquids at the contemplated power levels wit5hout ejecting any liquid from the vaporizer onto the externally heated vapor lines, These observations were borne out by the operation of the apparatus at

a number of flow rateso Any liquid thrown out of the vaporizer and subsequently vaporized by externally applied heat would have increased the observed mass of condensate over what it would have been under proper operating conditionso The mass of condensate appears in the denominator of Equation (75), and therefore the resulting latent heat would have been low. As the flow rate, which was controlled by the power supplied to the vaporizer heater, was increased the amount of liquid ejected from the vaporizer would have increased markedly, and the curve shown in Figure 12 on page 102 would have dropped off sharply with increasing flow rate, rather than level off and approach a nearly horizontal tangent as is actually shown. Estimate of Accuracy Estimates of the errors involved in the individual measurements and the results of the calibration data on pure components suggest that a conservative estimate of accuracy for the integral isobaric heat of vaporization is plus or minus 0.3 per cent. The compositions were measured to plus or minus 0.1 mass per cent for the isopropyl alcoholwater mixtures and to plus or milnus 0.2 mass per cent for the acetonewater mixtures0 The temperatures used in the vapor-liquid equilibrium data were measured to plus or minus 01 ~C; the inlet temperature to the vaporizer was good to plus or minus 0o2~Co The errors associated with measurements involved in the integral isobaric heat of vaporization can be broken down into four groups those associated with (1) power, (2) time, (3) mass of condensate, and (4) sensible-heat correction. The stated accuracy of the standard

-105resistors and the expected accuracy of the potentiometer measurements suggest that the power, including any uncertainties i.n the.interpolations on the power-time curve, is correct to plu.1s or minus 0 07 per cent. Errors in the time measurement which include possible errors of approximately 02 second for startirng and stoppi.ng the timer at the correct instarntj, totaled not more than 05 second3 or about o004 per cent, for the average interval of 22 minutes0 The mass of condensate was accurate to approximately plus or m.n.us 0,Q04 gramy w.hich armoi ur tl;s to about 0o12 per cent for the average collection of 35 gramso The specific-heat corrective term averaged only l15 per cent of the latent heat, so that errors as large as 7 per cent in the specific heat and the temperature difference would have caused only- abou.t 0a10 per cent error in the latent heato If all of the errors affected a latent-heaa t determination at the same time and in the same direction, the magnitude of the total error would be approximately 0o33 per cento

EXPERIMENTAL DATA AND RESULTS Summary Data in tabular and graphical form on both the integral isobaric heats of vaporization and vapor-liquid equilibria for atmospheric pressure are presented in this section for the isopropyl alcohol-water and acetone-water binaries. These data have been used to accurately derive enthalpy-concentration diagrams. Heats of mixing in the liquid phase and differential heats of condensation have also been calculated using these data as starting pointso A graph to facilitate the conversion between mass and mole per cent is shown in Appendix E on page 177 for convenience. Calibration Data The reliability of the apparatus, which, although designed specifically for use with mixtures, could be used successfully with pure materials, was checked by determining the heat of vaporization of the pure components of each mixture and comparing the values obtained with recent experimental data reported in the literature. The purecomponent heats of vaporization. were taken over a range of flow rates and extrapolated to infinite flow rate as indicated in the section entitled "Effects of Flow Rate," Table II on page 107 shows the data obtained and the comparison with recent experimental data reported in the literature. -106

-107TABLE II HEAT OF VAPORIZATION OF THE PURE COMPONENTS Heat of Vap, Heat of Vapo (cal/g) this Tempo (cal/g) from Component Investigation (~C) Liters atu- e Ref Acetone 119.9 55.2 120,0 (50) Isopropanol 1.593 81.6 1.59.6 (79) Water 540.2 99.3 540o13. (46) Integral-TIsobaric-Heat-of-Vaporization Data The data for the isopropyl. alcohol-water binary at atmospheric pressure are presented in Table III on page 112 and in. Figures 1.4 and 15 on pages 108 and 109 in the form of integral isobaric heat of vaporization as a function of composition. Figure 14 shows the data on a mass basis. The curve on Figure 15, which is on a mole basis, was obtained simply by conversion of the units of the curve shown on. Figure 1,4 from a mass basis to a mole basis. Smoothed values of heat of vaporizatiD onr! at even values of composition have been read from. a lar..ge plot G:f Figure 14 and are presented in Appendix E in Table XVo The data for the acetone-water binary are presented in the identical. fashion as the isopropyl alochol-water datao Table IV on page 112 and Figures 16 and 1.7 on pages 110 and 111 show the heat of vaporization data. The smoothed values of heat of vaporizaetiorn at. even compositions are shown in Appendix E in Table XVI, Figures 15 and 17 have ordinates which are nearly ten times larger than those of Figures 14 and 16. Due to this magnification the exact inflections of the curves on Figures 15 and 17 are not to be taken too literally.

-lo82540 _ 520 500 480 460 440 420 4j 00 o 380 N. 360 0 320 -J 300 280 260 240 220 - 0 —C — EXPERIMENTAL DATA ~CALCULATED FROM EQUATION 78 I 200 180 160 --- - -- - 0 20 30 40 50 60 70 80 90 100 MASS PER CENT ISOPROPYL ALCOHOL Figure 14. Integral Isobaric Heat of Vaporization of Isopropyl Alcohol-Water Mixtures on a Mass Basis. (Atmospheric Pressure)

-1090,050 %900.9,850 9,800 I5 %750 IV 9,700 z 9,650 9600 9,550............ 9,500 0 10 20 30 40 50 60 70 80 90 100 MOLE PER CENT ISOPROPYL ALCOHOL Figure 15. Integral Isobaric Heat of Vaporization of Isopropyl Alcohol-Water Mixtures on a Mole Basis. (Curve derived from Figure 14)(Atmospheric Pressure)

-110540 520 500 480 460 440 420 o 400 4 380 0 36o N 340 - 32O w 300 280 -E —----- 0 260 w 240 220 200 180 -M —--- EXPERIMENTAL DATA 160 --------- -----— CACULATED FROM EoUATION 79 140 M xr o 120 100_ 0 10 20 30 40 50 60 70 80 90 100 MASS PER CENT ACETONE Figure 16. Integral Isobaric Heat of Vaporization of AcetoneWater Mixtures on a Mass Basis. (Atmospheric Pressure)

-11110,200 h - 9,800 49,600 9,400 w J 9,200 0 9,000 z 0 8,800 N 0 4 o > 8,600 LL 0 8,400 w cr 8,200 0, -J 8,000 0..- 7,800 7,600 7,400 7,200 7,000 0 10 20 30 40 50 60 70 80 90 100 MOLE PER CENT ACETONE Figure 17. Integral Isobaric Heat of Vaporization of Acetone-Water Mixtures on a Mole Basis. (Curve derived from Figure 16) (Atmospheric Pressure)

-112TABLE III INTEGRAL ISOBARIC HEAT OF VAPORIZATION - ISOPROPYL ALCOHOL-WATER Atmospheric Pressure Mass Pct. Mole Pct. Heat of Vap. Heat of Vap. Isopropanol Isopropanol (cal/g) (cal/mole) 0 0 540.2 9732 5.1 1.6 528.0 9869 10.2 3.3 513.5 9964 15.1 5.1 495.7 9982 19.9 6.9 478.3 9991 24.7 9.0 461.4 10054 35.4 14.1 417.2 9976 44.9 19.6 378.9 9953 53.4 25.6 343.4 9879 63.9 34.7 301.3 9828 73.3 45.2 262.9 9726 80.0 54.5 234.4 9607 85.0 62.9 214.6 9523 90.2 73.4 195.1 9527 94.9 84.8 178.2 9564 100.0 100.0 159.3 9573 TABLE IV INTEGRAL ISOBARIC HEAT OF VAPORIZATION - ACETONE-WATER Atmospheric Pressure Mass Pct. Mole Pct. Heat of Vap. Heat of Vap. Acetone Acetone (cal/g) (cal/mole) 0 0 540.2 9732 5.2 1.7 529.1 9929 10.3 3.4 514.6 9982 14.9 5.2 498.1 9998 20.2 7.3 478.0 10005 30.2 11.8 436.2 9923 40.2 17.3 395.9 9873 50.1 23.8 353.9 9745 59.8 31.6 308.2 9449 69.7 41.6 262.1 9091 80.8 56.6 212.5 8653 90.5 74.7 164.4 7883 93.4 81.5 148Q(0 7496 97.0 90.9 132.9 7235 100.0 100.0 119.9 6964

-113The data for both binari.es rwere correlated very wee l'b. y the equation developed in. a previous section, entitled "'The Ent.;halpyTempeera ture -Diagram. Approach.o" V ZJ ^l @T Zk:' L z, + k ) C (' T1) 32 - zi Lj'p-1 Z T k LkjT ~ i 7 Neither Edmisterrs(16) equation nor the m:odification thereof wLhch was suggested in the section entitled "Appl.cati.on of Eq-ui.l.briui.m.K Valtes were successful, in correlating the in.tegral -sobarj.c-eat -of-vaporization data. A sample calculation demonstratiing the use of these eqiuati;ons is shown in Appendix D on page 1670 For the isopropyl alcohol,-water system Equation (34) in terms of temperatures in degrees centigrade and mass fractions becomes p = ZI[194o5 - 0o425t ] + Zw[599o8 - o600ot1 + {zz0oo341 + o~ooloo 7.,, ] + {Z[0 t5 0 + OOlO O 000 6 ~(ti + t2O1 + Zw[0o438 + 0o000125 l-(tl + ~ t2 ] }{t - t} (?78' For the acetone-water system it is Xp = ZA[1.344 - 0o262t;1] + Zw[599o6 0-0o598tz] {A[02+ [028 + ooo083 (0 + t2) - 000oO 0005 { (tl t2 ] + Zw[Oo4358 + 0.000125 ( + t2}{ t} (79) The resulting integral isobaric heats of vaporization are in ulnits of calories per gramo

-114The integral isobaric heats of vaporization calculated from Equations (78) and (79) at even values of composition are presented in Appendix E in Tables XV and XVI and are shown in, this section by the dashed curves on Figures 14 and 16. The maximum deviation between the predicted and smoothed experimental values for the isopropyl aloc:holwater binary occurs at 85.0 mass per cent isopropyl alcohol and amounts to 2.0 per cent of the latent heat. The average deviation without regard to sign is 0.8 per cent. For acetone-water the maximum deviation occurs at 25.0 mass per cent acetone and amounts of 0.5 per cent of the latent heat. The average deviation disregarding sign is 0.3 per cent. Whereas it would be desirable to write Equations(78) and (79) with only composition terms on the right-hand sidee, to do so would produce cumbersome expressions which would be difficult to handle. The bubble-point and dew-point temperatures in the equations would have to be replaced'by the appropriate temperature-composition relationships, which in. themselves are quite complex and which, in fact, do not usually lend themselves to explicit" expressions of t;emperature as a function of composition. As a result, computations with the correlating equations were performed in conjunction with vapor-liquid equilibrium data in the form of temperature-composition diagrams. A sample calculation showing the steps required for the prediction of the integral isobaric heat of vaporization of an aqueous mixture of 50 mass per cent acetone is shown in Appendix C. Vapor-Liquid Equilibrium Data The vapor-liquid equilibrium data for the isopropyl alcoholwater binary at atmospheric pressure are shown in t;he form of a

115temperature -composition diagram in Figure 1.8 on page 116 and i.n the form of a y - x diagram in Figure 19 on page 117o After smooth curves had been drawn on these figures for the data obtained in this:vesst~gation, two sets of experimental data recently reported in the literature(4y80) were plotted on the figures for comparative purposesO Smoothed values read from a large plot of Figure 18 at even valules of composition are shown. in Appendix E in Table XVIIo The following tiabu-. lar values supplement the data shomwn on the figures. TABLE V VAPOR-LIQUID EQUILIBRIUM DATA - ISOPROPTL ALCOHOLWAT.ER Atmospheric Pressure Isopropanol in Vapor Isopropanol in Liquid Tempo Mass Pct. Mole Pcto Masso Pct. Mole Pct. (~C) 00 0 0 100 o0 5.1 1o6 0.2 0o06 99.8 1.0.2 353 o.6 01.8 99o3 15.1 51.ol 8 0.24 98.8 19.9 6.9 1.o 0.5 9875 24 7 9o0 1.4 Oo4 97 o7 3554 1.4.1. 2.6 0.8 96o2 44.9 19,6 358 1.2 94o3 53,4 25.6 5.4 1.7 9223 6359 34.7 8.0 2 5 89ol 7353 45.2 14.0 4,7 8503 80,0 54.5 48.0 21.7 81.5 85.0 62.9 8101 56.3 80.7 90 2 73.4 91.2 75 7 80o6 94.9 84,8 96 0 87.8 8lo2 0 100 0 100o0 100 100.0 82,4 The data for acetone-water are presented in identical. fashion as the data for isopropyl alcohol-watero Table VI on page 120 and Figures 20 and 21 on pages 118 and 119 show the vapor -liqu.i.d egauil.Jibriujm

-116100 — 0 — EXPERIMENTAL DATA X LITERATURE, REF. 80 98 ---- ~* LITERATURE, REF. 4 Fiur 1.wetn irm oIpp AcoWrx 92 BUBBLE - POINT LINE DEW - POINT LINE 90 88 \ a, 86 X.\ 80 78 76 0 10 20 30 40 50 60 70 80 90 100 MASS PER CENT ISOPROPYL ALCOHOL Figure 18. Temperature-Composition Diagram for Isopropyl Alcohol-Water. (Atmospheric Pressure)

-1171001 90 80 O - / 6 /6 0 0 0 70 -J 0 0 0 0 0 0 0 0 0 0 0 00 0 MASS PER CENT ISOPROPYL ALCOHOL IN LIQUID 0 10 20 30 40 50 60 70 80 90 00 MASS PER CENT ISOPROPYL ALCOHOL IN LIQUID Figure 19. y - x Equilibrium Diagram for Isopropyl Alcohol-Water. (Atmospheric Pressure)

88~~~~ ~-1886 94 92 90 84 82 BUBBLE - POINT LINE DEW -POINT LINE W 80 \_\; 76 74 72 \ TO 66 64 62 58 --- EXPERIMENTAL DATA A LITERATURE, REF. 73 56 X LITERATURE,REF. 49 * LITERATURE,REF. 4 54 52 50 0 10 20 30 40 50 60 70 80 90 100 MASS PER CENT ACETONE Figure 20. Temperature-Composition Diagram for Acetone-Water. (Atmospheric Pressure)

-119100 70 0 a. z \ w 01 60 z 0 - 50 n 40 (n 30 20 C-),, -0 — EXPERIMENTAL DATA X LITERATURE, REF. 49 U LITERATURE, REF. 4 10 _ __ 0 10 20 30 40 50 60 70 80 90 i00 MASS PER CENT ACETONE IN LIQUID Figure 21. y - x Equilibrium Diagram for Acetone-Water. (Atmospheric Pressure)

-120data. Three sets of recent experimental data from the literature (449'73) have been plotted on these figures for comparative purposes. Smoothed values are shown in Appendix E in Table XVIII. TABEI VI VAPOR-LIQUID EQUILIBRIUM DATA - ACETONE-WATER Atmosphere Pressure Acetone in Vapor Acetone in Liquid Tempo Mass Pct. Mole Pct. Mass Pct, Mole Pct. (0C) 0 0 0 0 100.0 5.2 1.7 0,1 0,03 99.5 10.3 3.4 0.3 0.09 99.0 14.9 5.2 0.3 0.09 98.5 20.2 7.3 0.7 0.2 97o9 30,2 11.8 1.4 0.4 96.6 40.o2 173. 2.0 o.6 94.6 50.1 25.8 3.1 1.0 92.8 59.8 31.6 3,8 1.2 90.0 69o7 41.6 5.8 1.9 85.5 80.8 56.6 114 3.8 77.6 90,5 74.7 28.9 11.2 66,4 93.4 81.5 55ol 27.6 61.4 97.0 90.9 95 3 86,3 57.1 100.0 100.0 100100.0 1. 56.2 The vapor-liquid equilibria were correlated by both the Redlich-Kister(55) equation, -which is of the form log -Ls B(xk - xj) + C(6xjxk - i) + D(xk - xj)( - 8xjxk) + a. (80) 7k and by a modified version of the Redlich-Kister equation proposed by Chao (6) which is of the form log J- = a + b(xk x) + c(6x - x) + cd(xk -) d xj)(l - 8xjxk) +.. Y~~~~~~~~~~~~7k:~(81) (81)

-121where 7j and ak are the activity coefficients in the l..qui.d phase of components j and k, respectivelyj xj and xk are. mole fractions in the liquid phase of components j and k, respectively; and lett'.rs a a.nd b through d in both upper case and lower case are consta.nts used to fit the datao The Redlich-Kister equationr embodies the Duhem. reiatiorshi.p(l5) and inherently forces the data, when plotted on a grapLh of l.og 7 /7k versus the mole fraction of ij in the li.'.quid, t.;o fit a cu-rve whtl.ch bounds with the ordinates, xJ - 0 and x - i., areas of equal. gnitde above and below the abscissa, log Y7/7k = 0o Howeverr many experimental vaporliquid equilibrium data do not in fact fall in such a pat~terno Chao used this observation as a basis to modify the Redlich-Kister equationo The modified equation includes an additional term, Y"a" which is a constant -and has a magnitude equal to the net aea tat area that the area above the abscissa, log 7j/7k = 0, minus the area below. As a result, the modified equation is more complex than the Redlich-Ki.ster eqfatio:r o0 The acceptability of this added complexity must be judged for ea.cc system on the basis of tthe improvement.in the correlation., Graphs of log 7I1/7w versus the mole fraction of isopropyl alcohol. in the liquid for the isopropyl alcohol-wate:r binary are shown in Figure 22 on page 124. A similar graph for the acetone.-water system is shown in Figure 24 on page 126.Because of the primary objecti.ve of thi ns investigation, which was to obtaine integral-i.scbaricheat-ofvaporizatior data, it was necessary to evenly dist'ribute th.e vapor compositions of the runs over the entire range of concen.trationso.TTh.ere-& fore, due to the relative volatilities many of these rins.involved quite low concentrations of the more volatile component i.n. t;he equilibrium

-122liquid, As a result, much of the vapor-liquid equilibrium data, when plotted as a function of mole fraction of.the more volatile component in the liquid, appears, as in Figures 22 and 24, near the left-hand ordinate o The data for both binaries were fit to the correlating equations by the method of least squares. Only a few of the points at very low concentrations of the more volatile component were used in the correlations in order to avoid weighting the results excessively in favor of the low concentrationso The curves representing both equations are shown on each graph. For the isopropyl alcohol-water system the Redlich-Kister equation. is log 7I/yW = 0O661(xw-xI ) - 0.323(6x1xWl-) + 0.114(x-xI) (l-8xixw) = 1.9o8 - 4.4o0 x, + 4.674 xi - 1 824 xl (82) and the modified equation is log 7i/7W - 0.019 + O0669(xw-xI ) - 0.505(6xIxwx-i) +.03 (xw-xI) (l-8xixw) 1.096 - 4.198 x, + 4.502 x2 - 1.648 xf (85) For the acetone-water system the Redlich-Kister equation is log 7A/7W 0o825(xW - xA) - 0,127(6xAxw - 1) 0952 - 40 x 2760 x (84) 0.952 - 2.410 xA + 0.76o xA (84)

-123and the modified equation is log yA/7W = - 0o.46 + o.840(xW - xA) - 0.173(6xAXW - 1) = 0966 - 2.716 xA + 1.036 XA (85) The average deviations, without regard to sign, between the values of the term log yI/7W calculated from Equations (82) and (83) and those obtained directly from experimental data were 0.020 for the RedlichKister equation and 0o021 for the modified equation. For the acetonewater system these deviations amounted to 0.033 for Equation (84) and 0.023 for Equation (85). The small differences in the average deviations leave little to choose between the correlations on that basis; the Redlich-Kister equations are, on the whole, simpler. The shortage of the data at high concentrations of the more volatile components however, reduces the rigidity of the evaluation of the two correlations. Figures 23 and 25 on pages 125 and 127 show the individual 7's - 7WI 7A; and YW - plotted as a function of the mole fraction of the more volatile component in the liquid for the isopropyl alcoholwater system and the acetone-water system, respectively. The curves drawn on these figures represent the equations for the individual y's which can be developed by combining the relationship xJ log yj + xk log 7k = Xjxk[B + C(xj-xk) + D(xj-xk) + o.o] (86) with either the Redlich-Kister equation or Chao's modified version. Equation (86) was developed during the derivation of the RedlichKister equation.(55) The individual 7's are, therefore, consistent

1.2 1.0.8.8 v<<< —---------- ---- --- ---- --- ---- ---.6 A:!z.2 O6 -- ---- - 0\ 0.2 4 6 8 1.0 -.4 0 EXPERIMENTAL DATA - — REDLICH - KISTER, EQUATION 82 -,CHAO EQUATION 83 -.6 -.8- - ------ 0.2.4.6.8 1.0 MOLE FRACTION ISOPROPYL ALCOHOL IN LIQUID Figure 22. Log of the Ratio of Activity Coefficients Versus Concentration for Isopropyl Alcohol-Water.

-12510 7.. - O EXPERIMENTAL DATA - -- - EQUATIONS 87 AND 88 6 _ __ --- EQUATIONS 89 AND 90 5 4 II z CIL3~ ~ ~\ \0/ / -/ \IQ 0.2.4.6.8 1.0 MOLE FRACTION ISOPROPYL ALCOHOL IN LIQUID Figure 23. Individual Activity Coefficients Versus Concentration for Isopropyl Alcohol-Water.

-126 1.0.8.6.4 - - t - ---.2 0\ -.2 -.4 EXPERIMENTAL DATA --..... REDLICH - KISTER, EQU. 84 \ \ - CHAO, EQU. 85 -.6 -.8. 0.2.4.6.8 1.0 MOLE FRACTION ACETONE IN LIQUID Figure 24. Log of the Ratio of Activity Coefficients Versus Concentration for Acetone-Water.

-12710 7 -0 O EXPERIMENTAL DATA- ---- EQUATIONS 91 AND 92 ~61 ~ M FRACTION_ —- EQUATIONS 93 AND 94 _ \ I i I I I I I Y/ o x,/ 4 / Y.A\ Y/ a v I I u 1, I I // Figure 25 I A C V it'-)^~o\ /A / \ / 0 2 4.6./1\0 \4 / \ // \i \ /' \ 0.2.4.6.8 1.0 MOLE FRACTION ACETONE IN LIQUID Figure 25. Individual Activity Coefficients Versus Concentration for Acetone-Water.

-128with the correlating equations. For the isopropyl alcohol-water system the individual y's as obtained from the Redlich-Kister equation are log 7I = xW[0o661 + 0.323(1 - 4x1) - 0.14(xI - xw)(1 - 6xi)] = 1.098 - 4.400 x + 6.874 x2 - 4.940 x3 + 1.368 x4 (87) log 7w = x [0.661 - 0.3235(1 - 4Yx) + O.114(xI - xw)(l - 6xw)] = 2.200 x2 - 3.116 x3 + 1.368 x4 (88) and as given by the modified equation are log 7I = xIxw[O.661 - 0.323(xi-xW) + 0.114(xi-xw) 2 + xw[0.019 + o.669(xw-xi) - 0.305(6xxw-1) + o.l03(xw-xi)(1-8XIXw)] 1.096 - 4.196 x + 6.300 x2 - 4.392 x3 + 1.192 x4 (89) log 7W = xIx[0.661 - 0.323(xI-xw) + 011l4(xI-xW) ] - xI[0.019 + o.669(xw-xi) - 0.305(6xixW-l) + 0.103(x-xi)(1 - 8xjxw)] +,002 x + 1.98 x ~ xS (90) - 0.002 x + 1o998 x2 - 2.744 x + 1.192 x (90) For the acetone-water system the individual. 7's as obtained from the Redlich-Kister equation are log 7A = x[0.825 + 0.127(1 - 4xA)] 0.952 - 2.412 xA + 1.968 2 - 0.508 xA (91)

-129log 7YW - xA[0.825 - 0.127(1 - 4xW)] 1.206 x2 - 0.508,x (92) A A and as given by the modified equation are log YA -xAxW[0o825 - 0.127(xA-xw)] + xw[-o.046 + 0.840(xw-xA) - 0.173(6xAxW-1)] = 0.967 - 2.733 xA + 2.550 x - o0784 x3 (95) log 7Y = xAXw[0.825 - 0.127(xA-xw)] - xA[-0.046 + o0840(xw-xA) - Ool73(6xAXw-l)] -0,015 xA + 1.512 x2 - 784 x 3 (94) Enthalpy-Concentration Diagrams The integral-isobaric-heat-of-vaporization data have been used for the accurate construction of enthalpy-concentration diagrams for the two systems studied in this investigation, The diagrams are for atmospheric pressure, and the reference points for the enthalpies (H=O) were taken to be the pure liquids at O~C under atmospheric pressure. Tabular values of the saturated-vapor and saturated-liquid enthalpies, as well as a few values in the superheated-vapor and subcooledliquid regions, support the graphs presented herein. The first step in the construction of the diagrams required the enthalpy-temperature relationships for both pure components. For

-130the liquid phase the equation fjbp H -; p C1 dt (95) -7 o 90 was evaluated for a number of temperatures up to the boiling point of the pure component. The specific-heat data required by Equation (95) were taken from the literature (24,35,4664k) The experimentally determin.ed heat of vaporization of the pure component; was added to the enthalpy of the l.i.quid at the boiling point to ottain the ent+halpy of the vapor at the boiling point. For the vapor phase the equation t v satv. vv dt H.= H. + v C dt (96) -1 - - P,.I bp was evaluated for a number of temperatures above the boiling point. The specific-heat data required by Equation (96) for the pure components at atmospheric pressure were taken from the literatuirei (o54.5Q60) For water and isopropyl alcohol it was also necessary to evaluate Equation (96) at temperatures below the boiling point; A completely rigorous treatment would require the evaluation of the ert~halpy change which would accompany an. isothermal expansion of the saturated vapor to a pressure sufficiently, low so that the temperature (below the nornmal boiling point) at which t:he enthalpy was being evaluated woul1d be the saturation temperature. Near atmospheric pressure and over the small pressure ranges involved the pressure effect on enthalpy can be neglected safely. Thus, Equation (96) was used for the evaluation of enthalpies with a temperature either above or below the normal boiling point; as desired, for the upper li.mit on the integral.

-131The enthalpy of a given mixture in its saturated-vapor state was evaluated by (1) determining its dew-point temperature from the experimental vapor-liquid equilibrium data, (2) determining the enthalpies at that temperature of both pure components from the enthalpytemperature relationships in the vapor state, and (3) combining the pure component enthalpies according to the proportions of each. component in the mixtureo The final step involves an assumption of zero heat of mixing in the vapor phase, whjich is a satisfactory assumption at atmospheric pressure. A series of such calculations for a number of concentrations established the curve of saturated-vapor enthalpy versus concentration. The enthalpies of the mixtures in the superheated-vapor range were obtained by combining the pure-component enthalpies at the temperature of interest according to the concentration of each component in the mixture. The saturated-liquid enthalpy of a given mixture was calculated by subtracting the experimental integral isobaric heat of vaporization from the enthalpy of the saturated vapor for that mixture. A series of such calculations established the curve of saturated-liquid enthalpy versus concentration. The enthalpies in the subcooled-liquid region were calculated by application of the equation t H1 = Hsat.l + C dt (97) BP where C is the specific heat of the liquid mixture in question. No Pmh specific-heat data near the bubble points are available in the literature

-152for the mixtures studied in this investigation. Consequently, the available data for acetone-water mixtures(36) and isopropyl alcoholwater mixtures(l4156) at lower temperatures were adjusted for use at the higher temperatures, pursuant to the observed temperature variation of the mixtures over lower temperature intervals and the temperature variation of the pure-component specific heats (24,533464b ) These estimates are, therefore, reflected directly in the enthalpies given for the subcooled-liquid region~ The enthalpy-concentration diagram on a mole basis for the isopropyl alcohol-water binary at atmospheric pressure is shown in Figure 26 on page 133. Note the interruption of the ordinateo The experimental vapor-liquid equilibrium data were added to the diagram in the form of constant-temperature tie lines, which connect points on the saturated-liquid line with corresponding equilibrium points on the saturated-vapor line. Values of the enthalpy of saturated vapor and saturated liquid and a few values in the superheated-vapor and subcooledliquid regions are listed for even values of concentration in Table VII on page 135 o Similar information for the acetone-water binary are shown in. identical fashion in Figure 27 on page 134 and in Table VIII on page 135o The integral heat of mixing for a given mixture in the liquid phase at its bubble point temperature can be determined by subtracting from the saturated-liquid enthalpy, the molal-average enthalpy of the pure components at that temperature. The accuracy of the heat of mixing derived by this procedure suffers from the fact that a small answer

-13315000 14600 -- 14200 -- 13800 _ / \/ 13400 t 3400 [ |/ 1 T/ / / I/ I I I,1200 I I z 11800 400 0 & ~ r/ / / / 3400'. /-I -i "'Z/ (bl, CI 3200 -- 8 11/00 10 20 30 40 0 0 / I 90 100 2eoo I - L - I / I -I - — I! ------ Figure 26. Enthalpy-Concentration Diagram for sopropyl Alcohol-Water 1200 --- 800 -- --- 2400,_'' 0 10 20 30 40 50 60 70 80 90 100 MOLE PER CENT ISOPROPYL ALCOHOL Figure 26. Enthalpy-Concentration Diagram for Isopropyl Alcohol-Water (Atmospheric Pressure)(H = 0 for pure liquids at 0~C)

(co0 - sTmblTT acrd:oj 0 = H)(a mssa.l oa.eqdsonq.v) *'lq'VG^M-auoqsOV a10i wS-egT uoTI.^sIBq-uaouo3-SdTsquHa *iL anm9T 3N0133tV N33 83d 301NO 001 06 8 OL 09 09 0O O Oz 01 0 0 03lHdoozas | I,| / -L__/ __^ / --------— "......- OO -'3-0 0081 0091 I / // /0 / I,' -/ / / / 00 14"I / I // / /___!dlr: /o /r) /cp / ~ / /7 p / ^p /P co'' f/ i / / / / _-{-^^-2^^_^_-_^^_^y__i__>~ ~ootolz / // / I I I/ / I I I / / / / / iS, I I i / / / 008 /, / / I II^I I Is/ / / I1 -1 -4 — LL^^ -a —-T --- ----- ---- / ---- ---- 0098 ^^^^^^^/ / / 00001 I I I I/ / / / 2 / I ooe 00I /^^^^ / I^-^^ ^"^ ** ^^'^- --- -- 0080 I I~~~~~~~~~~ /I~~~~ ~00 9 00911 ---------------------------------------. -- /O Z /./

-155TABLE VII ENTHALPY OF ISOPROPYL ALCOHOL-WATER MIXTURES Atmospheric Pressure * Calories per mole Mole Pct Subcooled Liq, Superheated Vapo Isopropanol 25 ~C 70 C Sat. Liq. Sat. Vapo 90 C 120 C 0 450 1260 1800 11,540 11,710 5 380 1320 1640 11,620 - 11,820 10 340 1370 1670 11,700 - 11,940 15 400 1490 1790 11,780 - 12,050 20 440 1590 1900 11,840 - 12,160 30 540 1790 2120 11,970 - 12,400 40 630 1970 2320 12,080 12,130 12,630 50 710 2140 2510 12,170 12,300 12,860 60 780 2310 2700 12,260 12,470 13,090 70 840 2460 2870 12,400 12,640 13,320 80 870 2570 3010 12,560 12,820 13,550 90 870 2660 3160 12,730 12,990 13,780 95 870 2710 3250 12,820 13,070 13,900 100 860 2750 3340 12,910 13,160 14,010 TABLE VIII ENTHALPY OF ACETONE-WATER MIXTURES Atmospheric Pressure * Calories per mole Mole Pct. Subcooled Liq. Superheated Vapo Acetone 25~C 60~C Sat. Liq. Sat. Vap. 80 C 110~C 0 450 1080 1800 11,540 - 11,620 5 430 1130 1430 11 430 - 11,530 10 430 1190 1340 115320 - ll,440 15 430 1220 1310 11,210 - 11,350 20 430 1250 1310 11,100 - 11,270 30 460 1330 1360 10,850 - 11,090 40 500 1410 1420 10,590 - 10,920 50 510 1460 10,310 - 10,740 60 54o - 1500 9,990 10,070 10,570 70 650 - 1620 9,680 9,860 10,390 80 710 - 1670 9,300 9,640 10,220 90 710 - 1690 8,970 9,430 10,040 95 730 - 1710 8,830 9,320 9,950 100 760 - 1730 8,690 9,210 9,870

-136is obtained by subtracting two numbers of nearly equal magnitudeo Table IX on this page shows some heats of mixing for the bubble point temperature which were calculated by the above procedure The heats of mixing are, of course, not at a common temperature because each mixture has a different bubble point~ A similar procedure was adopted to calculate the heats of mixing at a single temperature, 25 ~C These values, however, reflect the errors introduced into the subcooled-liquid enthalpies by the estimations of the specific heats of the liquid mixtures, and they suffer from the aforementioned subtraction of numbers of similar magni-, tude. Thus, some of the heats of mixing calculated in the above fashion even have the wrong sign when compared to experimentally determined values 0(10 6) Table IX on thispage shows some calculated heats of mixing for both binaries compared to the experimentally determined values o TABLE IX CALCULATED HEATS OF MIXING COMPARED TO EXPERIMENTAL VALUES Isopropyl Alcohol Acetone Mole Pct. Heat of Mixing (cal/mole) Heat of Mixing (cal/mole) Isopropanol Bubble 25 ~C, Lito Bubble 25 ~C,Lit or Acetone Pt. 25~C Value(l0) Pt 25~C Value (36 0 0 0 0 0 0 0 10 -10 -150 -142 40 -40 -128 20 70 -90 -118 20 -80 -145 30 100 -40 -68 20 -80 -120 40 140 10 -21 20 -80 -72 50 160 60 16 0 -0 23 60 160 80 35 -20 -100 17 70 160 100 43 50 -20 51 80 130 90 31 50 10 70 90 60 40 17 0 -10 65 100 0 0 0 0 0 0

-137Differential Heat of Condensation The relationship between the integral isobaric heat of vaporization and the differential heat of condensation is given by Equation (9). AT P -AHv + ~AH - Ap (9) — M -heat P The working form of this equation was established by neglecting the heat of mixing in the vapor phase, which would be insignificant at atmospheric pressure, and by assuming that the specific heat of the vapor mixture would be equivalent to a mass average of the purecomponent specific heats at the average temperature between the bubble point and the dew point. Thus, the working equation for a binary becomes XAp = - + (x Cp + xk Ck)(t2 - t1) (98) Differential heats of condensation for isopropyl alcohol-water mixtures ind acetone-water mixtures at atmospheric pressure have been calculated by Equation (98) from smoothed values of the integral isobaric heat of vaporization taken at even values of composition. Table X on page 158 shows the values for isopropyl alcohol-water mixtures, and Table XI on page 158 gives the values for acetone-water mixtures. The equilibriumliquid values given in these tables are essential data required by the definition of the differential heat of condensation..

-158TABLE X DIFFERENTIAL HEAT OF CONDENSATION - ISOPROPYL ALCOHOL-WATER Atmospheric Pressure Mass Pct, Isopropanol Differential Heat of Vapor Equil. Liquid Condensation (cal/'g) 0 0 -540.2 10 0.5 -538.9 20 1.1 -5371 30 2.0 -534.4 40 3.0 -531.4 50 4.5 -526.7 60 6.7 -519.o2 70 11,1 -503,5 75 17.0 -481.7 80 475 -361.7 85 81,3 -228.7 90 89.4 -199.5 95 93 58 -182o0 100 100.0 -15903 TABLE XI DIFFERENTIAL HEAT OF CONDENSATION - ACETONE-WATER Atmospheric Pressure Mass Pct. Acetone Differential Heat of Vapor Equil. Liquid Condensation (cal/g) 0 0 -540.2 10 0.5 -539.1 20 0.8 -5379 30 1.53 536.3 40 2,0 -534o. 50 2.9 -5313. 60 4.0 -527.9 70 5.9 -521.8 80 10o8 -504.8 85 16.o -484.6 90 27.7 -436.2 93 50.5 -338.7 95 843 -1.89.4 100 100,0 -11o 9,9

CORRELATION OF OTHER INTEGRAL-ISOBARICHEAT-OF-VAPORIZATION DATA The success of the correlations given in the previous section for the integral isobaric heat of vaporization of the isopropyl alcohol-water system and the acetone-water system warrant application of the correlating equation to other systems for which experimental data are available. The values obtained from the general correlating equation, xp = zj Lj,T + Zk Lk,T1 + (Zj Cp,j + Zk CPk)(T2 - T1) (34) are compared to experimental data on Figures 28 through 355 on pages 140 through 145 for most of the binaries listed in Table I on page 49~ The bases for the graphs, either mass or mole, are consistent with manner in which the original experimental data were presented. The graphs are supplemented by Table XII on page 147 which summarizes the deviations between calculated and experimental values, as well as the references to the data used to make the calculations. All except three of the systems listed in Table I on page 49 for which experimental integralisobarich-eat-of-vaporization data are available have been included in this section. Those not included are the water-formic acid, the water-acetic acid, and the acetonechloroform binaries. The data for the first two can be adequately represented by a molal average of the heats of vaporization of the pure components taken at their normal boiling points; Equation (34) will yield a comparable correlation, but the molal-average method is much simplero Calculations for the third were restricted by lack of heatof-vaporization data as a function of temperature for chloroformo -139

-l4o280'' ce 260 0 < 0 240 1N 220,.- 160 -7160 g 120 z ---- DATA, REF. 68 - - -. — CALCULATED FROM EQU. 34 100 - 80 - 0 10 20 30 40 50 60 70 80 90 100 MASS PER CENT METHYL ALCOHOL Figure 28. Calculated and Experimental Integral Isobaric Heat of Vaporization for Methyl Alcohol-Benzene Mixtures.

-l4l 7500 | —-------------------------.J 0j 730 o 7200 0 <t 7100 ------ DTA, R-F. 67 -Il -- l -- --- I X o 7300 0 \ 7000 7100 -0 — DATA, REF.67o ---- CALCULATED FROM EQU. 34 7000 0 10 20 30 40 50 60 70 80 90 100 MOLE PER CENT ACETONE Figure 29. Calculated and Experimental Integral Isobaric Heat of Vaporization for Acetone-Benzene Mixtures.

-142540 500 lli I\460 Z 0 N u- \ 4 o 380 w\ - ) Fg 0 c _ E m InteI ga I < 340 0 wIz 300 0 DATA, REF. 53 X DERIVED FROM H-x DIAGRAM, REF. I 260 - -- - CALCULATED FROM EQU. 34 220 0 10 20 30 40 50 60 70 80 90 100 MASS PER CENT METHYL ALCOHOL Figure 30. Calculated and Experimental Integral Isobaric Heat of Vaporization for Methyl Alcohol-Water Mixtures.

-145540 z 20 0 I\0 0\ Qi\ 4 380.. 0 X I 3 <[ \< z I 340 260 - 0 DATA REF.53 - X DERIVED FROM H-x DIAGRAM REF.61 ---- CALCULATED FROM EQU.34 - 220 200 0 10 20 30 40 50 60 70 e 90 100 MASS PER CENT ETHYL ALCOHOL Figure 31. Calculated and Experimental Integral Isobaric Heat of Vaporization for Ethyl Alcohol-Water Mixtures.

-144560 520 480 r\\ 8 440 400 l360 320 280 ---- DATA, REF. 53 160 --- ----- --- CALCULATED FROM EQU -340 0 0 20 30 40 50 60 70 80 90 100 MASS PER CENT n- PROPYL ALCOHOL Figure 32. Calculated and Experimental Integral Isobaric Heat of Vaporization for n-Propyl Alcohol-Water Mixtures.

52 --- o 51 " — (L o 49 m 48 < - -- DATA, REF. 8 cI s ---. CALCULATED FROM EQU. 34.46.. 0 10 20 30 40 50 60 70 80 90 100 MOLE PER CENT NITROGEN Figure 33. Calculated and Experimental Integral Isobaric Heat of Vaporization for Nitrogen-Oxygen Mixtures.

-146The enthalpy-concentration diagrams of Ansell et al (l) and Smith et al,(61) for methyl alcohol-water and ethyl alcohol-water, respectively, provide additional comparative information for these systems. Their diagrams were derived in a manner similar to that outlined in the section entitled "The Enthalpy-Concentration-Diagram Approach." without the aid of any integral-isobaric-heat-of-vaporization data. The integral isobaric heats of vaporization obtained from these diagrams agree, as shown in Figures 30 and 31 on pages 142 and 143, almost identically with those predicted by Equation (34). The simplicity and ease with which Equation (34) may be used in comparison to the tediousness of constructing an enthalpy-concentration diagram is again pointed out. Or, in lieu of the construction of the diagram, the comparative cumbersomeness of Equations (62), (63) and (64) on page 36, which are tantamount to constructing the diagram is also noted. In the subsequent table, which supplements the graphs shown in this section, the first three columns following the list of systems give references to the data which were used to make the calculations, For cases in which the heat of vaporization of the pure components which made up the mixtures did not agree with the data taken from the literature, the latter had to be adjusted. For, if there is no agreement between the experimental values and the values used for calculations at the end points, x = 0 and x = 1, of a composition versus integral-isobaric-heat-of-vaporization curve, then any agreement between calculated and experimental values at intermediate compositions is merely fortuitous. In these cases the adjustment of the literature data was simply a constant displacement of the heat-of-vaporization

-147versus temperature curve, for the pure component in question at all temperatures, by the difference in the stated heats of vaporization at the normal boiling point. The heading "Avg. Diff." in the table is the arithmetic average of the percentage difference, without regard to sign, between the experimental curve and the predicted curve at the nine concentrations which are multiples of ten in the range between 10 per cent and 90 per cent. TABLE XII SUMMARY OF THE COMPARISON BETWEEN EXPERIMENTAL AND CALCULATED INTEGRAL ISOBARIC HEATS OF VAPORIZATION Vap.-Liq. Heats of Ideal-Gas Avg. Max. System Equilibria Vap. Sp. Heats Diff. Diffo Methanol-Benzene (68) (21)(79) (77) (57) 1.8% 3.4% Acetone-Benzene (48) (50)(79) (50) (57) 0.2% 0.4% Methanol-Water (25) (21)(46) (77) (34) 1.5% 3.1% Ethanol-Water (51) (21)(46) (37) (34) 1o35 2.2% n-Propanol-Water (18) (79)(46) (37) (34) 2.1% 4,0o Nitrogen-Oxygen (11) (23) (27) o.6% 1.0%

CONCLUSIONS 1. The apparatus designed, constructed, and operated for this investigation can be used for the precise measurement of the integral isobaric heat of vaporization with practically no heat leaks, even with mixtures which have a large temperature difference between the bubble point and the dew point. In particular, the integral. isobaric heat of vaporization of the isopropyl alcohol-water system and the acetone-water system were measured at atmospheric pressure with an accuracy of plus or minus 03 per cent. 2. Reliable vapor-liquid equilibrium data can be obtained simultaneously with the heat-of-vaporization data and in the same apparatus, as evidenced by the agreement between such data taken in this investigation for the isopropyl alcohol-water system and the acetone-water system and similar data which have been reported in the literature 35 The experimental integral-isobaric-heat-of-vaporization data for both binaries studied in this investigation are correlated by the equation XP = Zj LjyT + Zk hL,T1 + (Zj c + Zk P,k.)(T2 - T) (34) This equation is relatively simple to applyo The average difference, without regard to sign, between experimental and calculated results is 0.8 per cent for the isoproyl alcohol-water system and 0.3 per cent for the acetone-water system. -148

_l494o The equation given under 3 above is also very successful in correlating the data taken by other investigators for the methyl alcohol-benzene, acetone-benzene, methyl alocohol-water, ethyl alcoholwater, n-propyl alcohol-water, and nitrogen-oxygen systemso 5. Neither the equation relating the equilibrium - K values to the integral isobaric heat of vaporization, which was proposed by Edmister(16) nor the modification of that equation, which was suggested Lhereinbefore, is successful in correlating the data for the systems studied in this investigation~ 6. Both the Redlich-Kister(35) equation and a modification Df that equation suggested by Chao(6) are successful in correlating the vapor-liquid equilibrium data for both binaries studied in this investigation. The improvement of the correlation by the modified equation is not sufficient to justify its added complexity. However, it must De pointed out that the preponderance of the vapor-liquid equilibrium lata taken during this investigation were at low concentrations of the eiore volatile component in the liquid phase - a condition which reduces the rigor of the comparison.

NOMENCLATURE, UNITS, AND CONVERSION FACTORS Nomenclature Supers cripts 1 liquid phase o ideal-gas state sat.l, saturated-liquid condition sat.v saturated-vapor condition v vapor phase ~* equilibrium composition Subscripts A acetone B P. bubble point Com compression Cool cooling DoP dew point Exp expansion H heavy (less volatile) component I isopropyl alcohol In inlet to the vaporizer L light (more volatile) component P constant pressure T constant absolute temperature T1 bubble point temperature (absolute) W water -150

-151 b op normal. n boiling point; of a pure materi,al heat heating i jk pure components i., j, and k which. make up a mix'ture, leads heater leads m rmzsixture x mrole fraction in liqluid p:hase y mole fractio.n in vapor phase 1,2,3,4 reference t;o points orn some diagram 100 10,000; 0o1 nominal size of standard resistors 7355.7 760 pressures in mmr of mercury Latin Symb ols BC D arbitrary constants B Po,'' bubbo.le -poin t conditions Cp, sFecific heat at; constant pressure -o or v 0Cp c ideal. -gas or vapor -.:lhase specific heat of i at average P,i temperatu.r; e'between b'2abbl.e poin.t and dew point -1 Cp par tial-molal speci.fic he.at of i in the liluid phase P, e oexcept where it is noted to be the specific heat of i at some avee aerage tenperature D o P dew-point condi.. tions E potential drop F flow rate H enthalpy, intensive property 0 H. 2 ideal-gas enthalpy of i at temperature T2 Hi 2 partial. molal enthalpy of i in either vapor or liquid %,2? phase at poin. nt 2 on some diagram

-152-V O _V 1Hi 2 i,2 -~ i,2 Tl l Hil - Hl,1 AH o Ho - Ho ~ —1 -i2 -i 1 v or 1 LHM [integral heat of mixing in either the vapor or liquid phase I current K. equilibrium ratio, Yi/Xi L T1 heat of vaporization of pure j at temperature T1 Lj p heat of vaporization of pure j at pressure P M moles of liquid holdup in vaporizer N constant total composition P pressure P power R gas constant S entropy, intensive property T absolute temperature T1 bubble-point temperature (absolute) T2 dew-point temperature (absolute) V voltage drop V volume, intensive property Z mass fraction in any phase ab,c,d arbitrary constants d differential operator or 1 fugacity of component i in a mixture in either the vapor or liquid phase

-153h heat released by vaporizer heater i current log logarithm to the base 10 in logarithm to the base e Pi vapor pressure of pure i t temperature ~C tl bubble-point temperature ~C t2 dew-point temperature, ~C x mole fraction in liquid phase y mole fraction in vapor phase z mole fraction in any phase Greek Symbols A difference operator Ar1p differential heat of condensation Z summation over i 7' ^activity coefficient of component i in the liquid phase, YiP/xiPi ~a ~ partial differential operator Xp integral isobaric heat of vaporization XT integral isothermal heat of vaporization XTp differential heat of vaporization 9 time cp functional relationship

-154Units and Conversion Factors 1 calorie = 4.1840 absolute joules 1 absolute watt-minute = 14o3403 calories Gas constant, R = 1.9872 calories per gram mole-~K 0 C = 273 16~K Molecular weight of acetone = 58.078 Molecular weight of isopropyl alcohol = 60,094 Molecular weight of water = 18.016

APPENDIX A UNSTEADY STATE OPERATING PERIOD OF THE VAPORIZER An intuitive example is useful to illustrate the approach of the vaporizer to steady-state operation. Consider a binary mixture of L, the more volatile or light component, and H, the less volatile or heavy component Assume that the liquid holdup in the vaporizer amounts to ten grams and that the feed preheater is stocked with an infinite supply of a 50.0 per cent mixture. Table XIII on page 156 is a running inventory of the vaporizer contents and of the vapor composition, Vaporization is assumed to occur in. one-gram increments. In each of the increments 1, 2,,., n the following order of events is assumed? (1) one gram of vapor in equilibrium with the liquid contents is evolved, and (2) one gram of feed, immediately thereafter, enters the vaporizer and mixes perfectly with its contents. For the purposes of this example 1.5XL the relationship, YL,= -.. is taken as a representation of the 1 + 0,5XL vapor-liquid equilibria for the hypothetical L-H system. Prior to any vaporization (Increment 0) the 50.0 per cent mixture pervades the entire apparatus. For increment 1 the composition of the vapor, as calcullated from the equilibrium relationship and shown in the table, is 6o,0 per cent Lo At the n-th increment the vapor will have reached a composition of 50.0 per cent L, and the vaporizer contents will have reached 40.0 per cent L. A more sophisticated view point is the consideration of a timevarying material balance around the vaporizer. For the same, hypothetical L-H binary this material balance is MdX L F(XL)o - FYL - L (99) -155

-156where F = flow rate (constant) in moles per unit time (XL)o = mole fraction (constant) of L in liquid feed YL = mole fraction of L in vapor at any time M = moles (constant) of liquid holdup in vaporizer XL mole fraction of L in liquid holdup at any time = time TABLE XIII INVENTORY OF VAPORIZER CONTENTS Vapor Leaving Liquid Entering Vaproizer Contents (lOg) (50% Mixture) Increment L(g) H(g) L(g) H(g) L(g) H(g) O 5.000 5000 50OoL1 o.600 0o400 -o6o00 -0 400 4o400 4 600 0.500 0,500 +0 500 +0o500 4.900 5.-100 49 O%L 2 0,590 0o410 -0.590 -0o410 4 310 4.690 Oo500 O0500 +0,500 +0o500 4.810 ": 48/1%L 3 0o581 o,419 -0.581 -0.419 4o229 4.771 0.500 0.500 +0o500 +0 500 4.729 5.271 47o03%L o o o o000 o a 0 0o o00 0 0 0o 0 0 o o a a a a a a o 0 a o0 0 o 00a a 000 000 000 000 00. 000 0.0 4.000 6o000 n 0.500 0.500 -o500 -0.500 3.500 5.500 0.500 0,500 +0.500 +0.500 4.a000 6. 000 40. OL

-157The vapor composition is related to the liquid composition by some function YL P (XL) (100) For the purpose of expediting a solution to the equations an equili.brium relationship of YL = mX101 wi.Ll oe considered valid over the composition range of interest, Differentiation of Equation (107) and substitution into Equation (99) for dXL yields F[(XL)o - YL] M (102) m dO Separating variables, integrating'between limits, and collecting terms results in 0=g YL = YL dY Fm f f..Ld (103) M — 0 ( YL)= o m(XL) L)o - YL Q = -n[(XL)o YL] + ln[(XL))o - m(XL)o (104) -Fm = In (L) " YL (105) M (XL)o(l-m) -exp[Fm (XL) (106) M (XL)o o1-m) As Q becomes large the term on the right of Equation (106) must approach zero. Therefore, YL -+ (XL)o

-158as Q becomes large. The case of m=l is of no interest because m would equal one only for pure materials and azeotropic mi.xtures, and in those cases no steady-state problems are involved. Equatio:n (99) can also be solved with the use of the more realistic vapor-liquid-equilibrium relationship Y P -XL (1.07) 1 + (Pl)x^ in the place of Equation (101)o The result is, of course, the same, but the solution is much more tediousa The fact that in the actual apparatus the vapor was condensed and recycled to the preheater has been ignored in this analysis, In the apparatus the mass of the preheater contents was so large in comparison to the amount of material recycled that the composition of the original condensate had a negligible effect on the composition of the preheater contentso However, if the condensate had had an appreciable effect on the preheater contents, it would have been in a direction so as to hasten the attainment of the steady state, rather than delay it0,

APPENDIX B I. SAMPLE CALCUTATION OF ENERGY CONSUIbTION IN THE VAPORIZER The power consumed by the vaporizer heater was determined by the product of its voltage drop and currents P I El (108) Neither E nor I was measured directlyo From the circuit diagram, Figure 9 on page 75, it can be seen that E = V + V + V floQ) 100 +10,000 leads (109) where V100 is the voltage drop across the 100-ohm resistor, and similarly for the 10,000-ohm resistor and the leadso The use of Ohm's law and actual values of the resistances yields E - i1oo(l00000 + 10,000o5 + 0o2) (llO) Ohm's law can be used to express the current, i100, carried in this segment of the circuit in terms of the measured quantity, Vo100 and the actual value of the 100-ohm standard resistor0 Thus, E = V100 (100o000 + 10,000o5 + 0 2) = 101 007 VlO0 (111) 100o000 The current, as measured in the 0ol-ohm standard resistor, was corrected for the small amount which passed through the l00ohm - 10,000-ohm circuit. Application of Kirchoff's law yields I i0o1 i100 (112) -159

-160where iol is the current in the 0,l-ohm resistoro The application of Ohm's law and actual values of the resistances yields VO1 Vo 100 ( 0.099995 100o000 Combination of Equations (111) and (113) in the manner indicated by Equation (108) produces the final equation for the vaporizerheater power, P, in terms of the measured qugantities, ViQO0 and V01ol - 1007Vo0.1 V1.00oo p: 101007 Vloo (0099995 - 00-000 1010.12 V100 Vo. 1 01007 VO002 (114) Potential measurements of V1 00 and V 1'were made at intervals during the course of a determination, The measurements taken during Run No. A26-0 are shown in Table XIV along with the power, as calculated from Equation (1./.4), for each pair of potentials, The second term in Equation (114) amounts to only O0l per cent of the firsto TABLE XIV SAMPLE POTENTIAL MEASUREMENTS AND CALCULATED POWERS Run No. A26-0 Approxo Starting Time - 1l44 PM Time of Run - 19 582 mino Approxo Ending Time - 2~04 PM Time Vo00(Volts) Time VO 1 (V.olts) Power (Wat-ts) 1.41 0~25565 1o42 0o22619 585345 1:46 0,25549 1 47 0o22623 585318 1P48 0.25549 1.49 0.22608 58,280 2:01 0025556 2,02 0o22585 58,19.1 2 03 0o25526 2 04 0o22583 58a163

-16Figure 34 on page 162 shows the values of power as a function of elapsed time. The fall off in power with time, as in this example. usually amounted to about 053 per cent for a single run. The area under the curve between time-zero and time-190582 minutes, which is the energy consumed by the heater in that time, amounts to 1140o68 watt-minutes. Errors introduced by interpolation of the power are less than the uncertainties of the individual power termso II. SAMPLE CALCULATION OF INTEGRAL ISOBARIC HEAT OF VAPORIZATION FROM MEASURED QUANTITIES A calculation of the integral isobaric heat of vaporization from measurements obtained during a determination proceeded in two stepso The energy consumption of the vaporizer heater was determined first, as shown in the previous section, after which the basic equation Integral Isobaric _ (Energy Consumption) 0981Ci(TBp-TI ) (115) Heat of Vaporization (Mass of Condensate) was applied0 The following sample calculation is executed with the measurements obtained during Run No A26-0o The energy consumption, as shown in the calculation in the previous section, amounted to 1140o68 watt-minutes The net mass of condensate was 31.464 grams, which was calculated from a gross of 134 625 grams and a tare of 103 161 grams. The uncorrected latent heat, the first term on the right-hand side of Equation (115), becomes Uncorrected (1140o 68 watt-min) cal/) = — i; —- -. (1453403 cal/watt-min) (116) Latent Heat (31.464 g) 519088 cal/g

58.380 —-- 58.340 58.300 - 58.260 c 58.220 - 0~ 58. 180 58.140 58.100 -- -4 -2 0 2 4 6 8 10 12 14 16 18 20 TIME FROM START OF RUN (Min.) Figure 34. Sample Power-Time Curve (Run No. A 26-0)

l653Before the sensible-heat corrective term could be computed, it was necessary to know the exact composition of the mixture Densities of 0 9832 and 0.9850 grams per ml from two trials with the condensate and of 0.9830 and 0,9829 grams per ml from. two trials with the preheater li.quid established the composition of the mixture at 10o3 mass per cent acetoneo The bubble point temperature, TBp, for this composition was read from the temperature-composition diagram which was produced from the vapor-liquid equilibrium data obtained for the entire range of composition. After making the small correction for pressure to 73557 mm of mercury, the pressure at which the vaporization proceeded, TBp was determined to be 77.8~C. TIn, the only directly determined experimental quantity which. appears in the sensible-heat correction, was 72o7~C. Cp for 10o mass per cent acetone at the average temperature of 752~0C was estimated to be 0,996 cal/g~Co The value of the corrective term is calculated, as follows, to be Sensible Heat (0.981) (o0996 cal/gC)(77o8 - 72.7) Correction = 4o98 cal/g (117) The actual latent heat is the difference between the un.corrected latent heat and the sensible-heat correction, Thus, the integral isobaric heat of vaporization for an aqueous mixture of 10o3 mass per cent acetone has been determined to be 514-o9 calories per gram. For this particular mixture the composition of the vaporizer contents was determined from density measurements to be 0,3 mass per cent acetone. The temperature of the contents at 73557 mm of mercury was found to be 9800~Co This temperature was corrected for pressure

-164to 760 mm of mercury by a simplified version of the equation A log P = Slope (118) A l/T which expresses a linear relationship between log P and l1/To The simplified equation actually used., along with its application to this example. is TP2 760 Temp. Correction = T760 - Tp - logP Slope 2 (119) T T7,-(37ll16~K) og 760 o9~K T760 7357 -2l40oK 73557 The slope, -214U0-K, is tae mass average of the pure-component slopes of -1630(~K) for acetone and -2200(~K) for water. The corrected temperature is 98o9~Co Thus, at 9809~C on the temperature-composition diagram points of 1003 mass per cent acetone on the dew-point line and 003 mass per cent acetone on the bubble-point line have been established,

APPENDIX C SAMPLE CALCULATION OF INTEGRAL ISOBARIC HEAT OF VAPORIZATION FROM DATA. AVAILABLE IN THE LITERATURE The general equation developed in the section entitled "Enthalpy-Temperature-Diagram Approach" for the calculation of integral isobaric heats of vaporization is Xp - zj LT1 + Zk LT1 + (z. Cpj + zk CP k)(T2 T) (34) For acetone-water mixtures at atmospheric pressure this equation in terms of temperatures in degrees centigrade and mass fractions becomes Xp - ZA[1344 0262t1] + Zw[599.6 - 0.598t] + {ZA[0o283 tl+ +t t l+t2 + o0,00083( 1. ) -.000 0005( 2 2)] + Zw[O4358 + 0.000125(tl+t2)]} {t t (79) The units of Xp in Equation (79) are calories per gram. The following example shows the calculation of the integral isobaric heat of vapori. zation of an aqueous mixture of 50.0 mass per cent acetoneo The first step is to find the bubble-point and'dew-point temperatures from vapor-liquid equilibrium datao For a 50 0 mass per cent mixture of acetone and water at atmospheric pressure the bubble point, tl1 is 61.9~C and the dew point, t2, is 92.8~Co The mass fractions have, of course, been set by the statement of the problem at ZA - ZW = 0.500. If one desires to use Equation (34) directly, the heat of vaporization at 6190C of both pure water and pure acetone -165

would have to be determined from either graphs or tables which give the heat-of-vaporization - temperature relationships The ideal-gas eat capacities of the pure components at the average temperature of 773 ~C would have to be determined similarly~ However the temperature variance of each of these properties has already been incorporated in Equation (79) so that insertion of the numbers t1 - 619, t2 =- 92o8, l(tl+t2) = 7703, and ZA = ZW - 0O500 yields the desired answer immedi2 atelyo Xp 0. 500[134.4 - (0o262) (61.9)] + 0o500[599~6 - (0o598) (619) ] + {o0500[0.283 + (0.00083)(77o3) - (o.000 0005)(77.3)2] + 0o500[o.48 3 + (.o000125)(77y3)]} {92.8 - 61.9} - (0.500)(182) + (0.500)(562.6) + [(0o500)(0o344) + (o500) (o,448) 1309] = 59.1 + 281.3 + 1253 = 352~7 cal/g (120) Equation (34) can be used to make the calculation on a mole basis if the z's are mole fractions and the units of the L's and the C-'s are calories per mole and calories per mole -~C respectively The resulting Xp would be in the units of calories per mole,

APPENDIX D SAMPLE CALCUIATION OF INTEGRAL ISOBARIC HEAT OF VAPORIZATION USING THE EQUILIBRIUM-K-VALUE EQUATIONS The equation given in the section entitled "Application of Equilibrium-K Values" for the calculation of integral isobaric heats of vaporization is RT1T2 K 2 p _ z.ln - - + Zz AH~ T2-T1 i Kil i -i TlT2 T2 T -l + [ T in T1] Zi (CPi - CP i) (61) The following example shows the calculation of the integral isobaric heat of vaporization of an aqueous mixture of 50.0 mass per cent acetoneo The calculation is in three steps - one for each of the terms in Equa-, tion (61). The first term, when written out for an acetone-water binary, oecomes RTl T K.2 K 2 [ZA ln -A + W ln K (121) T2-T1 KA,1 KW,1 The z's here refer to mole fractions, The mixture corresponding to 0.500 mass fraction acetone contains 0.2368 mole fraction aceton.e From vapor-liquid equilibrium data the bubble-point temperature, T, is found to be 335.1~K (61.9~0C) and the dew-point temperature, T2, is found to be 566.0~K (92.8~C). Vapor-liquid equilibria also contribute the y - x values for calculating the K So The definition of KA 2 is -167

-168YA 2/XA 2 The value of YA 2 is, of course, 0.2568, and the composition of the equilibrium liquid, x2, at the dew-point temperature, T2, is 0.00918, Similarly, the definition of KA,1 is yl/XA,lo The values of the equilibrium-vapor YA l and the liquid are 0.805 and 0.2368, respectivelyo Substitution of these values into Statement (121) yields RT1T2 Z z ln RT1T ~ zi In -i 2 T2-T1 i Ki, (1.987) (3351.) (366.0) [0.2368 Ln 0.2368/0o 00918 (3660 - 3355.1) 0.803/0.2368 + 0.7632 in 0-7632/0.99082] 0.197/0.7632 = 7890(0.481 + 0.834) = 10,390 cal/mole (122) The second term in Equation (61) is evaluated from the following expression (ZA P + ZW PJ,W)(T2 - T1) (125) The z's and T's have been given in the previous paragraph. ~ and PA Co are 19.97 cal/mole-~C and 8.07 cal/mole-~C, respectively, ApplyP.W ing these values to Statement (123) yields Z zi A = [(0.2368)(19.97) + (o.7652)(8.07)1][66.0 - 335o1] = (lo,87)(30o9) = 366 cal/mole (124) The third term in Equation (61), when written out for an acetone-water binary, becomes rT1T2 l T2 - C-^ + _(o[ -- C c-2' (125)

-169The z's, T's and C's have been given previously~ The partial molal specific heats in he e liquid phase were evaluated from specific-heat data for acetone-water mixtures. Cp A is 56o7 cal/mole-~C, and Cp, is 20.5 cal/mole-~C. Substitution of these values into Statement (125) yields T1T2 ln - CT i ) (33551)(566.0) 366,o =( i ln - 335. 1] [0.2368(36.7 - 19.97) (366.o - 335.1) 335.1 + 0.7632(20.5 - 8.07)] = (15.9)(13.4) = 213 cal/mole (126) The sum of the first two terms of Equation (61), which constitute the Edmister equation, is 10,726 calories per mole, while the total of the three terms is 10,939 calories per mole. The smoothed experimental value for an aqueous mixture containing 253.68 mole per cent acetone is 9699 calories per mole. The results for another typical mixture of 80 mass per cent acetone (55.37 mole per cent) show that the integral isobaric heat of vaporization as calculated from Equation (61) is 17,893 calories per mole. The corresponding experimental value is 8662 calories per moleo Some of the reasons for the inability of Equation (61) to predict the experimental results can be seen by referring to the first term on the right-hand side, In this example this term is written out in Equation (122), where the value of 0.00918 (or 0.918 per cent) is entered for xA 2. If the equilibrium compositions are known to, say, plus or minus 0,2 per cent, then an error of approximately 20 per cent could be

-170introduced into KA,2 which is not compensated elsewhereo This error would, of course, be reflected severely in the final answer because the first term is much larger than either of the other twoo In addition, it should be observed that the term (T2 - T1) appears in the denominator of the first term on the right-hand side of Equation (61)o Thus, for any mixture which has a small temperature difference between the bubble point and dew point, and in particular for mixtures which have a high concentration of either component, the first term in Equation (61) will become quite sensitive to any small error introduced in the estimation of the dew-point - bubble-point temperature difference.

APPENDIX E SMOOTHED DATA CALIBRATIONS -171

-172TABLE XV SMOOTHED INTEGRAL ISOBARIC HEATS OF VAPORIZATION AT EVEN COMPOSITIONS - ISOPROPYL ALCOHOL-WATER Atmospheric Pressure Mass Pct. Experimental Calculated (Eq. 78) Isopropanol Heat of Vap. Heat of Vap. (cal/gram) (cal/gram) 0 540.2 539.8 5.0 528.3 527.6 10.0 513.8 513.9 13.0 496.0 496.5 20.0 477.8 477.7 25.0 459.4 458.6 30.0 439.5 439.2 40.0 398.3 399.9 50.0 357.6 360.4 60.0 316.9 320.3 70.0 276.0 279.9 75.0 255.4 259.2 80.0 234.3 238.6 85.0 214.5 218.7 90.0 195.7 199.3 95.0 177.7 179.5 100.0 159.5 159.3 TABLE XVI SMOOTHED INTEGRAL ISOBARIC HEATS OF VAPORIZATION AT EVEN COMPOSITIONS - ACETONE-WATER Atmospheric Pressure Mass Pct. Experimental Calculated (Eq. 79) Acetone Heat of Vap. Heat of Vap. (cal/gram) (cal/gram) 0 540.2 539.8 5.0 529.7 531.5 10.0 515.5 517.3 15.0 498.1 499.8 20.0 478.6 480.7 25.0 458.6 460.9 30.0 438.3 440.0 40.0 396.3 397.0 50.0 352.6 352.6 60.0 307.1 307.3 70.0 21.261. 261. 75.0 238.4 238.2 80.0 215.5 214.5 85.0 191.5 190.8 90.0 166.1 166.7 95.0 142.2 142.3 100.0 119.9 119.7

-173-'TABLE XVII SMOOTHED VAPOR-LIQUID EQUILIBRIA AT EVEN COMPOSITIONS - ISOPROPYL ALCOHOL-WATER Atmospheric Pressure Mass Pct. Mass Pct. Isopropanol Isopropanol Temperature in Vapor in Liquid (~C) 0 0 100.0 10.0 0.5 99.4 20.0 1.1 98.3 50.0 1.9 97.0 40.0 3.0 95.3 50.0 4.5 93.1 60.0 6.7 90.5 68.2 10.0 87.5 70.0 11.1 86.9 76.3 20.0 83.3 78.6 30.0 82.0 79.6 40.0 81.6 80.0 47.5 81.5 80.1 50.0 81.5 80.7 60.0 81.3 81.9 70.0 81.0 84.5 80.0 80.7 89.4 90o. 80.5 90.o 90.7 80.5 95.0 96.1 81.2 100.0 100.0 82.4 TABLE XVIII SMOOTHED VAPOR-LIQUID EQUILIBRIA AT EVEN COMPOSITIONS - ACETONE-WATER Atmospheric Pressure Mass. Pct. Mass Pct. Acetone Acetone Temperature in Vapor in Liquid (0C) 0 0 100.0 10.0 0.2 99.1 20.0 o.6 98.0 30.0 1.3 96.7 40.0 2.0 94.9 50.0 2.9 92.8 60.0 3.9 89.8 70.0 5.9 85.3 79.0 10.0 79.1 80.0 10.8 78.2 87.1 20.0 70.6 90.0 27.7 66.8 90.5 30.0 66.3 92.3 40.0 63.4 92.9 50.0 62.3 93.6 60.0 61.0 94.1 70.0 60.3 94.7 80.0 59.4 95.0 84.5 59.1 95.7 90.0 58,4 100.0 100.0 56.2

-174TABLE XIX SMOOTHED DENSITY-COIPOSITION DATA AT 25~C FOR ACETONE-WATER MIXTURES Mass Pcto Density Acetone (g/cc) 0 o09971 5.0 0o9904 10o 0 9836 15.0 0.9765 20.0 09693 25.0 0o9618 30.0 0.9539 35o0 0.9454 40o.0 09365 45.0 0.9265 50.0 0o9160 55.0 0.9051 60o.0 o8940 65.o 0.8824 70.0 o.8700 75.0 0.8569 80.0 o084534 85.0 0.8294 90.0 o.8153 95.0 0 7999 100.0 0.7846

-175164 - Z 0;g 162 0 <>.: 160 0-5 <0 2 158 bJ z 1 156 -J 154 -~- - 0.2.4.6.8 1.0 1.2 1.4 1.6 1.8 2.0 I/FLOW RATE,(min./gr.) Figure 35. Heat of Vaporization of Isopropyl Alcohol as a Function of the Reciprocal Flow Rate to the Third Power. 126 124 Z 122 0 4 N, 120 0 u. 118 0 uu 116 I 112 0.2.4.6.8 1.0 1.2 1.4 1.6 1.8 2.0 I/FLOW RATES, (min./gr.) Figure 36. Heat of Vaporization of Acetone as a Function of the Reciprocal Flow Rate to the Third Power.

0.50C_ __ _ I I __ _ _ __ _ _ __ _ _ __ _ _0.50"C.020.016 0.250C.016 --- -- -- -- -- - --- -- - --- - -- -- -- -- -- -- -- -- -- -.008 1MAERA 15 COPR16NTNA ~'^ " -^^'"^- -,t -!.004 D04 13 04 w 02 ___EDM AGTTE _QI BATH ___ ____ __ __ __ __ __ __ _ __ __ __ __ TEMP. STD.: Hg IN GLASS THERMOMETER ~~~~~~~~~-0.25~OC 0 H 0 14......... -.008__ __ _ - O )-0-250C 3 -.0 1 2 F02 5 C - _ _ _ __ _ _ __ _ _ 2.3 2.5 2.7 2.9 3.1 3.3 3.5 3.7 3.9 4.1 4.3 POTENTIALMATERIAL: COPPER - CONSTANTAN mI -.016Figure 7. Thermocouple Calibrations.IZE: NOS. 15,16,AND 17 - 24 GA. NOS. 12 THROUGH 14 a - 30 GA. L 4 -.020 MEDIUM: AGITATED - LIQUID BATH TEMP. STD. Hg IN GLASS THERMOMETER -. (PRINCO NO. 253197) 2.3 2.5 2.7 2.9 W. 3.3 3.5 3.9 4.1. POTENTIAL READING, mv. Figure 37. Thermocouple Calibrations.

-177100 90 80 W 70 ISOPROPYL ALCOHOL - WATER - 0 60 - 50 1. 40 0 MOLE PER CENT ISOPROPYL ALCOHOL OR ACETONE Figure 38. Graph Relating Mole Per Cent to Mass Per Cent. 0 10 20 30 40 50 60 70 80 90 100 MOLE PER CENT ISOPROPYL ALCOHOL OR ACETONE Figure 38. Graph Relating Mole Per Cent to Mass Per Cent.

APPENDIX F RAW DATA -178

-179TABLE XX RAW DATA FROM ISOPROPYL ALCOHOL-WATER RUNS Avg. Avg. Density (g/cc) Avg. Temperature (~C) Bar. Time Power Net Con- at 35~C Point Point Point Press. Run No. (min.) (watts) densate(g) Condensate Vap. Liquid 12 13 14 (mm Hg) T12-0 27.947 49.587 36.188 Pure Water 90.1 99.4 99.2 737.8 T12-N 29.793 49.569 38.479 Pure Water 90.0 99.4 99.2 737.8 T13-0 30.587 26.851 21.495 Pure Water 95.3 99.3 99.3 738 0 T13-N 28.437 27.364 20.351 Pure Water 94.9 99.2 99.2 738.0 T14-0 25.052 66.448 43.356 Pure Water 88.7 99.3 99.2 738.0 T14-N 28.642 66.238 49.4L0 Pure Water 88.9 99.3 99.1 738.0 T15-0 30.548 36.637 29.299 Pure Water 92.7 99.2 99.3 740.9 T15-N 25.028 36.975 24.220 Pure Water 92.9 99.2 99.2 740.9 Ill-0 14.360 12.300 14.970 Pure Isopropyl Alcohol 70.3 81.6 81.6 738.0 Ill-N 24.996 12.286 26.055 Pure Isopropyl Alcohol 70.4 81.6 81.6 738.0 112-0 17.429 16.355 24.054 Pure Isopropyl Alcohol 68.3 81.6 81.6 737.2 I12-N 22.387 16.344 30.952 Pure Isopropyl Alcohol 68.4 81.6 81.6 737.2 I13-0 19.380 9.477 15.754 Pure Isopropyl Alcohol 73.4 81.7 81.7 740.5 I13-N 20.043 9.455 16.265 Pure Isopropyl Alcohol 73.5 81.7 81.7 740.5 I14-0 15.337 20.257 26.141 Pure Isopropyl Alcohol 67.7 81.7 81.7 740.3 I14-N 22.198 20.219 37.849 Pure Isopropyl Alcohol 67.7 81.7 81.7 740.3 I15-0 15.152 15.913 20.454 Pure Isopropyl ALcohol 68.9 81.6 81.6 734.4 I15-N 22.095 15.916 29.832 Pure Isopropyl Alcohol 69.1 81.6 81.6 734.4 I16-0 14.775 20.270 22.799 0.78552 - 67.0 80.4 80.4 738.4 I16-N 23.110 20.303 35.644 0.78565 - 66.8 80.4 80.4 738.4 117-0 16.150 13.946 17.265 0.78548 69.2 80.3 80.3 735.7 I17-N 23.166 13.953 24.804 0.78570 0.78260 69.2 80.3 80.3 733.7 118-0 17.740 19.618 24.388 0.79744 - 68.0 79.8 79.9 739.7 I18-N 23.012 19.604 31.624 0.79767 - 68.0 79.8 79.8 739.7 119-0 14.639 14.703 15.160 0.79751 - 70.2 79.7 79.8 737.9 119-N 24.461 14.689 25.363 0.79755 0.79481 70.2 79.7 79.8 737.9 120-0 13.652 25.142 21.880 0.81031 - 67.3 79.8 79.8 736.6 I20-N 23.680 25.112 37.925 0.81043 - 67.2 79.8 79.8 736.6 121-0 15.297 16.722 16.436 0.81031 70.0 79.7 79.7 733-5 I21-N 24.038 1i.702 25.806 0.81013 0.81906 70.1 79.7 79.7 733 5 122-0 15,516 27.902 25.407 0.82192 - 68.2 80.8 80.7 735.7 I22-N 23.730 27.933 38.943 0.82215 - 68.2 80.8 80.7 735.7 I23-0 16.966 17.713 17.873 0.82188 72.3 80.8 80.6 738.5 I23-N 25.153 17.726 26.469 0.82196 0.89841 72.3 80.8 80.6 738.5 I24-0 14.075 27.961 20.908 0.83825 -72.3 84.5 84.5 737.4 I24-N 25.344 27.988 37.767 0.83813 72.4 84.4 84.5 737.4

-180TABLE XX (CONT'lD) RAW DATA FROM ISOPROPYL Al tCOITOL-WATER RUNS Avg. Avg. De],.:;ty (g/cc) Avg. Temperature (~C) Bar. Time Power Net Con- at 35 C Point Point Point Press. Run No. (min.) (watts) densate(g) Condensate Vap. Liquid 12 13 14 (mm Hg) 125-0 14.142 20.174 15.317 0.83869 - 76.1 84.4 84.5 736.7 I25-N 22.405 20.147 24.198 0.83861 0.97119 76.2 84.5 84.5 736.7 I26-0 16.038 33.155 24.954 0.86076 - 75.6 88.3 88.3 739.3 I26-N 23.052 33.084 35.781 0.86072 - 75.6 88.3 88.3 739.3 127-0 18.137 22.721 19.452 0.86089 - 79.0 88.3 88.3 738.1 I27-N 23.472 22.638 25.164 0.86076 0.98022 79.2 88.4 88.3 738.1 128-0 20.023 36.252 30.083 0.88558 - 77.5 91.3 91.3 734 6 I28-N 23.401 36.136 35.038 0.88585 - 78.0 91.3 91.3 734.6 129-0 14.619 25.211 15.347 0.88601 79.2 91.3 91.3 733.5 I29-N 22.145 25.208 23.201 0.88597 0.98463 79.2 91.4 91.4 733-5 130-0 15.062 41.384 23.635 0.90603 - 81.2 93.4 93.3 734 8 I30-N 19.969 40.424 30.429 0.90617 - 79.5 93.5 93.2 734.8 I31-0 12.804 26.353 12.686 0.90630 80.5 93.4 93.5 735.1 I31-N 22.419 26.394 22.281 0.90624 0.98727 80.5 93.4 93.5 735.1 I32-0 14.070 48.216 23.018 0.92860 -75.8 95.4 95.2 737 7 132-N 20.400 48.082 33.242 0.92866 - 75.7 95.4 95.3 737 7 133-0 14.577 32.050 15.892 0.92909 - 78.4 95.4 95.2 732.5 I33-N 25.384 32.161 27.809 0.92865 0.98978 78.5 95.4 95.3 732.5 134-0 15.264 47.326 22.335 0.95177 - 80.3 97.1 97.0 742.5 I34-N 23.032 47.538 33.917 0.95137 - 80.9 97.0 97.0 742.5 I35-0 13.700 33.092 14.024 0.95155 81.3 96.9 97.0 741.5 I35-N 21.207 33.109 21.735 0.95154 0.9918, 81.5 97.0 97.1 741.5 136-0 15.838 50.448 23.830 0.96153 - 80.5 97.6 97.5 741.0 I36-N 23.053 50.412 34.613 0.96160 -80.5 97.6 97.5 741.0 137-0 15.418 34.908 16.087 0.96159 - 81.7 97.5 97.6 736.6 I37-N 26.844 35.058 28.032 0.96146 0.99218 81.6 97.5 7.5 736.6 138-0 14.020 53.794 21.604 0.96925 - 79.6 98.2,'.1 741.1 I38-N 20.033 53.751 30.862 0.96932 - 79.3 98.3 5',.2 741.1 I39-0 15.138 36.921 16.002 0.96938 78.8 98.1 93.0 738.6 I39-N 20.352 36.852 21.396 0.96944 0.99278 78.6 98.1 98.0 738.6 I40-0 13.335 56.848 20.921 0.97680 - 81.1 98.6 98.6 738.0 I40-N 20.238 56.859 31.862 0.97664 81.5 98.6 9" 6 738.0 I41-0 14.127 39.324 15.333 0.97684 -81.6 98.8 9t.6 742.3 I41-N 20.120 39.320 21.847 0.97676 0.99328 81.4 98.8 98.6 742.3 142-0 12.012 57.856 18.609 0.98495 - 85.4 99.3 99.0 743.3 I42-N 18.871 57.841 29.305 0.98461 - 85.6 99.3 99.1 743.3 I43-0 13.425 38.757 14.004 0.98551 - 87.5 99.3 99.0 741.6 I43-N 22.010 38.858 23.035 0.98528 0.99373 87.2 99.3 99.1 741.6

-181TABLE XXI RAW DATA FROM ACETONE-WATER RUNS Avg. Avg. Density (g/cc) Avg. Temperature (~C) Bar. Time Power Net Con- at 25 ~C Point Point Point Press. Run No. (min.) (watts) densate(g) Condensate Vap. Liquid 12 13 14 (mm Hg) A1-0 23.583 14.968 40.741 Pure Acetone 48.1 55.3 55.1 734.3 A1-N 17.915 15.000 31.039 Pure Acetone 48.2 55.4 55.2 734.3 A2-0 19.278 12.601 28.121 Pure Acetone 49.5 55.3 55.1 732.6 A2-N 14.155 12.600 20.649 Pure Acetone 49.5 55.3 55.1 732.6 A3-0 21.375 8.895 22.145 Pure Acetone 51.7 55.3 55.3 730.0 A3-N 18.260 8.892 18.873 Pure Acetone 51.7 55.3 55.2 730.0 A4-O 22.796 7.076 18.371 Pure Acetone 52.4 55.3 55.2 731.0 A4-N 20.245 7.068 16.301 Pure Acetone 52.4 55.3 55.3 731.0 A5-0 19.137 14.980 30.019 0.7940 -48.7 56.3 56.2 737.1 A5-N 13.672 14.956 21.422 0.7938 -48.9 56.4 56.2 737.1 A6-O 24.165 9.939 25.333 0.7939 - 51.7 56.4 56.2 736.7 A6-N 15.450 9.904 16.147 0.7938 0.7986 51.7 56.4 56.2 736.7 A7-0 18.484 15.541 27.516 0.8049 - 53.8 60.6 60.6 738.7 A7-N 13.784 15.565 20.506 0.8049 - 53.5 60.6 6.6 738.7 A8-0 21.981 11.161 23.645 0.8044 - 55.8 60.7 60.5 738.8 A8-N 13.333 11.176 14.343 0.8045 0.9051 55.9 60.7 6o.5 738.8 A9-0 18.o60 17.912 28.180 0.8131 - 56.0 65.0 65.4 732.1 A9-N 13.700 17.864 21.208 0.8138 -56.0 65.3 65.5 732.1 A10-0 21.394 12.262 22.628 0.8147 - 57.4 65.1 65.3 732.3 A10-N 14.200 12.240 14.882 0.8150 0.9559 57.4 65.3 65.6 732.3 All-0 20.077 23.061 30.992 0.8411 - 55.8 76.6 76.6 733.1 All-N 15.937 23.057 24.588 0.8412 55.9 76.5 76.6 733.1 A12-0 19.714 16.970 22.360 0.8410 0.9816 57.1 76.8 76.5 733.7 A12-N Run Discarded. Shield Line Plugged. A13-0 18.833 28.074 28.903 0.8705 -58.1 84.7 84.6 736.5 A13-N 16.717 28.027 25.467 0.8708 0.9893 58.0 84.7 84.5 736.5 A14-0 Intermittent plugging of liquid line upset the steady state. A14a-0 20.975 32.328 31.468 0.8944 - 58.4 88.6 88.7 726.5 A14a-N 15.375 32.292 23.002 0.8944 -58.3 88.6 88.7 726.5 A15-0 25.297 22.996 26.811 0.8947 - 59.6 88.5 88.7 723.9 A15-N 15.178 23.116 16.177 0.8947 0.9920 59.4 88.5 88.6 723.9 A16-0 21.012 37.352 31.629 0.9157 - 59.2 91.6 91.6 728.7 A16-N 17.594 37.351 26.546 0.9158 - 59.0 91.6 91.7 728.7 A17-0 21.896 26.066 23.021 0.9155 - 60.8 91.6 91.6 728.0 A17-N 14.835 26.015 15.615 0.9158 0.9929 60.8 91.6 91.6 728.0 A18-0 19.510 42.520 29.973 0.9360 - 61.0 94.2 94.0 744.6 A18-N 18.222 42.419 27.806 0.9362 - 60.6 94.2 94.0 744.6 A19-0 20.123 29.852 21.653 0.9360 -62.1 94.0 93.9 744.6 A19-N 16.835 29.792 18.028 0.8358 0.9944 61.9 94.0 93.9 744.6 A20-0 22.565 48.343 35.713 0.9535 - 63.4 96.3 96.0 745.0 A20-N 18.032 48.381 28.554 0.9535 63.1 96.3 96.0 745.0 A21-0 14.841 30.980 15.047 0.9534 - 64.7 95.9 96.0 743.7 A21-N 15.008 31.138 15.241 0.9535 0.9953 64.4 96.2 96.0 743.7 A22-0 20.145 51.233 30.920 0.9691 - 68.0 96.6 96.6 725.5 A22-N 14.293 51.142 21.833 0.9689 -68.0 96.7 96.6 725.5 A23-0 20.805 35.682 22.226 0.9689 69.2 96.6 96.6 726.8 A23-N 20.200 35.680 21.423 0.9690 0.9962 69.2 96.6 96.6 726.8 A24-0 20.595 54.730 32.252 0.9767 71.6 97.8 97.8 742.2 A24-N 17.990 54.724 28.281 0.9766 71.6 97.8 97.8 742.2 A25-0 19.799 38.977 22.144 0.9766 -72.9 97.8 97.8 741.7 A25-N 15.575 38.908 17.378 0.9768 0.9966 72.6 97.8 97.8 741.7 A26-0 19.582 58.251 31.464 0.9831 -72.7 98.2 98.0 735.7 A26-N 18.432 58.061 29.554 0.9832 -72.7 98.2 98.0 735.7 A27-0 20.409 39.111 22.065 0.9830 -75.3 98.2 98.1 737.0 A27-N 16.302 38.979 17.525 0.9831 0.9966 75.0 98.2 98.1 737.0 A28-0 21.065 59.268 33.469 0.9900 -79.1 98.7 98.6 736.9 A28-N 19.258 59.295 30.531 0.9901 -79.0 98.7 98.6 736.9 A29-0 22.192 40.354 24.017 0.9901 83.1 98.7 98.6 736.6 A29-N 19.187 40.242 20.730 0.9902 0.9969 83.0 98.7 98.6 736.6

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UNIVERSITY OF MICHIGAN U JO III IlmlMIlrolIl Ili l