THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING MASS TRANSFER WITH CHEMICAL REACTION IN VIEW OF VARIOUS MODELS Lalitkumar H. Udani A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Science in The University of Michigan Department of Chemical Engineering 1961 October, 1961 IP-536

Doctoral Committee: Associate Professor Kenneth F. Gordon, Chairman Professor Lloyd Lo Kempe Professor Joseph J. Martin Associate Professor Donald Ro Mason Associate Professor Milton Tamres ii

ACKNOWLEDGMENTS I extend my sincere thanks too Professor Kenneth F. Gordon, whose interest and continued encouragement were a tremendous and indispensable source of inspiration in my work and who has been to me a 0friend, philosopher and guide" in every senseo Dr. Gordon"s philosophy and example will have continued influence in my future life. Professors Jo J. Martin, Lo L. Kempe, D. R. Mason and M. Tamres for their generous help and guidance during the course of this study and for their criticism and valuable suggestions during the preparation of this dissertation. The members of my family, whose many sacrifices, ceaseless support and abundant affection thousands of miles away from home made my education in this country possible. I hope I will have opportunities to repay the great debt I owe them in years to come. Dr. Mo R. B. Klinger, Dean John Bingley, Dr. Ro L. Hess, Mr. Ro Wo Hodges, Mr. Eo O Johnson and many friends in Ann Arbor for their sustained interest in my well-being and education. Mr. F. Ro Harrell of the Engineering Library and his staff and the staff of the Chemical and Metallurgical Engineering Department office and shop for fine cooperationo The Industry Program of the College of Engineering for assistance and cooperation in preparing this dissertationo iii

TABLE OF CONTENTS Page ACKNOWLEDGMENTS. o.... o......... iii LIST OF TABLES.................. o vii LIST OF FIGURES... o o. o o. o a. a... x ABSTRACT.. o o. o. o........ o. xii STATEMENT OF THE PROBLEM..........o xv I. MASS TRANSFER WITH CHEMICAL REACTION..... 1 1. History and Objectives........ 1 A. Introduction.........1 a. Models based on film theory. 2 b. Models based on penetration theories.... o..... 5 c. Model based on Kishinevskii theory............. 6 d. Model based on film-penetration theory.... o........ 6 Bo Previous Experimental Work...... 8 C. Objectives.... o....... 12 2. Determination of Liquid Phase Mass Transfer Coefficients........ 13 A. Selection of a System and Apparatus o 13 a. Selection of a system..... 13 b. Apparatus............ 14 iv

TABLE OF CONTENTS (Continued) Page B. Procedure.. o.... 17 ao Determination of k..... 17 L L C. Results... o.. o...... 19 ao Calculations of k0... 19 L b. Calculations of k....... 21 L 30 Comparison of Models with Data..... 35 II. CHEMICAL KINETICS OF SODIUM SULFITE OXIDATION. o........ 40 1. Experimental Work.......... 41 a. Modification of the apparatus.... 41 b. Procedure...... o.. 41 2. Results............... 43 a. Uncatalysed reaction........ 43 ++ bo Reaction catalysed with Co ++ or Cu............. 46 c. Determination of mass transfer resistance for kinetic study.... 48 d. Determination of chemical kinetic coefficient, k' from k..... 55 L eo Reaction inhibited by mannitol.. 59 f. Reaction inhibited by benzyl alcohol...o. o....... 61 g. Reaction inhibited by catechol. 6. 62 III. CONCLUSIONS................ 65 NOMENCLATURE.................. 68 v

TABLE OF CONTENTS (Continued) Page REFERENCES. o o o o.. o. o o.o o o. o. o..o. 74 APPENDIX I - DERIVATION OF kL VIA VARIOUS MODELS.L MODELS o e. o o o o o o o e. o o. 78 A. The Film Models. o.... B The Penetration Models..o. Co Kishinevskii Model.. O.. D. The Film Penetration Model. o.. 79 *o * 88..a o 92 o o. 96 APPENDIX II APPENDIX III APPENDIX IV APPENDIX V - ION FLUX EQUATION o o o.. 99 - THE DATA AND CALCULATIONS OF k~ L AND THE VISCOSITY DATA o o. o o o 104 - DATA AND CALCULATIONS OF k L WITH VARIOUS CATALYSTS.... o 107 - DATA AND CALCULATIONS OF kL WITH DIFFERENT STIRRER SPEEDS. o o 140 APPENDIX VI APPENDIX VII - DATA AND CALCULATIONS OF k FOR L THE EFFECT OF OXYGEN CONCENTRATION ~ - DATA AND CALCULATIONS OF k WITH L VARIOUS SODIUM SULFITE CONCENTRATIONS WITH AND WITHOUT CATALYST. 157 165 183 APPENDIX VIII - CALCULATIONS OF 7 FROM VARIOUS MODELS........... APPENDIX IX - DATA AND CALCULATIONS FOR CHEMICAL KINETIC COEFFICIENTS o.... 188 vi

LIST OF TABLES Table Page 1 Factor y = (kL/k) - 1 for various models. o....... 9 2 Data for 7 = (kL/kL) - 1... o.. 37 Properties for Equations 50 and 51 84 3 Properties for Equations 50 and 51 o o 85 4 Properties for Equations 50 and 51.. o. 85) 5 Data and Calculations of k.. o. 105 L 6 Viscosity of Na2S04... o o... 106 7 Viscosity of Na2SOs o... o.... 106 8 i. Determination of k..... 110 g(02) ii. Determination of % resistance due to gas phase. o 110 iii. Sample calculations for CAi and k o. o o... o...... o 111 L 9 Calculations of k for various catalysts L from Figures 24-78. o o o.. o 113 10 Calculations of kL for effect of stirrer speed from Figures 79-103..0. o o 141 11 Calculations of k for 99.5 per cent L oxygen from Figures 104-111.... 158 vii

LIST OF TABLES (Continued) Table Page 12 a. Calculations of kL and y with data from Figures 112-136 and CAi from Figure 111........... 166 b. Calculations of k and y for L reaction without catalyst (data from Figures 137-143)........ 166 13 Calculation of the diffusivity of sodium sulfite............... 184 14 Calculations of (k/k0)- 1 from Hatta, L L Higbie, Danckwerts and Kishinevskii models...... o... 185 15 Calculations of (k /k)- 1 from Sherwood L L and Wei model....... o o 0 186 16 Reaction rates without catalyst..... 187 17 Recalculation of k3(cu++) from FullerCrist data from Equation 25... 189 18 Recalculation of k3Co++) from Equation 27.............. 190 19 Reaction rates with Cu catalyst... 191 ++ 20 Reaction rates with Co catalyst... 192 21 Data for the determination of k~ a'.. 193 L 22 Data obtained from Figure 11 for the determination of k' from k~ a' and L KR a' for reaction without catalyst... 194 viii

LIST OF TABLES (Continued) Table Page 23 Calculation of 7 from Equation 33 for k~ = 1100 o.. o o o o o o o o 195 24 Estimation of k8 from k for L reaction without catalyst...... 196 25 Estimation of kU from k for L reaction with Cu catalyst. 197 26 Estimation of kg from k for L ++ reaction with Co catalyst... 198 27 Estimation of k' from Fuller and Crist data... 0 0 0. o o. 199 28 Calculation of k' for mannitol from k and Equation 34...... 200 L 29 Calculation of k' for benzyl alcohol from k and Equation 35...... 200 L ix

LIST OF FIGURES Fi.gure 1 Flow-sheet. o.... 2 Reactor. o o o.. 3 (CAi CAo) versus time. o 4 Oxygen absorbed versus time. o. 5 ao kL versus catalyst concentration for CBo = 0.048-0.17 gm equiv/Q o bo kL versus catalyst concentration for CBo = 0.07-0.12 gm equiv/A. o 6 Effect of stirrer speeds on kL.. 7 Comparison of results for air and oxygen o..ooo ooo 8 Effect of CBo on kL with and without catalyst........ 9 Comparison of models for infinitely fast reaction with data for reaction with high catalyst concentration.. o o o 10 Reaction without catalyst, logarithmic plot o o. oo.o o o o o. o 11 Reaction without catalyst, arithmetic plot...oo ooo o 12 Reaction with Cu++ catalysto o 13 Reaction with Co++ catalysto. 14 Determination of kL a" o. L Page 15 o 16 22 23 26 27 o 29 31 o 33 39 45 0 49 0 50 0 53 x

LIST OF FIGURES (Continued) Figure 15 Determination of k' for reaction without catalyst.. 16 Second order kinetic coefficients from k versus calculated catalyst ion L concentration........... 17 Second order kinetic coefficients versus mannitol concentration......... 18 Second order kinetic coefficients versus benzyl alcohol concentrations.. 19 Hatta model.............. 20 Sherwood and Wei model......... 21 Ion concentration gradient....... 22 Sample data sheet.......... 23 Sample calculation sheet........ 24-78 Rate data for various catalysts.... 79-103 Rate data for various stirrer speeds 104-110 Rate data with 99.5 per cent 02 for ++ various Co concentration. 111-143 Solubility of 02 in aqueous Na2SO4 [Seidel (36) 1 and rate data for varying sodium sulfite concentrations..... Page 54 57 60 63 79 83 100 108 109 114-139 14.2-156 159-164 167-182 xi

ABSTRACT Liquid phase mass transfer coefficients with and without reaction for a gas-liquid system were obtained to interpret the effect of chemical reaction kinetic coefficients on the rate of absorption of the gas. The effect of chemical reaction on the rate of absorption for a fluid-fluid system is expressed in terms of the factor 7 = (kL/kL) - 1 where k and kL are the liquid phase mass transfer coefficients with and without reaction respectivelyo Various models describing this factor have been developed, the Hatta, the Sherwood-Wei, and the Sherwood-Ryan models based on the classical two film theory, the Higbie and the Danckwerts models based on penetration theories and the Kishinevskii model based on surface renewal theoryo The liquid phase mass transfer coefficients with reaction were determined in a stirred pot reactor where both the gas and the liquid phases are stirred, the interface between the two fluids smooth and the interfacial area known. The system used was the absorption of oxygen by solutions of sodium sulfite alone or with CuS04 and CoCl2 as the positive catalysts, and mannitol, CH20H (CHOH)4 CH20H, benzyl alcohol, C6H5CH20H, and catechol, C6H4(OH) 2 as the negative catalystso Runs with positive catalysts show increased rates and those with negative catalysts decreased rates. Increase in stirrer speed, at constant catalyst concentration, increased the absorption rateo Use of 99.5 per cent oxygen gas in place xii

of air gave slightly lower coefficients except at catalyst concentrations less than 10-9 gm mol CoCl2/l. Varying the sulfite concentration showed that the absorption rate was first order in sulfite concentration up to 0.14 gm equiv/i and as the concentration was increased further the rate increased and then declined. The liquid phase mass transfer coefficient for absorption without reaction, kL, was determined by the absorption of oxygen in pure water. The factor 7 = (kL/kL) - 1 for various models was compared with the data. Measured absorption rates 4-50 times those without reaction showed the increase as expected from the various models for infinitely fast reaction, namely those of Hatta, Sherwood and Wei, Higbie, Danckwerts and Kishinevskii. The data cross the various theoretical lines as the rate increases. In order to determine the chemical kinetic coef++ ++ ficients for Cu and Co catalysed reaction air was sparged through sodium sulfite solution in the rapidly stirred baffled reactor. Previously reported coefficients obtained by conventional techniques were found not to be true chemical kinetic coefficients since the mass transfer resistance was found to be important, as established by lower stirrer speed and air rate giving lower transfer rates. The chemical kinetic coefficient for reaction without catalyst determined by taking into consideration the mass transfer resistance was found to be 11 x 102 liters/gm equiv min Using a recently published computer solution of the diffusion equation for the case of absorption with reaction in view of the penetration model the chemical kinetic coef++ ficients for reaction catalysed by Cu, Co, mannitol and benzyl alcohol as well as for reaction without a catalyst xiii

were determined. The chemical kinetic coefficient for reaction without a catalyst was found to be 12 x 102 liters/gm equiv min which compares favorably with that determined by the technique where air was sparged in a rapidly stirred solution. xiv

STATEMENT OF THE PROBLEM Present theory on mass transfer with chemical reaction is based on the assumption that the fluid dynamics of the system, gas-liquid or liquid-liquid, remains unchanged by the reaction. Various models have been proposed based on classical two film theory0 the penetration theories and the surface renewal theory for mass transfer with chemical reactiono Inadequate experimental evidence indicates that these models are far from satisfactory when each phase is turbulento The purpose of this research is to obtain mass transfer coefficients with and without chemical reaction for a gas-liquid system and to interpret the effect of chemical reaction kinetic coefficients on the absorption of the gas in view of various modelso In order to incorporate the effect of reaction on the absorption rate a knowledge of chemical kinetic coefficients is necessary The chemical kinetic coefficients should be determined for the reaction. xv

I. MASS TRANSFER WITH CHEMICAL REACTION 1. HISTORY AND OBJECTIVES Ao INTRODUCTION Chemical reaction accompanies mass transfer into a fluid for a large number of biological, chemical, metallurgical and geological processes of either engineering or purely scientific interest. Examples include corrosion, fermentation, combustion, digestion, electrolysis, oxygenation of haemoglobin, smelting and a host of industrial chemical processes such as the manufacture of nitric acid and sodium bicarbonate and refining of petroleum. In order to study the kinetics of mass transfer into fluids with simultaneous chemical reaction models have been developed by various workers. These models are based on the classical two film theory and the recent penetration and surface renewal theories. The film theory assumes the existence of physical films of finite resistance. The penetration theories assume unsteady state molecular diffusion of the solute into the surface elements

-2 of the fluid which are continually being replaced. The theory of surface renewal without penetration precludes the molecular diffusion of the solute into the surface element. The effect of chemical reaction on absorption is measured by the factor y = (kL/k - 1) where k and kL L L L L are the liquid phase mass transfer coefficients, with and without chemical reaction respectively defined by Equations 1 and 2. N = kL(CAi - 0) ( N = k(C C ) (2) A L Ai Ao (2) Expressions for 7, for each model will be derived. a. Models based on film theory The film theory assumes the presence of a stagnant layer of each fluid at the interface. The'thickness' of the fictitious film is calculated by assuming that the flux through the film is due to molecular diffusion only. The thickness is usually small enough for the transfer to be treated as steady state diffusion through the stagnant layer. (50) Whitman imagined that the turbulence in the liquid is damped out near the surface. The scale of turbulence and

the eddy diffusivity get progressively smaller as the surface is approached until the transport by the eddy diffusion becomes of negligible importance. Although it is realized that both molecular and eddy diffusion may be present the total resistance is supposed to be caused by the stagnant film through which transfer is solely by molecular diffusion. There are three models based on film theory; the Hatta model, the Sherwood-Wei ion diffusion model and the (18) Sherwood-Ryan boundary layer model. Hatta modified the two film model for the case of absorption with chemical reaction by assuming that the chemical reaction takes place in the liquid film. He derived an expression for the liquid phase mass transfer coefficient, k, for a rapid irreversible reaction as a function of the molecular diffusivities, the concentrations of the reactants and the film thickness. (43) Sherwood and Wei() modified the Hatta model correcting the diffusivities of the ions for the presence of (48) other ions. Using the treatment of Vinograd and McBain for diffusion in mixed electrolytes, Sherwood and Wei derive diffusion equations for each ion imposing the condition of electrical neutrality for the ion mixture. From these equations an expression for the liquid phase transfer coefficients as a function of diffusivities of individual ions

and their concentrations was derived. Their test of this model in a diffusion cell showed excellent results. The model has not been tested in a stirred pot or a flow system where eddy diffusion is also important. (41) Sherwood and Ryan propose the turbulent boundary layer model for a flow system. Following the film theory they assume that one mole of component A reacts rapidly and irreversibly with b moles of component B at a plane a distance YR from the interface. The mass transfer coefficient is then expressed as a function of the Schmidt number and the dimensionless distance from the interface, y This leads to results similar to those of Hatta with the important difference that the resistance per unit length varies with the distance from the interface. (12) Friedlander and Litt present a solution for the case of rapid chemical reaction in the laminar boundary layer on a flat plate. Their theory also leads to results (30) similar to Hatta's. Potter has reported theoretical work on instantaneous and irreversible reaction in the laminar boundary layer. Chambre and Young(5) made a similar study from a physicist's viewpoint.

b. Models based on penetration theories (19) Higbie proposed the penetration theory, later (6) greatly modified by Danckwerts in his'random surface renewal theory' which postulates that turbulence extends to the liquid interface so that the eddies are constantly bringing elements of fluid from the interior to the surface where they are exposed for a finite time before being replaced. Unlike in the film theory the surface is being constantly renewed. Higbie examined a wetted wall column assuming each element of the fluid surface to be exposed for the same length of time with transfer taking place at the same decreasing rate as into an infinite stagnant layer. Danckwerts modified the Higbie model so that the surface does not have an element of fluid exposed only once as in the wetted wall column, but the surface is repeatedly renewed by elements coming from the interior for various lengths of timeo Thus, the difference between these two models is in the concept of the surface age distribution. The average rate of absorption per unit area is obtained by integrating the rate of all surface elements of various ages.

-6 c. Model based on Kishinevskii theory (22) Kishinevskii proposed a theory which can be described as surface renewal without penetration. Eddy diffusion is taken to exist up to the interface with molecular diffusion into the surface element not playing a role. Danckwerts, on the other hand, considered that during the period of exposure of the surface element the absorbed gas molecules move from the interface into the element by molecular diffusion. Kishinevskii derived expressions for absorption with chemical reaction for two limiting cases, the complete and a negligible degree of unsaturation or neutralisation of the interface. In Kishinevskii's expression the ratio of diffusivities of reactants in the Hatta equation is replaced by a stoichiometric factor. If the concentrations are expressed as equivalents per unit volume this factor becomes unity. d. Models based on film-penetration theory (7) Following the observations made by Danckwerts and (16) Hanratty regarding the limitations of the film and the penetration models in their application to specific cases, (45) Toor and Marchello show that for purely physical ab

-7 sorption the two models are not separate unrelated concepts but rather are limiting cases of a more general model and that the two theories are complementary rather than being mutually exclusive. Toor and Marchello considered the transfer between a gas and stirred liquid which has its surface randomly replaced by eddies from the bulk of the liquid. If the eddies remain at the surface a short time, each may be assumed to absorb matter at the interface by unsteady state transfer. As the life of the element increases the penetration into the element increases and again after a long time a steady gradient will be set up in the element of film thickness, no more accumulation will take place, and material will be transferred through the element. Thus, the young elements follow the penetration theory and the old elements the film theory. The middle aged ones have the characteristics of both theories. In this intermediate case the penetration has reached the edge of the element but the steady gradient has not been established. If elements of all ages are present all three types of transfer take place simultaneously. This model is described as the film-penetration model. However, as shown in Appendix I in the case of absorption with

-8 reaction this model gives an expression for kL similar to Danckwerts' equation which covers all ages of surface elements. The effect of a chemical reaction on the rate of absorption can be measured by the factor 7 = (kL/kL - 1) L L the fractional increase due to chemical reaction. Table 1 gives this factor for various models as derived in Appendix I for the limiting case of infinitely fast reaction. B. PREVIOUS EXPERIMENTAL WORK (44) Stephens and Morris recognized the effect of diffusivity of the reactants and their concentrations in the bulk and at the interface obtaining a good correlation for the Cl -FeCl system, empirically based on the 2(gas) 2(aq) Hatta model, 0.83 kL' CBo L 1 = 0.75 [C.L [ Ai. (3) (34) Roper used a Stephens-Morris column for the absorption of chlorine (Component A) from air into solutions of 2-ethyl-hexene-l (Component B) in carbon tetrachloride with iodine as a catalyst. His correlation is 0.5 k (C + 0.0005) C - - 1 = 39.2 --— (a= kL C Ai (4) or

TABLE 1 Factor y for various models for infinitely fast reaction _ — ~- -` —.. I. Model r 7 = k /k - 1 A. Film models: i. Hatta model ii. Sherwood and Wei model iii. Sherwood and Ryan Boundary layer model B. Penetration models: i. Higbie model ii. Danckwerts model C. Kishinevskii model: D. Film-penetration model: i -- -- - -- I DB/DA. CBo/CAi B A Bo Al 9.16 x 10-4 q [ 6000n + 9600m 1* DA x CAi 7800(n + m) - 1356 q A A1L * For oxidation of sodium sulfite, the reaction used in this thesis, based on the equation for diffusion of ion: RT u+z / - F -G ~ n u+G+ n+ F n + _ + u C - + -CZ + + u G /nu C z -C \ \.0 I Cannot be applied to present work 1 erf (p/D) - 1 1 erf(P/W/A) - 1 CBo/CAi Expression same as that for the Danckwerts model. /

-10 0.5 k'. CB L CAi (5) In Equation 3 the increase in the coefficient is proportional to 0.83 power of CBo/CAi unlike Hatta's equation, Table 1, which has the exponent of one. According (39) to Sherwood and Pigford this is "just what would be expected if the reaction should become slow and effectively first order." However, the increase in the reaction rate due to catalytic action does not alter the index as seen in Equation 4. Roper concludes that this might be due to the index being a function of diffusivities. The correlation in Equation 4 was not satisfactory. Comparable results have (28) been reported for the C12-H20 system by Peaceman. To both Roper and Peaceman the most significant aspect of the failure was that while the film or penetration theory predicts that the liquid film coefficient should decrease with increasing concentration of chlorine it was found experimentally that kL remains constant for low concentrations and then increases sharply at higher concentration. Danckwerts and Kennedy concluded that the two penetration models lead to closely similar predictions about the effect of chemical reaction on absorption rates. Attempts to verify the penetration model have not been highly successful.

(19) Higbie found poor correlation between the experimental and theoretical values. He found that the data agreed with theory if he assumed the gas to undergo a'first order process' i.e. a process whose rate is proportional to the degree of unsaturation instead of being at equilibrium at the surface. Ripples at the interface and unknown end effects make the verification all the more difficult. Lynn, (26) Straatemeier and Kramers studied absorption in long and short wetted-wall columns in the light of the penetration theory. Their data has a remarkably low scatter, while the total uncertainty due to a systematic error was ~5 per cent mainly due to the film surface temperature. Danckwerts(1 has shown how to calculate the surface film temperature rise. Lynn, et al. could not eliminate the end effect when working with short columns. Pozin( concluded that the liquid film coefficient should be proportional to the 1/6th power of the density divided by the 5/6th power of the liquid viscosity. In their work on Cl2-air or S02-air and NaOH(a) system Pozin (aq) (32) and Opykhtina(3 confirm this observation. Van Krevelen and (47) Hoftijzer give an empirical correlation for k in terms of dirmensionless groupsL of dimensionless groups.

-12 C. OBJECTIVES Present theory on mass transfer with chemical reaction is based on the assumption that the fluid dynamics of the situation is unchanged by the reaction. Thus for a fluidfluid two phase system, liquid-liquid or gas-liquid, the resistance of one phase to mass transfer is assumed to be unaltered by the presence of chemical reaction in the other phase. The resistance of the other phase, where the reaction takes place, can be calculated from the various model's described above. However, the present theories are suspect as the inadequate experimental evidence available indicates that they are far from being satisfactory. This may be due to a change in the fine structure of the fluid dynamics in (42) the region close to the interface. Sherwood and Wei( in their study of liquid-liquid extraction observed differences in gross fluid behavior but this change usually cannot be detected. The purpose of this research is to obtain accurate values of kL for a gas-liquid system and to interpret the effect of chemical reaction on the absorption of the gas in terms of the various models. The chemical kinetic coefficients will be determined for the reaction using nonclassical techniques.

-13 2. DETERMINATION OF LIQUID PHASE MASS TRANSFER COEFFICIENTS A. SELECTION OF A SYSTEM AND APPARATUS a. Selection of a system In order to obtain accurate values of k and kL L L the system used must have a known interfacial areao Such is the case in a stirred pot reactor where both phases are stirred and turbulent, yet the interface between the two (36) fluids is smooth. Searle and Gordon and Sherwood and (42) Wei used such a reactor for their liquid-liquid studies. A gas-liquid system with negligible gas phase resistance offers a better opportunity for the study of various models as the larger interfacial tension may minimize the spontaneous (42) interfacial activities.( The oxidation of sodium sulfite (13) is such a system. Fuller and Crist studied the kinetics of this reaction using CuSO4 as a positive and mannitol as a negative catalyst. They reported a thousandfold variation in the values of reaction rate constants obtained by varying the concentration of the positive and the negative catalysts. The system selected for the present study was the oxidation of aqueous sodium sulfite by air or oxygen.

-14 b. Apparatus The apparatus, Figure 1, includes a metered supply of air or oxygen, gas heating and scrubbing equipment and a stirred pot reactor in a constant temperature bath. Air from a 30-psi main or cylinder oxygen is passed through a pressure regulator to a Drierite-glass wool air filter, a florator and a tubular heater. A mercury manometer gives the pressure drop. The heated gas is saturated with water before entering the reactor, Figure 2. The pyrex jar is 23 cm tall with a cross sectional area of 167 cm2. It is held tight between a platform and a gasketed stainless steel cover. Thermometers yielded the liquid phase, wet bulb and dry bulb gas tempera-. tures. The gas inlet and outlet ports, as well as the sampling port with a tube extending below the liquid surface, are located at the periphery of the cover. A Swagelok male connector welded at the center of the cover holds a teflon stirrer which has two blades, each 1 in. x 1/2 in., located 2 in. above the liquid surface and at the lower end a 1/8 in. rod 2 in. long kept 1 in. below the liquid surface. An electric motor and gear reducer runs the stirrer at 70 rpm. The reactor is maintained at 25~1~C by a constant temperature bath. All thermometers were calibrated against N.B.S. thermometers.

GAS EXIT REACTOR FLORATOR -----,, —,N.V. 30PSI AIR B S FILTER' -OR OXYGEN P. R.-PRESSURE REGULATOR IV V -VARIAC N.V. -NEEDLE VALVE T - THERMOMETER Figure L Flow Sheet.

S.S. COVER IBBER GASKET) It: HgTHERMOSTATKNIFEHEATER TUBE T. T2 T3 To - DRY BULB THERMOMETER - LIQUID - WET BULB - WATER BATH,, Figure 2. Reactor.

-17 B. PROCEDURE a. Determination of k - L One liter of sodium sulfite solution freshly prepared with analytical reagent grade sodium sulfite in double distilled water was placed in the reactor. Every precaution was taken to avoid contamination of the solution by metallic ion to which the reaction is very sensitive. A predetermined amount of the catalyst solution was added to the sulfite solution. The reactor was then covered, placed in the constant temperature bath and gas line and stirrer connected. The saturated gas flow passed at 0.5 SCFM with a line pressure drop of 32 cm Hg. The small pressure built up in the jar, about 1/2 cm of water, was neglected. When a thermal equilibrium was established in the system, i.e. when the wet bulb, the gas and the liquid temperatures reached 25 + 1~C, sampling started. A 10 ml sample of the solution was withdrawn each time by a pipette through the sampling tube and replaced by an equal amount of double distilled water, maintaining a constant liquid level. Since the gas was saturated with water only the oxygen transfer was important. All temperatures, pressures and the florator were kept constant. Samples, taken every 15 min, were analysed for

-18 sulfite by the standard technique. Runs were usually made for 3 hr. Positive catalysts were CuSO4 and CoCl2 and the negative catalysts were mannitol, CH2OH(CHOH) 4CH2OH, benzyl alcohol, C6HsCH2OH, and catechol, C6H4(OH) 2 b. Determination of k~ L Values of k~ for oxygen in pure water (without L reaction) were measured. The oxygen concentration in water (15) (38) was measured by Winkler's method. Sherwood and Holloway claim 1 per cent accuracy for their results with this method. A stream of nitrogen gas was passed over one liter of freshly boiled double distilled water in the reactor to provide an oxygen free atmosphere while thermal equilibrium was being established. As soon as it was reached nitrogen was turned off and air turned on for the remainder of the run. The runs lasted for 0, 20, 60, 120 and 240 min. At the end of each run air was turned off and nitrogen turned on simultaneously and the entire content of the jar was fixed for its oxygen content by injecting 4 ml of Winkler's manganous sulfate solution immediately followed by 4 ml of alkaline potassium iodide solution through calibrated hypodermics with extended needles reaching below the liquid surface. The

precipitate, Mn(OH) 2, was allowed to settle with nitrogen gas still on. Finally, 12 ml of conc. HC1 were introduced and the solution mixed thoroughly. The precipitate dissolved completely while a brown coloration appeared due to liberated iodine equivalent to the amount of oxygen absorbed. A 100 ml sample of solution was analysed for its iodine content, yielding the oxygen concentration and the rate of absorption. kL was then obtained from Equation 2. L C. RESULTS a. Calculations of k~ - L The rate of absorption of oxygen in pure water is given by N' = ko(C - C ( A Ai Ao (2) or N = k a. (C. CAo (6) A L Ai Ao Again, V dCA N = A dt (7) Therefore, dCA - = a (CAi CAo) (8) dt L Ai AO Hence

-20 ko dt = - L V dCA a. (CAi - C ( Ai Ao (9) On integrating, kL. =. nV k. At = - -. A in(C L a Ai - Ao) (10) With V = 1000 cm3 and a = 167 cm2 for a given run o 0_ 2.303. 1000 kL - 167 For a series of values of C samples or a series of runs samples or a series of runs A log (CAi - CAo) At from either a number of (11) k~ = - 13.75 [slope of log (CAi - CA) vs t] L Al Ao (12) To determine the amount of oxygen in the modified Winkler's method 100 ml of the sample was titrated against N/40 thiosulfate solution. For iodimetric estimation we have the following stiochiometric relation~ 1000 ml of N/10 thiosulfate = 0.8 gm of 02 (13) Therefore, 1 ml of N/40 thiosulfate = 2 ppm of 02 (14) and C - (ppm). 10-3 Ao 8 (15) The data and results are given in Appendix III. The average value of kL for nine runs is 0.057 cm/min or 0.118 ft/hr.

-21 A check of the consistency of the results is given in Figure 3 where Equation 12 is plotted. The line in Figure 13 has a slope corresponding to the mean value of kL = 0.057 L cm/min. The slope appears to be higher than that which might be obtained by drawing a line through the data'by the eye'. b. Calculations of k The data for each run were recorded on a data sheet, Figure 22, Appendix IV. The 02 absorbed during the period between samples equivalent to the sulfite consumed was calculated after making a suitable allowance for dilution by make-up water. Figure 23, Appendix IV is a typical calculation sheet. In the rate equation N' = k (C - 0) A = kLAi - (1) N' was determined for each run from a plot of gm equiv. A of oxygen absorbed vs time as in Figure 4. The interfacial area was taken as the cross section of the jar, 167 cm2. The interfacial concentration of 02 CAi was obtained from the equation N' = kg(pA- i) A g A A (16)

-4 15X 10 -4 IOXiO.......1 1 1 I EACH POINT IS A SEPARATE RUN THE LINE HAS A SLOPE CORRESPONDING TO k. =0.057 CM/MIN. -—' —— _-,.-L' C. - -4 5X10 -4XIO 4 X10 -4 3XO10 -4 2xlO klm \D r i i i I I -4 l xO M i..j I I I - -L -- I "'k I ft, % J-k 0 40 60 80 100 120 140 160 180 200 220 240 260 MIN. Figure 3. (CAi - CAo) versus Time,

.016 nlA^.012 0 co 0 C) w.008 0 ZS.006.004.002 0 n~~~~~~~~I J A / F r.- RUN 64 1.5xl1 GMMOL CuSO4/A I I I I I / l / i i i i.iiiii........ ok. - 0 30 60 90 120 150 180 210 MIN. Figure 4, Oxygen Absorbed versus Time.

assuming that Henry's law applies to this system. The value of k the gas phase mass transfer coefficient g for oxygen was estimated from that for water in air-water (46) system obtained by Udani and Gordon for a similar apparatus. The gas resistance was about 0.06 per cent of the total resistance, Table 8, Appendix IV. A sample calculation of CAi and kL is shown in Table 8, Ali L Appendix IV. i. Effect of catalyst concentration on k: _ _~__ _ _ _ __ - L The catalysts were CuS04, 4 x 10-9 to 2 x 10-5 gm mol/, CoC12, 1 x 10-ll to 2 x 10-5 gm mol/l, and the negative catalysts were mannitol, 5 x 10-6 to 1 x 102 benzyl alcohol, 5 x 10-7 to 1 x 10-4 gm mol/1 and catechol, 1 x 10-4 to 1 x 10-3 gm mol/l o In the case of positive catalysts greater concentrations resulted in visible black. precipitates presumably of copper or cobalt hydroxide. Figure 5-a is the plot of kL against the amount of catalyst added from the data in Table 9, Appendix IVo The data plotted in Figure 5-a were obtained for sulfite concentration range of 0.048 - 0.17 gm equiv/1. This was done during the earlier period of experimental work having relied on the statement by Fuller and Crist1 that

the catalysed rate was independent of sulfite concentration above 0.03 gm equiv/1. Later in this study the reaction was found to be first order in sulfite concentration below 0.1 gm equiv/1 o The data for k within a narrow range L of sulfite concentration, 0.07 - 0.12 gm equiv/1 taken from Figure 5-a and plotted in Figure 5-b indicates better the effect of the catalysts without confounding the results with change in sulfite concentrations. The effect of sulfite concentration on the rate for reaction without catalyst is indicated by the band between the dashed lines in Figure 5-a and Figure 5-b. While the rates obtained with mannitol and benzyl alcohol fall between the limits of kL without catalyst and kL as would be expected the rates with catechol fall L below k~ presumably because of the plugging of the L interface by the alcohol as reported by Udani and Gordon. (46) ii. Effect of stirrer speed on kL Gaden and (14) Schultz found the stirrer speed had no effect on k up L to 100 rpm and above that speed kL decreased. They added a relatively high concentration of catalyst, 10-4 gm mol CuSO4/l which is above the solubility limit. Possibly at

5_0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0 I 0'\ I -4 -9 -8 -7 -6 -5 -4 -3 0 10 I0 t o0 10 I0 10 10 GM MOL CATALYST/ Figure 5. a. k versus Catalyst Concentration for C 0.048 - 0.17 gm equiv/1. L Bo -2 10

5.0 4.5 4.0 3.5 3.0 2.5 _i -~c 2.0 1.5 1.0 0.5 0 I 1 Co0.121 - - c,_ =0.068 - - - - - - 0 kL FOR NO REACTION~....-. — --—. 0 ~I -10 -9 -8 -7 -6 -5 -4 -3 10 10 10 10 10 10 10 10 GM MOL CATALYST/ t Figure 5. b. k versus Catalyst Concentration for C = 0.07 - 0.12 gm equiv/1 L Bo -2 10

-28 high stirrer speeds the catalyst precipitates out as Cu(OH) 2, reducing the effective catalyst concentration and (29) lower values of k were obtained. Phillips and Johnson( L added 1 x 10-5 gm mol CuSO4/l as catalyst to their baffled reactor. With pure oxygen their data showed k to be L proportional to the 0.66th power of the stirrer speed up to 250 rpm. At higher speeds they observed a sharp increase in k. Yoshida et al. find similar results for Na2SO3-air L and Na2SO3-O2 systems. They have not specified the catalyst concentration used. Hyman and Van Den Bogaerde( have published a summary of similar work done by various workers on gas-liquid contactors using Na2SO3-air system. All used sparged reactors showing kL proportional to 1.6 (49) to 3.0 power of the stirrer speed. Voznesewskii and Klucharev observed the rate of absorption of oxygen in aqueous sodium sulfite to be unaffected by stirring. They explain this by assuming that the diffusion takes place during reaction between oxygen and sodium sulfite and additional stirring adds little to it. In view of the conflicting reports the effect of stirrer speed on kL was examined from 35 to 210 rpm using the best catalyst concentration, 2 x 10-6 gm mol CoCl2/l. At and above 21]0 rpm a vortex was formed increasing the

I! 1( A.-J,-.I 4 1 4 EFFECT OF STIRRER SPEEDS ON k L 7 ________ l _____ __ 0 ______.5 ____L.._, -- 2 ------ -------- ---.~ I 41 i 11.1ak 10 15 20 30 40 0 60 70 80 STIRRER SPEED R.P.M. 90 100 150 200 300 400 Figure 6. Effect of Stirrer Speeds on kL.

-30 interfacial area. Below 35 rpm a lack of turbulence was noted as indicated by suspended balsa shavings in the liquid. At low stirrer speeds a +2 per cent fluctuation in speed was observed due to reduced voltage employed which resulted in loss of torque. At high speeds the rpm varied less than +1/2 per cent Figure 6, k versus stirrer speed from L data in Table 10, Appendix V, shows kL increasing conL tinuously with stirrer speed. The stirrer speed of 70 rpm used in the determination of k in the absorption studies is well within the turbulent L region and is adequate as no ripples are formed at the surface at this speed. ii. Effect of 99.5 per cent 02 on k 99.5 per cent oxygen gas was used instead of air. In order to economize on oxygen each run was started with air until thermal equilibrium was reached. Air was then turned off and oxygen turned on for 20 min before starting to take samples. Figure 7 is a plot of k as a function of CoCl2 concentration for both Na2SO3-air from Figure 5-a and Na2SO3 from data in Table 11, Appendix VI. For the Na2SO3-O2 system k is L slightly lower than for the Na2SO3-air system except at low catalyst concentrations (below 10-9 gm mol/l ).

-31 I. ^~ 35 NogSCO-AIR 3D Na-SO —02,...'X... z.oi Ob OJB —-------------- ---------------- ------- a8 e e -7 GM MOL CoCt(, Figure 7. Comparison of Results for Air and Oxygen. 1C0

-32 When pure oxygen is used in place of air the interfacial concentration of oxygen increases, resulting in a higher driving force than that with air. But at high catalyst concentrations the reaction rate, which is high already, does not change commensurately indicating a higher'resistance due to chemical reaction'. iv. Effect of sodium sulfite concentration on k L (13) According to Fuller and Crist the oxidation of sodium sulfite in aqueous solution is of first order with respect to sulfite ion concentration when the concentration of the Cu catalyst was no more than 10-9 gm mol/l. Phillips (29) and Johnson report that the oxygen uptake rate was dependent on sulfite concentration only up to 0.2 gm mol/l. (14) Gaden and Schultz report that the rate is independent of sulfite concentration between 0.015 and 1.0 gm mol/1. In the present study kL was determined for the Na2SO3-air system with highest catalyst concentration, 2 x 10-6 gm mol CoC12/l, with 0.00135 - 0.894 gm mol Na2SO3/l. The solubility of oxygen in the sulfite solutions decreases with Na2SO3 and Na2SO4 concentrations thus decreasing the interfacial concentration of oxygen. In the absence, naturally, of the solubility data for oxygen in sulfite solutions the data for sodium sulfate solution as

2 5 I I I I —- - _ — I-I-I -- — + —- ----- - 041 0 - -j Y PREDICTED FOR k'=1100 FROM EQ 33. 2~ - eCBo, GM EQUIV.(SO3)/e Figure 8. Effect of CB on kL with and without catalyst. I I

(37) reported by Seidel was used after extrapolation, Figure 111, Appendix VII. Figure 8 is a plot of (kL/kL - 1) L L versus CB from data in Table 12, Appendix VII. It is seen Bo that k displays a first order dependence on sulfite ion L concentration up to about 0.14 gm equiv./l. Above this concentration the solubility of 02 in aqueous sodium sulfate decreases rapidly and presumably also in sodium sulfite. The viscosity of the solutions also increases, Tables 6 and 7, Appendix III, with corresponding decrease in diffusivity of 02. As a result the rate of absorption decreases at higher concentration. Some of the data obtained in this section will be used in Section 3 for the evaluation of various models. Runs were also made without any catalyst with 0.02 - 0.485 gm equiv Na S 3/1. In order to estimate values of the second order reaction rate constant, k', and compare them with those obtained without catalyst. The data, Table 12-b, Appendix VII, is plotted in Figure 8.

-35 3. COMPARISON OF MODELS WITH DATA It will be shown in Section I that the kinetic data (13) presented by Fuller and Crist are not true reaction rate constants but volumetric liquid phase mass transfer coefficients. The rate of sodium sulfite oxidation reaction is so rapid that the mass transfer resistance predominates and true kinetic coefficients cannot be measured. Such being the case, the comparison of k from various models L will be made for the limiting case of instantaneous irreversible reaction obtained with high positive catalyst concentrations. The film models of Hatta and of Sherwood and Wei, and penetration models of Higbie and of Danckwerts and the Kishinevskii model will be examined. The expressions for 7 from each model are given in Table 1 and the calculations in Appendix VIII. (33) As suggested by Reid and Sherwood the diffusivity of Na2SO3 was obtained from (l/n + l/n ) RT DB = (1/ + 1/A (7) + l/)(17)

-36 In the penetration models the factor 3, defined by (CAi//DB). e 2/DB - (CAi/VB) erf(p/DBN). e2/D" (CBo//D). e f P/DA ef(P (18) Bo.A A (18) is determined by trial and error. When C is large Bo compared to CAi, as in the present work, D is extremely small. For CAi less than 10.54 x 10-4 gm equiv./l the second term in Equation 18 can be neglected. Equation 18 then reduces to (CAi/ D) - (CBo/ A) erf(/vD ) = 0 (19) or erf(p//D) = [ CAi/CBO (20) The experimental values of y for rapid reaction were obtained from the runs with CoC12 concentrations between 5 x 10 7 and 2 x 106 gm mol/1, runs 33-49, Appendix VII and 87-92, Appendix IV. The data, Table 2, are plotted as (kL/k~ - 1) vs [(DB/D) (C Bo/C) ] in Figure 9 L L B A Bo Ai for comparison with lines predicted from various models, Tables 14 and 15, Appendix VIII. It appears that at low [DB/DA CBo /CAi] values the Danckwerts model fits the data and at high values the Higbie model is better.

-37TABLE 2 Data for 7 = (kL/k) - 1 L L Run # Amt of Co Cl2 gm mol/2 CB gm equiv.. CBo B Ai A dimensionless kL L k ~ 1 L 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 87 88 89 90 91 92 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 5x 5x 7 x 1. x 1 x 2x 10-6 10-6 10-6 10-6 10-6 10-6 10-6 10-6 10-6 10-6 10-6 10-6 10-6 10-6 10-6 10-6 10-6 10-7 10-7 10 -7 10-6 10-6 10-6 0 00270 0.00470 0.00656 0.00714 0.00764 0.0116 0.0172 0.0182 0.0196 0.0238 0.0344 0.0426 0.0490 0.0616 0.0716 0.0926 0.1426 0.081 0. 120 0.0772 0 106 0.081 0.052 1.40 2.43 3.40 3.69 3.95 6.05 9.02 9.40 10 30 13.00 19.20 23.80 27.90 35.90 41.60 56.40 88.60 42.00 61.97 36.14 54.89 41.85 26.48 3.35 3.78 4.13 4.34 4.86 9.20 11.85 20.00 13.20 11.10 12.70 24.80 29.00 32.00 29.10 39.90 48.40 17.10 28.07 32.28 35.14 34.09 42.63

-38 It is seen from Figure 9 that the data is not represented by any one of the theories but cross the various theoretical lines as the rate increases. At low absorption rates the data are best represented by those theories indicating greater rates while at high absorption rates the data follow those theories indicating lower rates. These theories assume that the hydrodynamics of this system remains unchanged. The lack of correlation between the theories and data may possibly be due to reaction induced turbulence at the interface of which the models do not take cognizance. Searle and Gordon (36) and Sherwood and Wei42) observed such an effect in liquid-liquid systems. They report higher rates than those expected if the fluid dynamics of the system were not affected.

-39 100 50 40 30 20 yea 10 5 4 3 2 I LINES FOR INFINITELY FAST REACTION / /f/// ////" / / /o 0 /______; / // _ / /> / // ____./ -. / IA_____T //// // /. / i /// / / // /0 /// *// / // DATA FOR FINITE REACTION / ----—, —--- _/ ^r ~ I 0 10 gm mMl CoC12/l 4// > < c; % 2x10" I m mol CoCI2/l /'.,_:,_, +~G/ 2 3 4 5 10 20 30 40 50 100 ('B C) DA CA, Figure 9. Comparison of models for infinitely fast reaction with data for reaction wiath high catalyst concentrations.

II. CHEMICAL KINETICS OF SODIUM SULFITE OXIDATION To understand the effect of reaction on the absorption of oxygen by sodium sulfite solutions the chemical kinetic coefficients of the reaction should be known. The reaction rate was varied during absorption with Cu in CuS04 and Co in CoC12 as the positive and mannitol, benzyl alcohol and catechol as the negative catalysts. Published kinetic coefficients are those of Fuller (13) ++ and Crist for reaction without catalyst or with Cu (1) and mannitol catalysts and Alyea and BSckstrom for reaction with benzyl alcohol. Those for reaction with Co catalyst could not be found in the literature. An attempt was made to determine the chemical kinetic coefficients with Co catalyst.

1. EXPERIMENTAL WORK a. Modification of the apparatus To reduce the diffusional resistance to oxygen a 20 mm diameter pyrex glass sparger of medium coarseness was attached to the air inlet tube submerged 2 in. below the normal liquid level. The stirrer was provided with an extra blade at right angles to and 1 in. above the first blade. The gas phase stirrer blade was removed. Four plexiglas baffles shaped like inverted truncated right angled triangles were provided along the periphery of the jar below the liquid level. They were 1/8 in. thick, 2 1/4 in. high with 1 in. base and 1/2 in. wide at the opposite end, kept in position by two plastic rings while the baffle assembly was held in the jar by two 1/2 in. polystyrene rods attached to the upper ring and reaching to the cover. b. Procedure Air was bubbled through the charge of 900 ml of double distilled water at 0.5 SCFM. When thermal equilibrium was reached a definite amount of the catalyst solution was

-42added. A known weight of sodium sulfite as crystals, or dissolved in 100 ml of double distilled water, was added. Two or three minutes later 10 ml samples were withdrawn at 1 min intervals and analysed iodimetrically for SO3. To withdraw bubble free sample the stirrer was stopped for 4-6 sec. Runs without catalyst were also made in the same manner.

-43 2 RESULTS a. Uncatalysed reaction (13) Fuller and Crist(1 assumed that sodium sulfite oxidation was first order in SO3 while oxygen concentration remained constant at saturation: d(SO3) kl(SO3) dt 3) (21) or k - A en(S03) kl At (22) The slope of log(SO3) versus time should give the pseudo first order reaction rate coefficient, kl o Figure 10 is such a plot for runs without catalyst, Table 16, Appendix IX. It is seen that the slope is not a constant but increases with decreasing S03 concentration showing that the data are not true first order. When plotted on an arithmetic plot, Figure 11 the rates appear constant for a given run yet decrease with decreasing sulfite concentration. Also, when the stirrer speed and the air rate are reduced, as in run J, Figure 11, the rate is considerably reduced. This indicates that the oxygen uptake is controlled by diffusion at high sulfite concentrations.

0.4 0.3 I I Runs A-I: 1300 RPM, 0.5 SCFM Run J: 400 RPM, 0.25 SCFM A 0.2 0.1 "..o 0 r) w 0.05 Q04 0.03 0.02 - -______ ^'"""*M ^(400R7M,025SCFM) D H G \ E I 0.01 0005 0.004 0003 0.002 0.001 0 I c. MIN t4 0 I 6 Figure 10. Reaction without catalyst, logarithmic plot.

Q30 Runs A-I: 1300 RPM, 0.5 SCFM Run J: 400 RPM, 0.25 SCFM 1 0.28 0 0.24 0.22 020 0.18 Q16 A'N~_ (400 RPM,0.25 SCFM) 1 * ~~~~~~~~~~~~~~~~~~C 0 0.14 0.12 0.10 0.08 \ n' Q04 0.02 0 0 2 4 5 0 1 2 3 4 5 MIN Figure 11. Reaction without catalyst, arithmetic plot. 6

-46 ++ ++ b. Reaction catalysed with Co or Cu (13) Fuller and Crist regarded the catalysed oxidation ++4 = reaction to be first order in both Cu and SO3 taking Cu as an additive factor in their equation d(SO3+ -- d(t3) = {(kl + ks(cu++) (Cu } (so+) (23) dt 3(CU (Cu)) (SO) (23) where kl has the same significance as before and k3 (C++ 3(CU+) was taken as a constant. Above about 10-9 gm mol CuSO4/l when Cu(OH) 2 precipitates the Cu concentration is dependent on SO3 concentration as the latter determines the OH concentration. The solubility product for Cu(OH) 2 is taken to be 1.6 x 10-19 (gm mol/l) (25) and the secondary equilibrium constant for sulfurous acid 6.24 x 10 8 (gm mol/), (25). Cu concentration is then ++ 10 12 ) (SO3) (24) Substitution of Equation 24 in Equation 23 and integration gives kl(S03) 1 + ks(C++). 1012 (t2 t) okl(SO )2 + 10 2.303 3(Cu++) (25) Fuller and Crist used 1 x 10-l9 (gm mol/1) 3 as the solubility

-47 product of Cu(OH) 2 and 5 x 10-6 for the secondary equilibrium constant of sulfurous acid. The average value of k 3(C++) they obtained was 2.5 ~0.33 x 106 liters/mol sec. The value of k 3(C++) calculated from Equation 25 for the Fuller and Crist data varied from a negative value to 1.734 x 10s, Table 17, Appendix IX. An average value of k (++) would be meaninglesso Similarly, if the Co catalysed reaction were assumed to be of first order in SO3 and Co and the solubility product of Co(OH) 2 taken as 2.5 x 10-16 (25) then ++ 1o56 x 10-9 ( ) (SO() (26) which on substitution in the rate equation and on integration gives kl(SO3)1 + 1.56 x 10- k3(C (t - t)k log (t2 - tl)kl g kl(SO)2 + 1.56 x 10-9 k(C++) 2303 3 3(Co++) (27) Values of k 3(o++) calculated from Equation 27, Table 18, Appendix IX, vary from negative to 0.068 x 106 and an average value would be meaningless. As kl and k3 are not constant Equation 25 and Equation 27 are invalids Figure 12 is a plot of rate data with Cu catalyst, Table 19, Appendix IX, and Figure 13 for the Co data, Table 20, Appendix IX.

The rates in Figure 12, Runs I and II, and in Figure 13 for maximum stirrer speed, approximately 1300 rpm, and air rate of 0.5 SCFM are constant; for Runs III and IV, Figure 12, where low sulfite concentration was used the rate seems to fall exponentially with time as in a first order reaction. Lowering the stirrer speed and air flow rate reduces the rate of oxidation, Run V, Figure 12, showing that the mass transfer is important. One therefore concludes that the reaction is so fast that the diffusion is always controlling even for runs without catalyst and the published rate constants are not true rate constants but usually correspond to volumetric liquid phase mass transfer coefficients. c. Determination of mass transfer resistance for kinetic study It has been shown that the kinetic coefficients reported for sodium sulfite oxidation reaction are not true kinetic coefficients because the mass transfer resistance controls. In order to estimate the true second order reaction rate coefficient the mass transfer resistance is determined as follows.

-49 V) 0 0 1 2 3 4 5 6 MIN. Figure 12. Reaction with Cu++ catalyst.

-50 0.14 Q12 1300 RPM; 0.5 SCFM AIR o Ixl7 GM MOL Co C 2a/ b IxlOT GMMOL CoCt2/t c IxIO GMMOL CoCt/t d IxlO GMMOL CoCt/l e IxlO GMMOL CoCl2a/ f xl6 GMMOL CoCta/L g2xl16 GM MOL CoCt2/l hSxlO GM MOL CoC2/C f* "0 U) m 0 CJ 0.02 0 I 2 3 4 5 6 MIN. Figure 13. Reaction with Co++ catalyst.

In liquid phase the rate of oxygen uptake can be represented as NA V R= a'(CAi - = k~ a ( - C L Ai Ao k. C ~ C k Bo Ao (28) where K is the overall liquid phase transfer coefficient with reaction and a~' - a/V or V 1 N [CAi -] a - ^'^Ai-^o C -0)] N [(CAi CAo) + (CAo ~) ] A k1 1 L a k~ CBo (29) For reaction without catalyst a plot of --- KR a versus - with intercept of k — would have a slope Be L a of 1/kg. The coefficient ki a" was determined in the same manner as kL in Section I, B, b, except that the air was L bubbled through the water and the stirrer speed was 1300 rpm with baffles provided as in the kinetic study. Slope of the

-52 curve, in Figure 14 from the data in Table 21, Appendix IX, using the experimental value of CAi gave the value of k~ a' as 12.2 min. L The experimental value of CAi is about 10 per (21) cent below that in the literature. Despite great effort and careful checking of solutions this discrepancy could not be explained. If the error in all oxygen determination was of the same percentage magnitude then the value of k~ a~ will be unaffected for it is obtained as a function L of the slope of a ratio on a semi-logarithmic plot. If the analysis of low concentration of oxygen is correct while the high saturated one is in error then the value of the slope obtained by using experimental CAi is about 20 per cent higher than the slope obtained by using the literature value. The corresponding value of kL a~ is 20 per cent lower. It appears from Figure 15, which is a plot of KRa versus - with intercept of k0, that any KR aU Cv ekr a' lower value of 1. will not be consistent with the rest k0 a of the data on that plot. Therefore the value of kL a' obtained with experimental CAi is accepted. The curve in Figure 15 is obtained from data in Table 22, Appendix IX for 5 runs and with intercept of [kol = 0.0822. The data for CB is taken from the L

-53-.& 0. 4 o 49 -5 0 - 72,OO 5 20 25 ( 300 SECONDS Figure 14. Determination of kL a'. L

-54 0.18 016 0.14 I I I I I FROM THE SLOPE kTIIOO LITRES ^ ^ ^s i' GM EQUIV. X MIN. -' m m mb'a, 0.12 0.10 0.08 * RUN H A RUN D, FI G 0.06 0.04 0.02 0 0 20 40 60 80 100 120 I/C8o LITRES/GM EQUIV. Figure 15. Determination of k' for reaction without catalyst.

lines in Figure 11 between the range of 0.01-0.1 gm equiv/l as the concentration below 0.01 gm equiv/l is subject to analytical error and at concentrations above 0.1 gm equiv/l the reaction is no longer first order in SO3, Figure 8. The slope of the curve in Figure 15 gives kQ = 1100 liters/gm equiv min do Determination of chemical kinetic coefficient, k" from kL L_ Brian, Hurley and Hasseltine( give a computer solution for second order reaction in mass transfer processes with penetration theory. They developed an approximate expression for 7 o a +1 o (/7T) t+ 1 anh [ v/. M 1 - (/T)] (30 [a/M ~ (30) Where M =E /4 (k C ) (31) Bo (31) a = (k /k) - 1 is obtained by the Danckwerts equation for a L L infinitely rapid reaction, Table lo When [ /M o /l - (7 )] is greater than 5, as for the thesis data, the denominator in Equation 30 approaches unity and Equation 30 can be written as

-56 My + 1 = / J / yi r ) (7 r (32) or 7a o (Y + 1) 2 M a ( j'a 7 (33) which will give the values of second order reaction rate coefficient k' According to Equation 33 the value of k' for reaction without catalyst is about 1200 liters/ gm equiv min, Table 24, Appendix IX. This value is based on the average of five runs at different sulfite concentrations which gave k' = 1203 liters/gm equiv min o It compares favorably with the value of k~ obtained from Figure 15, 1100 liters/gm equiv min o Using the results of Figure 15 and those of Brian, et alo, Equation 33, the dashed line in Figure 8 is predicted for reaction without catalyst. This line could be drawn before any rate data is taken for a smooth surface. The agreement between the data and the predicted line for reaction without catalyst, Table 23, Appendix IX, plotted in Figure 8 is excellent. Values of k' estimated from Equation 33, Tables 25 and 26, Appendix IX, for reaction catalysed with Cu and Co are plotted as a function of catalyst ion concentration,

.-6 r E u z 2 (, -j Q: -1 10 3 i 2 CY w if) - I-I 101 —-----------— I (b)k'FOR CO, El WITH VARIOUS AMOUNTS OF COCe2 ADDED A WITH 2 x 10 GM MOL COCt2z/ ADDED 1 dt04L __ I 4_ I I.A A A A -El A UNCATALYSE O 10~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ I -'1 10 CALCULATED Cu CONCENTRATION, GM MOL/E 168 167 CALCULATED CO CONCENTRATION, GM MOL /t 5xl67 Figure 16. Second order kinetic coefficients from kL versus calculated catalyst ion concentration.

-58 Figure 16. For the sake of comparison k' for Cu -catalyst computed by using the constants ki and k3 by Fuller and (25) Crist and those corrected by using constants from Latimer, Table 27, Appendix IX, are also plotted in Figure 16. It Is seen that the values of k' obtained by Fuller and Crist are much lower than those calculated here as would be expected if their values were low because of mass transfer resistance. (29) Phillips and Johnson report that oxygen absorption by sulfite solutions in unsparged vessel is not gas film or liquid film controlled because they observed no change in transfer rate due to agitation. To them it appeared that as the reaction took place in the bulk liquid and since the rate was dependent on the chemical reaction the major resistance to oxygen transfer must be in the liquid phase and that diffusion through a stagnant liquid film would not be the rate controlling step. It has already been shown in Section I, 2, c, that contrary to Phillips and Johnson, increased agitation in the liquid phase increases the rate of absorption. In Figure 10, Run J shows that the rate of absorption with stirrer speed of 400 rpm and air rate of 0.25 SCFM is lower than those with higher agitation and air rate, 1300 rpm and 0.5 SCFM. This indicates that the rate

-59 of oxygen uptake is controlled by mass transfer resistance. This is further supported by the kinetic data where the absorption rate is zero order in sulfite concentration as required if mass transfer were controlling. The value of the second order reaction rate constant, k' obtained from Figure 15, which takes into account the mass transfer resistance according to Equation 29, compares favorably with the value of k' computed from k obtained in a:n L unsparged reactor definitely establishing the effect of mass transfer resistance on the oxygen uptake. e. Reaction inhibited by mannitol For reaction inhibited by mannitol Fuller and (13) Crist report d(SO3) _ 1 x 10-5 k (S1 ) dt [l x 10l + (mannitol) 3 (34) Figure 17 is a plot of values of k~ obtained from. Equation 34 and from k as a function of mannitol concen-r L tration, Table 28, Appendix IX. As would be expected the values from k are larger than those from Equation 34 since L the latter does not give true reaction rate coefficients.

102 z 2 5 1 w I-O I: i-I,.0! _|______ ____{FROM k,__ - I: ~ ~., h I,i F I L ---- j ------------------ FULLER AND CRIST CORRELATION _Y - - -- -- - - -- II iI, _ -. _ _____ _= I | =, | | | =:= = = ==I 0 O. a d10' 106 10" I GM MOL MANNITOL/e Figure 17. Second order kinetic coefficients versus mannitol concentration. 10

-61 f. Reaction inhibited bd benzyl alcohol For reaction inhibited by benzyl alcohol in the (1) presence of light Alyea and BSckstrom give for 0.6 molar sodium sulfite solutions d(S03) - k dt zero 0.000019 gm equiv 0o0012 + (benzyl alcohol) 2. min (35) The constant 0.000019 includes a constant equal to the ratio of rates in darkness and light. Unlike mannitol the rate here is considered to be independent of SO3 concentration. For benzyl alcohol concentrations used in the present work, 5 x 10-7 to 5 x 10-5 gm mol/l, the rate predicted is practically constant as the denominator in Equation 35 is hardly affected. But the k data shows it L to be a function of benzyl alcohol concentration in this range, Table 9, Appendix IV. The rate given by Equation 35 is pseudo-zero order k =' k0 C C zero Ai Bo (36) or k zero (Ci A Co) (37)

-62 Figure 18 is a plot of k~ obtained from Equation 37 and those from k as a function of benzyl alcohol concentration L using Equation 33, Table 29, Appendix IX. The values of k~ from kL are higher than those of Alyea and Bgckstrom. This is in part due to their sulfite concentration being in region where the reaction is no longer first order in sulfite concentration whereas the thesis data was obtained at much lower sulfite concentration. g. Reaction inhibited by catechol Catechol is such an effective inhibitor that it (27) completely kills the reaction.( Also, the plugging of the interface by the alcohol reduces the mass transfer. The data on absorption in presence of catechol, Figure 5-a or 5-b, supports this. The kinetic coefficients for reaction with catechol would be meaningless. From the runs for chemical kinetic coefficients made here and elsewhere for the oxidation reaction with and without catalyst one can conclude that the coefficients previously reported are not true coefficients as mass transfer resistance is important. They are lower than those computed from mass transfer coefficients with reaction, k. This L

-63 0 w Li - K Wc 10 5x107 106 5xlo0 1 5xl10 GM MOL BENZYL ALCOHOL/I. Figure 18. Second order kinetic coefficients versus benzyl alcohol concentrations.

is to be expected if mass transfer were important. The existence of mass transfer resistance in the kinetic process is established. The chemical kinetic coefficients estimated from k with the numerical solutions of the diffusion equation L (3) published by Brian, et al. are consistent with present knowledge. This is very easily seen when one compares the value of the second order kinetic coefficient k' = 1100 liters/gm equiv min for reaction without catalyst determined by taking into consideration the resistance due to mass transfer with that computed from kL by the Brian solution, which is 1200 liters/gm equiv min

III. CONCLUSIONS Liquid phase mass transfer coefficients with and without chemical reaction for a gas-liquid system were determined using sodium sulfite oxidation reaction. From the absorption of oxygen into a turbulent solution of sodium sulfite with knwon interfacial area the following may be concluded. 1) Measured absorption rates 4-50 times those without reaction showed the increase as expected from the theories for infinitely fast reaction; namely those of Hatta, Sherwood and Wei, Danckwerts, Higbie and Kishinevskii. The data are not represented by any one of the theories but cross the various theoretical lines as the rate increases. At low absorption rates the data are best represented by those theories indicating greater rates while at high absorption rates the data follow those theories indicating lower rates.

-66 2) As expected the runs with positive catalysts, Cu and Co, show increased absorption rates and those with negative catalysts, mannitol, benzyl alcohol and catechol, decreased rates. The rate of absorption with reaction increased with increased stirrer speed in the range 35-210 rpm. The study of the effect of varying the sulfite concentration showed that the rate was first order in sulfite concentration below 0.14 gm equiv SO3/1. At higher concentrations the rate increased and then declined. Using 99.5 per cent oxygen in place of air gave slightly lower coefficients except at low catalyst concentrations (below 1 x 10-9 gm mol CoCla/l). 3) Previously reported chemical kinetic coefficients obtained by conventional techniques for the oxidation reaction with and without catalyst are not true coefficients but are lower because of mass transfer limitations. Kinetic coefficient for reaction without catalyst as determined by taking into consideration the mass transfer resistance is 11 x 102 liters/gm equiv min 4) Chemical kinetic coefficients were determined from absorption of oxygen using the solution of diffusion

equation with reaction based on penetration model. The kinetic coefficient for reaction without catalyst was determined to be 12 x 102 liters/gm equiv min. This compares favorably with one obtained by another method referred to above.

NOMENCLATURE A Component A in gas phase a rea, sq cm a~ Area per unit volume of the solution, a/V, cm2/cc b Gm mol of B reacting with one gm mol of A B Component B in liquid phase CA Concentration of A in bulk, gm equiv A/cc C Ai Concentration of A at the interface, Ai gm equiv A/cc CBo Concentration of B in bulk at the start, gm equiv B/cc Ca Concentration of A at a distance i from interface, gm equiv/cc CI2 Concentration of I2-,catalyst, gm mol I2/cc C, C Concentration of positive or negative ion, gm equiv ion/cc AC Difference in concentration (driving force) DA Diffusivity of A in liquid phase, cm2/min D Diffusivity of B in liquid phase, cm2/min -68

-69 DAB Diffusivity of the product AB in liquid phase, cm2/min F Faraday or 96,500 coulombs/gm equiv G, G Concentration gradient of ions, Ac/Ax, gm equiv/cc o cm g Conversion factor between M-L-T and F-L-T c systems, dimensionless H Henry~s law constant k Pseudo-zero order reaction rate coefficient, zero gm equiv/liter o min k Pseudo-first order reaction rate coefficient, min-1 k' Second order reaction rate coefficient, liters/gm equiv o min kl Homogeneous reaction rate coefficient, mink(Cu++) Catalytic coefficient for Cu ++ k 3(C + Catalytic coefficient for Co k Gas phase mass transfer coefficient, g lb mol/atmos o ft2 o hr k Liquid phase mass transfer coefficient with L reaction, cm/min or ft/hr kL Liquid phase mass transfer coefficient without L reaction, cm/min or ft/hr K k~ o kL e L

-70 KL Overall mass transfer coefficient based on k, cm/min or ft/hr L K Overall transfer coefficient in liquid phase, min-1 Distance from the interface, cm M Factor defined as (k' CBo e) m Concentration of 1/2 SO4, gm equiv 1/2 S04/cc n Concentration of Na, gm equiv Na /cc n, n Valence + N Stirrer speed, rpm NA Rate of absorption of A, gm equiv A/thin N' Rate of absorption of A per unit area, A gm equiv A/cm2. min N' Rate of absorption of AB per unit area, AB gm equiv AB/cm2 o min NB Rate of absorption of B per unit area, gm equiv B/cm2 o min N(e) Amount of gas absorbed in time e per unit area, gm equiv/min. cm2 N', N' Rate of diffusion of ion, gm equiv ion/cm2 o min + PA Partial pressure of component A in gas phase, atmos PAi Partial pressure of A at the interface, atmos

-71q Concentration of 1/2 SO3, gm equiv 1/2 SO3/cc R Gas constant, 8.3144 joules/~K gm mol of electrolyte s Fractional rate of surface renewal, 1/time t Time, min T Temperature, ~Absolute u, u Equivalent conductance of an ion, mhos o cc/cm o gm equiv ion U~ Mobility of Cation, cm2/sec o volt V Volume, cc V" Mobility of Anion, cm2/sec. volt xl Distance between the reaction zone and interface, cm X2 Thickness of the reaction zone in the liquid film, cm XL Thickness of the liquid film, cm + y Dimensionless distance from the interface or wall y Dimensionless distance from the wall to the R reaction zone A factor defined by the Equation 18 (kL/kL)- L L a 7 according to Danckwerts model for rapid reaction

-72 cp(t) Eddy diffusivity, cm2/min Surface age distribution function cp(y, C T + +. [ f Ai-C 0) The integral, dy ='C [A A jl/cr + E/V p NAi p. A stoichiometric factor, number of moles of A reacting with one mole of B 77 Viscosity, gm/cm o min V Kinetic viscosity, cm2/min p Density, gm/cc Schmidt number, dimensionless, (v/DA) e'Time Shear stress at the wall, dynes/cm2 Electrostatic potential, volts Subscripts A AB B g i L relates relates relates relates relates relates to Component A to product AB to component B to gas phase to interface to liquid phase

-73 o relates to bulk R relates to the reaction zone +, - relates to cation and anion respectively Superscripts o indicates absence of reaction per unit area when it refers to the flux

REFERENCES 1. Alyea, H. N. and Ho Lo BSckstrom, JoAoCoS., 510 90, 19292. Barth, Ko, Z Physo Chemo, 9, 176, 1892. 3o Brian, P. Lo T., Jo Fo Hurley and Eo Ho Hasseltine, A.IoCh.EoJ., 7, 226, 1961. 4. Carslaw, Ho S. and J. Co Jaeger, Conduction of Heat in Solids, 2nd edo Oxford University Press, 1947. 5. Chambre, P. Lo and J. D. Young, Physics of Fluids, 1, 48, 1958. 6. Danckwerts, P. V., Indo Engo Chemo, 43, 1460, 1951o 7. Danckwerts, Po V., Ao.ICh.E.J., 1, 456, 1955. 8. Danckwerts, P. V., Transo Faraday Soc., 46, 300, 1950o 9. Danckwerts, Po V., Trans. Faraday Soc., 46, 701, 1950o 10. Danckwerts, P. Vo, Appo Scio Reso, 3A, 385, 1953. 11o Danckwerts, Po V. and A. Mo Kennedy, Transo Insto Chemo Eng., 32, S49, 19540 12. Friedlander, So Ko and Mo Litt, Chemo Engo Scio, 7s 229, 19580 13o Fuller, E. Co and R. H. Crist, JoAoC.So, 63, 1644, 1941o 140 Gaden, E. Eo and J. E. Schultz, Indo Eng. Chem., 48, 2209, 1956o -74

-75 15. Grant, Jo, Sutton~s Systematic Handbook of Volumetric Analysis, 13th edo, Butterworth Scientific Publications, London, 1955. 16. Hanratty, T. J.0 AoIoCh.EoJo, 2, 359, 1956o 17o Haskell, Ro, Physical Review, 27, 145, 1908. 180 Hatta, S., Technolo Reports, Tohoku Imperial Univo, 8, 1, 1928o 19. Higbie, R., Trans. Amer. Insto Chem. Eng., 31, 365, 19350 20 Hyman, Do and Jo Mo Van Den Boaerde, Indo Engo Chem o 52, 751, 19600 21. International Critical Tables, McGraw-Hill Publishing Company, New Yorko 22. Kishinevskii, M. Kho Zho Prikladnoi Khimii, 24, 542, 1951. 23. Kishinevskii, M. Kh., Zho Prikladnoi Khimii, 27, 382, 1954 24 Kishinevskii, Mo Kh. and Ao Bo Pamfulov, Zho Prikladnoi Khimii, 22, 1173, 1949. 25. Latimer, Wo Mo, Oxidation Potentials, 2nd ed., Prentice Hall, 1952o 26. Lynn, S., Jo Ro Straatemeier and Ho Kramers, Chemo Engo Sci., 4, 2, 49, 19550 27. Mellor, Jo Wo, A Comprehensive Treatise on Inorganic and Theoretical Chemistry, Vol X, Longmans Green, New York, 1956. 280 Peaceman, Do Wo, Thesis, MoI.To 1951o 29. Phillips, Do Ho and M. J. Johnson, Indo Engo Chemo, 51, 83, 19590 30. Potter, 00 Do, Trans. Insto Chemo Eng., 36, 415, 19580

31o Pozimn M. E., Jo Applied Chemo, U.S.S.Ro, 19, 1201, 1956o (English summary, Ind. Engo Chem., Vol 41, 12, 1949) 32. Pozin, M. E. and Ao Mo Opykhtina, J. Applied Chemo, U.S.S.Ro, 20, 523, 1947. 33. Reid, R. Co and T. Ko Sherwood, Properties of Liquids and Gases, McGraw-Hill Publishing Company 34. Roper, G. H., Chem. Eng. Scio, 2, 18, 1953. 35. Scriven, Lo E. and R. L. Pigford, A.I.Ch.EoJ., 4, 429, 1958. 36. Searle, Ro and Ko Fo Gordon, AoIoCh.E.Jo, 3, 490, 1957. 37. Seidel, A., Solubilities of Inorganic and Metal-organic Compounds, Vol I, 3rd ed., D. Van Nostrand Company, 1940 38. Sherwood, To Ko and Fo A. L. Holloway, Trans. A.IoCh-Eo, 36, 39, 1940. 390 Sherwood, To K. and R. L. Pigford, Absorption and Extraction, 2nd ed., McGraw-Hill Publishing Company, 1952. 40. Sherwood, To K. and C. E. Reed, Applied Mathematics in Chemical Engineering, McGraw-Hill Publishing Company, 1939. 41. Sherwood, T. Ko and Jo M. Ryan, Chem. Eng. Sci., 11, 2187, 19590 42. Sherwood, To Ko and J. C. Wei, Ind. Eng. Chem., 49, 1030, 1957. 43. Sherwood, To Ko and Jo C. Wei, A.IoChoEoJo, 1, 522, 1955o 440 Stephens, Eo J. and Go Ao Morris, CoE.P., 47, 5, 232, 19510 45o Toor, H. L. and Jo Mo Marchello, A.IoCh.E.J., 4, 97, 1958. 46. Udani, Lo H. and K. Fo Gordon, A.I.Ch.EoJ., 5, 510, 1959.

-7747o VanKrevelen, D. WO and Po J. Hoftijzer, CoEoPo, 44, 529, 1948o 48o Vinograd, Jo Ro and J. W. McBain, J.A.CoSo, 63, 2008, 1941o 49. Voznesewskii, So Ko and Lo A. Klucharev, J. Geno Chem., UoS.Se.R. 2, 506, 19320 50. Whitman, Wo Go, Chem. Met. Eng., 24, 146, 1923. 510 Yoshida, F., Ao Ikeda, So Imakawa and Yo Miura, Indo Engo Chem., 52, 438, 1960o

APPENDIX I THE DERIVATION OF k L VIA VARIOUS MODELS -78

APPENDIX I DERIVATION OF kL VIA VARIOUS MODELS The effect of chemical reaction on mass transfer is measured by the ratio of liquid phase mass transfer coefficients with and without chemical reaction, k and kL L L respectively. To derive this ratio consider a rapid irreversible reaction, (gas) + (aq) = (aq) (38) A. The Film Models i. Hatta model: Figure 19 shows the reaction of (18,39) U Equation 38.139) W Q S i | I I R I I I I C I c I I I I I V Figure 19o Hatta Model -79

-80 The component A in the gas phase on contact with liquid at the interface PQ establishes an instantaneous equilibrium (35) with the liquid phase. Scriven and Pigford have demonstrated that such an equilibrium exists in the gas-liquid system during absorption. At the interface A dissolves physically in the liquid. The component B in the bulk is transported towards the interface. During this movement A and B react with each other in a reaction zone RS parallel to the interface and the product of the reaction, AB, is transported out of the reaction zone. For the gas film the rate of absorption per unit area is given by NA = kg(PA P Ai ) N' = k( - (39) When the solvent concentration is large compared to those of the components A, B or AB we can write the rate equation for the QS section of the liquid film as DA NA - (CAi - 0) (40) For the SU section similar rate equation is D' = - (C -0) = N' - NB x2 Bo A (41) and

-81 DAB N' = -- (m - n + ) = N' AB x2 (Bo NA (42) Now if the gas-liquid interfacial equilibrium is assumed to follow the Henry's law we have PAi = H Ai (43) Equation 39 to 43 give on elimination of PAi, CAi, n m, xj, and x2 (PA/H) + (DB/DA) Co A (x/DA) + (1/Hk) (44)...L A g (44) or CAi + (DB/DA) CBo N - A L/DA (45) The liquid film coefficient with reaction, k, defined by the Equation 1 N = kL(CAi - 0) (1) is obtained from Equation 45 as DA DB CB| k - -^ 1 + - o kL X L DA Ai (46) The rate equation for mass transfer without reaction can be written as D N' = A (C -C A xL Ai Ao(47)

-82 From Equations 2 and 47 we have k = DA/x L = L (48) From Equations 46 and 48 we then have kL DB Bo = o - 1 = -l L DA CAi (49) (48) ii. Sherwood and Wei model: Vinograd and McBain write diffusion equations for each ion imposing electrical neutrality for the ion mixture. For cation, IRT + G u+G+/n+ - u-G /nN+ F= + G +- nC+ + uC+C -+ F nC / i (50) For anion, RT u_ Z u+G+/n+ - Z uG -/n N' = - F G + n CuC ~- -F - Fan_ t - - - u C + Z u C (51) The derivation of these equations from first principles, ignoring the activity coefficients, the collision effects and the effects of ion pairs or ionic complexes, is given in RT u Appendix II. It may be noted that the factor 2. - in these equations is the diffusion coefficient of the ion in its free state and the factor in the parenthesis is the concentration gradient of that ion corrected for the presence of the other ions.

-83 The reaction Na2SO3a) + 1/2 O2(a) - Na2SO4, (aq) (gas) (aq) or following the electrochemical convention 1/2 Na2SO3(aq) + 1/4 02 (gas) - 1/2 Na2SO4 tag) (g-as) ~~~~(aq) (52) (53) is shown in Figure 20 according to the Hatta theory. Tables 3 and 4 give data required in Equations 50 and 51. I I.. L - I Figure 200 Sherwood and Wei model For Na - ion in x2 - layer, the rate of diffusion is obtained from Equations 50 and 51, using data in Tables 3 and 4, as - 7.97 x 10-4 9600(n2 - m2) - 2712 n q; NNa+ = x 7800(n + m) - 1356 q qm equiv. cm2 x min (54) Similarly for 1/2 SO3 - ion

TABLE 3 cm2 AC gm equiv gm equiv RT u cm2 u, ~. G = __, C, Ion Valence sec volt Ax cc cm cc F n min Na I 1 50/F (48) n m n+m 7.97 x 10-4 x2 2 /2 SO3 1 57o4/F (2) q o g 0 9.15 x 10-4 x2a 2 1/2 SO4 1 |80/F (48) n q mn + m q 12 75 x 10-4 SX- 2 2 I I

TABLE 4 u G gm equiv gm equiv Ion n min volt o cm2 u min volt cm Na 3000(n - m) 3000(n + m) Na..... F X2 2F /2 SO- 3444 q 3444 q F X2 2F 4800(n - q - m) 4800(m + n - q) F x2 2F \Jl I 13 u G z ++ n + 3000 (n - m) F x2 u G n 4800(n - m) - 1356 q F X2 4800(n + m) - 1356 q 2F Z u+ C+ + + 3000(n + m) - 2F -; u

-86 N = 1/2 SO"3 - 9.15 x 10-4 X2 6000 n + 9600 m 1. q 7800(n + m) - 1356 qJ' gm equiv. cm2 x min (55) In the case of Na - ion NNa (56) Equations 54 and 55, then yield m = ~+ n2 - 0.281 n q Positive values of m will be used to eliminate m in Equation 55. Now, the rate of absorption of oxygen with reaction is given by Equation 1: NA = kL(C - 0) A L Ai (57) (1) or N' k = A L C.Ai Al (58) In xl - layer D A N' = - (CAi A xi A - 0) (59) For the entire xL - layer, L But N' x = N' x NA kx = A- A. x LL =. L CAi N (/2 SO-) 4' N. NA. x CAi CAi Ci C. (60) (61)

Therefore Equations 55, 59 and 60 yield 9.16 x 10-4 k X = D + - L L A CAi Al 6000 n + 9600 m 1 cm2 q 7800(n + m) - 1356 qI min (62) Dividing Equation 62 by DA and using Equation 48 we get.A. k L - 1 = L 9.16 x 10-4 DA o CAi 6000 n + 9600 m a q 7800(n + m) - 1356 q (63) iiio Boundary layer modelo For the turbulent (41) boundary layer model Sherwood and Ryan obtain kL p(yo, aA) CBo kL R (YR' B) CAi ~p(yo, O)A) [ap(yo Og) - (P(y+, oB) ] (64) where + cp (y' A) = o + c.-c dy Ai Ao --- 1/a + ~- ~/N v wgc/P Ai The integral in Equation 65 represents the mass transfer resistance from the wall or the interface to y o It is interesting to note that for CA = a Equation 64 gives A JD kL CBo - 1 = L Ai for DA = DB (66) Equation 66 is similar to the Equation 49. The same result is obtained when the ratio kL/ L approaches unity as R Jprocscnt Ij yR

-88 becomes very large and the value of a is not important. Thus, this theory leads to relations similar to Hatta's with the difference that the resistance per unit length varies with distance from the wall. B. The Penetration Models The difference between the Higbie and the Danckwerts models is in the definition of the surface age distribution function, cp(t). To find the average absorption rate per unit area, the product of the fraction of surface which has age t and the stagnant liquid absorption rate for an exposure time t is integrated over all surface ages. Thus, the expression for average rate is 00 Jo (67) where N(e) is the amount of gas absorbed by unit area of stagnant surface in time e. It is now necessary to determine the surface age distribution function p(t) for both (7) the models. For the Higbie model the distribution function cp(t) for the exposure time e is 1 cp(t) = for t (6 e e (68) and

-89 cp(t) = 0 For Danckwerts model cp( for t > e (69) t) is given by -se cp(t) = s. e (70) where s is the fractional rate of renewal of the surface. By substituting Equations 68 and 69 in Equation 67 we get the rate equation for the Higbie model, as N re N(e).O o de (71) (6) Danckwerts has published the derivation of expressions for N(e) for different cases. For the case of purely physical absorption the partial differential equation and the related boundary conditions are as followso ac a2c as DA ax2 1. ii. 111ii. C=C C = CAo Ai C = CAi C = CAo' x > 0, = x = 0, e > O x = 0 e > o (72) (4) Solution for Equation 72 as given by Carslaw and Jaeger is C = CA + (CAi - CA) erfc [x/2JeD] ~~AAHence (73) Hence, N(e) = - D[dxa x=o = (CAi - CAo)DA/ T (74)

-90 Equations 71 and 74 yield A = 2ADA/ (CAi - Ao (75) On comparing Equations 2 and 75 we get, for the Higbie model kL= A2 v(76) For the Danckwerts model, the rate equation can be written as 00 N' = N(e) s. e de o (77) Equations 74 and 77 give N = DA. s (CAi CAo) (78) A A(Ai8Ac Therefore, for Danckwerts model we have, L = (79) (9) Danckwerts ( has shown that for instantaneous reaction between the absorbed gas and the reagent in solution, both the gas and the reagent obey the normal diffusion equations, but the boundary conditions are complicated. As Danckwerts has shown, for this case the flux, given by N(e) (= C Ai erf (P/VDA) A (80) where D is given by Equation 18.

-91 The expression for absorption rate with reaction for the Higbie model is obtained from Equations 71 and 80 as 2CAi. - 2^ -D- / - A er f (/) 81) From Equations 1 and 81 k for Higbie model is, L 2 L erf(/ A) DA/ (8 A) (82) Equations 76 and 82 give L 1 kL [erf(P/A)] (83) and L 1 S L [erf( //DA) (84) Similarly, the rate of absorption for the Danckwerts model is obtained from Equations 77 and 80 as ci -D As A erf(p/ A) (85) Equations 1 and 85 give k for Danckwerts model as L VDA s L = erf(P/8 A) (86) Equations 79 and 86 give

-92 k L 1 kO er f(/ D L A) (87) and k kL 1 kL erf(~/ DA) - IL A (88) C. Kishinevskii Model (24) Kishinevskii and others assumed that during the period of surface renewal the passage of gas molecules from the surface element to the bulk takes place by turbulent or convective mass flow and derived an expression for kL as follows: For pure physical absorption the rate is given by N = - DA. grad C (89) A A A (89) For unidirectional diffusion normal to the interface N = k(CAi - C) (2) A IL Ai Ao (2) Also, for the case of absorption with reaction the rate is given by N = k A - PAi (39) The amount of A diffusing in the direction normal to the

interface where chemical reaction is present is given by dN A d = ko( dA L ABi Al - AB - C ) dA (90) Letting A CAB = CAB AB ABi - C and taking C = 0 ABO AO Equation 90 gives dN A dA dA = k~(A C + CAi) L AB Ai (91) Also, dC d Therefore, AB t = f(CBo CAi) = I f(CBo' CAi) de; t 0 (92) A CAB e = Time of contact of surface element. Substitution of Equation 93 in Equation 91 gives (93) dNA dA dA = dA On integration, k~ T f(CBo, CA) de + CAi dA Equation 94 gives Equation 94 gives (94) A L f(CBo CA + CAi N, 0 ~f (C_, C.) de + C dA A L L Bo Ai Ai (95) or

NA = kL f(CBo, CA d A A L Bo Al A Ci,Jo. (96) or NA kL f(CBo, CAi) de + C'L = 0 aBo Ai Ai (97) For homogeneous reaction, the function f(CB, CAi) k'. C. CAi for there is no reaction in the bulk where Bo Ai C = 0. Therefore, AO N 0 1 N = k~| k' C C.de + C. A kL J CBo Ai Ai (98) (98) When the reaction is slow, k', CB and Ci can be Bo Ai considered constant so that e k' C C C. d = k'. C.C J Bo Ai Bo Ai o 0 (99) and N'= ka [k'C C e + C ( A = [k Bo Ai Ai (100) = K C C +ka C K Bo Ai + k Ai (101) where K = k' k. L Equations 39, 43 and 101 give K CB + kk A 9g PA [K CB + kL + k /H g Bo L 9 (102)

-95 For the case when unreacted gas molecules are present in the bulk, Equation 101 can be written as N' K CBo Ci + k(A - C(103) A Ba Ai L Ai Ao (103) Equations 39, 43 and 103 then give K CB k + ko p - k. C /H N' = NA = k K C + k + k /H (1 Bo L g (104) For the case of rapid reaction Equations 102 and 104 are found to be inadequate and inaccurate. In this case k' Co C.Ai d i k' CB CAi e o A B A(105) For rapid reaction case let k' CB. CAi de. CB 0 o (106) where PI is the stoichiometric factor. This is an element from the bulk with concentration CB which reacts completely using pi CB moles of absorbed gas per unit volume of the liquid. When concentrations are expressed in gram equivalents per unit volume pJ becomes unity. Substition of Equation 106 in Equation 98 gives N = k [CBo + Ai] for Pi equal 1. (107) A L B Ai ()

-96 Equations 39, 43 and 107 give k PA k C q A L Bo Ai o H +k L g (108) From Equations 39, 43 and 108 the rate is obtained as CB + H PA A - l/kAO+ H/k L g (109) Equations 102 and 109 show the effect of chemical reaction on the rate of absorption for different degrees of turbulence. Equations 1 and 102 give for low turbulence k k p L g A (k' e + 1) kO ko C 1(k, e + 1) + k /H L Ai L g (110) and Equation 109 gives for high turbulence k C kL CBo k C L Ai (111) Comparing Equations 49 and 111 we see that they differ in the factor Ji = 1 replacing the ratio of diffusivities. D. The Film Penetration Model To the partial differential equation for physical absorption,

-97 acA a 2C _ A = - D A se A ox2 (45) Toor and Marchello impose the following boundary conditions (112) i. e= ii. x= 0 iii. x = and obtain a solution similar (4) Jaeger as follows: Short times CA CA' C = C A Ai CA = CAi to the one by Carslow and NA = (CAi A n 00 (113) - CAi ) /DA/e 1 + 2 Y exp (na2/DAe) n=l. (113) Long times N' = (CAi A Ai D r -c A) -A 11+2 Z (- n27T2 Dee/2) n=l A (114) The difference between this model and the penetration models is the boundary condition iii. It is assumed here that at some distance i below the surface the concentration remains constant at CAQ and that a freshly formed surface has this concentration. Equations 113 and 114 show that for short times the penetration theory is approached and NA = vDA /e. (CAi - CA) (115)

-98 For long times the film theory is approached and DA NA = (CAi CA) (116) However, when the absorption with infinitely rapid reaction is considered the boundary condition iii for Equation 112 can no longer hold as CA = 0. The solution to Equation 112 is then the same as Equation 80 for the case of instantaneous reaction.

APPENDIX II THE ION FLUX EQUATION -99

APPENDIX II ION FLUX EQUATION Consider a diffusion cylinder, Figure 21, of cross section a sq cm containing a dissociated electrolyte of concentration C gm equiv./cc. In the diffusion process let C - dC gm equiv./cc be the concentration at a distance, dx, from the solution of concentration C -c.s.= a dx-^ C-dC C Figure 21o Ion concentration gradiento Let U' and V' be the mobilities of cation and anion respectively. The amounts of the ions migrating per unit time through the cross section of the diffusion cylinder for the two ions of valence n and n respectively are d C+ U'. a d C+ RT dt N dx dt + n+ dx F(117) -100

-101 and -dC_ V'. a dC_ RT dt - n dx F (118) The electrostatic forces that come into play as a result of such a gradient will be _ and + d_/ volts per cm dx dx respectively. The rate of migration of ions through the cross section as a result of these forces of attraction and repulsion are N =- U' a C d + + dx (119) and N = V' C d_ N =- V dx (120) When the rates of diffusion for the two ions under the combined influence of the concentration and the electrostatic potentials are equal it follows that for cation, U' a RT dC+ d+/ N - + + n F dx + d+ + (121) and for anion, N - + n - C n F dx dx (12 -(122) N' E N/a, gm equiv./cm2. min U' u+/F and V' -u /F Substitution for cation gives,

-102 N + U+ RT 1 F F 0 n dC+ C+ d@ dx + + n dx or — u+ C+RT F2 n RT F n+L d log C+ dLa dx + dF n+ dx + dxj (123) and for anion, U_ RT 1 dC_ C_ d] N = F F n d - or u C I d log C- dJ F2- n RT - --- F n Fan[ dx - dx.J (124) d- is eliminated from the above by subtracting the sum of Equation 124 for all anions from the corresponding sum of Equation 123 for all cations and by the condition of electrical neutrality, i.e. Z n = Z n + or or Z dN = Z dN + Z dN - dN + = 0 (125) Thus an expression explicit in ddx follows, 0 u+C+ - 2 F2n + [ d log C+ l RT -d-+ F n ddx +dxj u+C+ + F2 F n d log C_ d/ RT — - Fn dn dx - dx

-103 =u d F [C+ u_ dC_] = - RT _ d - d - F x [u+C+ + u C_] n dx n dxd n+ (126) Therefore, dx1 dx - RT [u+/n+. dC+/dx - u_/n. dC_/dx] [u+C+ + u C_] (127) d - _ R (Z u+G /n+ - z u G/n.) F. dx - - RT -+ dx (( u+C+ + Z u C_) (128) dC+ where G = + dx dc and G = - - dx Substitution of Equation 128 in Equations 123 and 124 gives N' = - n C + F n + + + Z u+G+/n+ - Z u_G_/n_ Z u C + Z uC + + (50) and. RT u N = - F n [G + n C Z u G /n - Z u G /n' + + (51)

APPENDIX III THE DATA AND CALCULATIONS OF k0 AND THE VISCOSITY DATA L -104

TABLE 5 Data and Calculations of kL L Duration of run min CAo gm equiv/i C - C CAi - Ao gm equiv/e A log(CAi -CAo) At min-1 ko L cm/min No. log(CAi - Ao) A log(CAi - CAo) 1 2 3 4 5 6 7 8 9 0 20 20 60 60 120 180 240 240 0.42 2.50 2.46 4.81 5.22 6.92 8.58 9.00 9.02 x 10-4 x 10-4 x 10-4 x 10-4 x 10-4 x 10-4 x 10-4 x 10-4 x 10-4 10.14 8.06 8.10 5.75 5.34 3.64 1.98 1.56 1.54 x 10-4 x 10-4 x 10-4 x 10-4 x 10-4 x 10-4 x 10-4 x 10-4 x 10-4 -2.9940 -3.0912 -3.0937 -3.2427 -3.2725 -3.4388 -3.7033 -3.8125 -3.8068 0.0000 0.09717 0.09953 0.2485 0.2783 0.4448 0.7092 0.8183 0.8127 0.004858 0.004976 0.004124 0.004639 0.003706 0.003940 0.003410 0.003386 0.0670 0.0685 0.0568 0.0638 0.0510 0.0543 0.0469 0.0465 I 0! z 62 = 5.32 x 10-4 a =,2/n = 8.3 x 10-3'3a' test shows all data within 3a limit Average value of ko = 0.0568 cm/min or 0.118 ft/hr L

TABLE 6 Viscosity of Na2SO4(aq.) at 25~C (21) water = 1 C.P. Concentration gm mol Na2S04/i 0.1 0.25 0.50 0.75 1.00 ~250 1.040 1.160 1.227 1.340 TABLE 7 Viscosity of Na2SO3(aq.) at 25~C with Cannon 100 Viscometer water = 1 C.P. (Density was measured with NBS hydrometers) Concentration gm mol Na2SO3 Sp. gr i gm/cc Cannon Visometer Time Na2SO3 - Min 77 t P water H20 H20 tso 3PS3 1.00 0.50 0.25 0.125 0.00 1.1146 1.0556 1.0263 1.0122 1.000 1.655 1.365 1.300 1.225 1.212 1.562 1.185 1.102 1.023 1.000 (pure water)

APPENDIX IV DATA AND CALCULATIONS OF kL WITH VARIOUS CATALYSTS -107

Figure 22. Sample Data Sheet Date: 10-30-60 Run # 64 Amt of Catalyst 1.5 x 10-7 gm mol CuSO4/i System0 S03-Air Other Conditions: Time No. hr Titration ml Temperatures ~C Florator 0.05 N 0.05 N 0.05 N A P I2 added Titer, (SO3) Water W.Bo DoB. Air Fo'R. cm, Hg 1 1715 20.10 2.90 17.20 24.8 24.6 24.8 25 50 32 2 1730 20.10 3.25 16.85 24.9 24.8 25.0 25 50 32 3 1745 20.10 3.68 16.42 24.9 24.8 25.0 25 50 32 4 1800 20.10 4.00 16 10 5 1815 20.10 4.36 15.74 6 1830 20.10 4.72 15.38 7 1845 20.10 5.12 14.98 24.9 24.8 25.0 25 50 32 8 1900 20.10 5.43 14.67 9 1915 20.10 5.87 14.23 10 1930 20.10 6.23 13.87 24.9 24.8 25.0 25 50 32 11 1945 20.10 6.60 13.50 12 2000 20.10 6.89 13.21 13 2015 20.10 7.24 12.86 24.9 24.8 25.0 25 50 32. l _ =. _- _ -......~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~_ I 0 oC I

Calculation Sheet Run # 64 Date 10-30-60 Actual Actual Cummulative Time, hr gm equiv S0~ / 1% correction gm equiv SO /e gm equicorre /ion gorrection gm equiv Na /I gm equiv 02/a gm equiv 02/a gneuvi~ ~ 1 orcinIgnAta M gin + Acua J 1715 1730 1745 1800 1815 1830 1845 1900 1915 1930 1945 2000 2015 0.08600 0.08425 0.08210 0.08050 0.07870 0.07690 0.07490 0.07335 0.07115 0.06935 0.06750 0.06605 0.06430 0.00086 0.00084 0.00082 0.00080 0.00079 0.00077 0.00075 0.00073 0.00071 0.00069 0.00068 0.00066 0.00064 0.08514 0.08341 0.08128 0.07970 0.07791 0.07613 0.07415 0.07262 0.07044 0.06866 0.06682 0.06539 0.06366 0.08514 0.08429 0.08345 0.08262 0.08179 0.08097 0.08016 0.07936 0.07857 0.07779 0.07701 0.07624 0.07548 0.00085 0.00084 0.00083 0.00083 0.00082 0.00081 0.00080 0.00079 0.00078 0.00078 0.00077 0.00076 0.00075 0.08429 0.08345 0.08262 0.08179 0.08097 0.08016 0.07936 0.07857 0.07779 0.07701 0.07624 0.07548 0.07473 0.0 0.00089 0.00131 0.00078 0.00100 0.00101 0.00123 0.00080 0.00147 0.00109 0.00116 0.00077 0.00109 0.0 0.00089 0.00220 0.00298 0.00398 0.00499 0.00622 0.00702 0.00849 0.00958 0.01074 0.01151 0.01260 I H \O I ~~~I I I I I I I_ _ L _ _ _ _ _ _ _ _ _ _I__ _ _ Figure 23. Sample Calculation Sheet.

-110 TABLE 8 io Determination of kg (2) = 0.853 ft2/hr (21) Dg (02) = 0.69 ft2/hr (21) Using Equation 110 g (02) from Sherwood and Pigford39) from Sherwood and Pigford 0.56 = k Dg(02) g (H20) Dg(H20)J and g (H O) lb mol = 0.31 hr0 ft2 atmos' hr o ft. atmos (46) We have 0, 56 k(02) 0 31 [0 8531.9(02) [0.853. 0 2 5 ^ rr-lb mol = 0.2755 h ft. atmos hr. ft. atmos 2.25 x 10-3 am mrol (min. cm2. atm) ii. Determination of % resistance due to gas phases For k = 1.104 cm/min L 1 1 H K k k L g L H = 7.884 x 10-5 atmos cc erry, 3d Ed gm mrol

-111 TABLE 8 (Continued) 1 1 7.884 x 105 KL- 2.25 x 10-3 + 1.104 = 4445 x 102 + 7.14 x 105 40445 x 102 % Resistance due to gas phase = 7 -1 x 100 = 0.062% Although the estimated value of k (O, is not exact, it is clear that the gas phase resistance is negligible. 0~ K L = k L iiio Sample calculations for CAi and k Ali L Run # 64 From Figure 26 N = 4.18 x 10-7 m equiv 02 A cm min l05 lb mol 02 = 5.16 x 10-5 lb 1 02 ft2. hr Equation 39 gives NA = k (PA -i) A g -A Ai pAi = A - N'/k Ai =A Ag PA = 0.2085 Atm k = 0.2755 t Table 8, i g hr. ft2 atm

-112 PAi TABLE 8 (Continued) 5.16 x 105.= 02085 - 0.2755 0.2755 = 0.2085 atm Ai H CAi 4.38 x 107 H 4 x 55.55 Perry, 3rd Ed. CAi 0.2085 x 4.00 x 55.55 4.38 x 107 = 10.54 x 10-7 gm equiv. cc From Equation 1 k L N' Ai 4.18 x 10 -7 cm 10.56 x i —7 = 0.397 in or 0.783 ft/hr 10.56 x 10- min

TABLE 9 Calculations of kL for Various Catalysts with Data from Figures 24-78 Amount of catalyst added gm mol/2 CBo gm equiv/Q A gm equiv cm2 x min kL, ft/hr Catalyst Amount of catalyst added gm mol/2 CBo gm equiv/Q N' A gm equiv cm2 x min kL, ft/hr Run # Catalyst Run # 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 CuSO4 CoC12 4 x 10-9 4 x 10-9 4 x 10-8 4 x 10-8 4 x 10-8 1.5 x 10-7 4 x 107 4 x 107 1 x 10-6 1 x 10-6 l'x 10-6 1 x 10-6 1 x 10-6 4 x 10-6 4 x 10-6 3 x 10-6 4 x 10-6 4 x 10-6 8 x 10-6 1 x 10-5 1 x 10-" 1 x 10-1 1 x i0-8 1 x 10-9 1 x 10-8 1 x 10-7 X 10-8 1 x 10 2 x 10-7 3 x 10-7 0.097 0.070 0.090 0.066 0.062 0.086 0.080 0.072 0.063 0.062 0.086 0.088 0.084 0.077 0.112 0.074 0.048 0.096 0.122 0.158 0.168 0.158 0.150 0.106 0.082 0.170 0.070 0.100 3.22 4.44 2.99 3.22 3.74 4.18 4.8 4.44 6.09 5.68 4.92 5.48 6.06 6.28 7.11 7.36 8.0 4.16 4.24 4.48 5.04 7.2 6.96 5.52 7.44 8.0 8.72 12.91 x 10-7 x 10-7 x 10-7 X 10-7 x 10-7 x 10-7 X 10-7 x 10 x l0ox 10-7 x 10-7 x 10-7 x 10-7 x 10-7 x 10-7 x 10-7 x 10-7 x 10-7 x 10-7 x 10x 10-7 x 10-7 x 10-7 x 10-7 x 10-7 x 10-7 x 10-7 x 10x 107 0.602 0.756 0.891 0.600 0.697 0.783 0.891 0.826 1.137 0.657 0.917 1.023 1.131 1.170 1.330 1.378 1.496 0.775 0.793 0.836 0.944 1.340 1.200 1.030 1.385 1.490 1.627 2.400 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 Mannitol Benzyl Alcohol Catechol None 5 x 10-7 5 x 10-7 7 x 10-7 1 x 10-6 1 x 10-6 2 x 10-6 5 x 10-7 5 x 10-6 1 x 10-5 5 x 10-5 1 x 10-4 2.5 x 10-4 5 x 10-4 5 x 10-3 1 x 10-2 5 x 10-7 1 x 10-6 2.5 x 105 x 10-6 1 x 10-5 5 x 10-5 1 x 10-4 1 x 10-, 1 x 10-4 1 x 10-3 0.081 0.120 0.077 0.106 0.082 0.052 0.086 0.097 0.130 0.090 0.116 0.092 0.048 0.068 0.156 0.100 0.124 0.092 0.096 0.136 0.124 0.152 0.146 0.092 0.098 0.0812 0.4780 11.28 x 10 16.88 x 10-7 19.48 x 10-7 22.04 x 10-7 21.28 x 10-7 25.60 x 10-7 4.16 x 10-7 3.68 x 10-7 3.46 x 10-7 3.28 x 102.88 x 107 2.40 x 107 1.22 x 107 1.00 x 10-7 0.84 x 107 3.4 x 10-7 3.44 x 107 3.16 x 10-7 1.50 x 107 1.42 x 107 0.34 x 10-7 0.62 x 10-7 1.39 x 10 8 3.68 x 10-8 8.40 x 10-8 3.54 x 107 3.68 x 107 2.100 3.155 3.620 4.120 3.940 4.790 0.776 0.685 0.646 0.622 0.532 0.440 0.228 0.187 0.157 0.629 0.642 0.590 0.275 0.266 0.065 0.114 0.026 0.069 0.157 0.76 1.01 I I

FIGURES 24 THROUGH 78 REPRESENT THE RATE DATA FOR VARIOUS CATALYSTS -114

-115-.012.010 LJ O.008 en Cx I I I I RUN * 59 4xlO GMMOL CuS04/L.. -,-, —I - I.._I____ 0.UU6.004.002 0 30 60 90 120 150 180 MIN. Figure 24..014 1 * - - RUN *60 /.012 - 4x10 GM MOL Cu S04/e o.010 - a. J 0 U).008..... _. G3 0.006 CY.004.002 z. 0 30 60 90 120 150 180ISO 210 MIN. Figure 25.

-116-.00.0 ~.00 i (.O0 13 )8 -- - ~ ~ ~ ~ ~ - I IIIII i 4x10 GM MROL CuS 4x lCdGM MOL CuSt~ )6 0 )4. 4 — - X,Z,.. o0 0 60 MIN. Figure 26. 90 120.012 0.010 0 ~.008 co - 0.006 0 X.004 0.002 0 0 I RUN #62 4xlO GM MOL CuS04 / ( I I I - - - I I~.... I I I / Kr 0 -— ~........... - ^ —- - - -~~~~i ) 30 60 90 120 150 180 210 MIN. Figure 27.

-117-.00.014 -........ I.... 1" I I I I RUN * 63 24xlO GM MOL Cu SO4/t 010 I _I 1 0, _-. 0 to 4 a.008 0 m 5.006 0 CD.004.002 0 0 I /r"I I i i i i i i -- Z C L -= I 30 60 90 120 150 180 MIN. Figure 28. 0.13 co RUN *664.012 - 1.5x10 GM MOL CuSO4/e z.V IV 0 o U) Go 5.oo0 0 CD.004.002 0 ( / /A L ~ ZZ I ZZ- - -- I I-GI ) 30 60 90 120 150 180 210 MIN. Figure 29.

co I 0.012! I —- ] - -- -- I RUN # 66.010 4xl GM MOL CuSLO/t.008.006 - 04 I 1.009 -- -—!- - -- --:^rz 0 30 60 90 MIN. 120 150 180 Figure 50,.0 0 s ed a 23.01.oc.00 RUN l65 F 10 4xl GM MOL CuSOQ/ )6 )2, 0-....- --- O.K - - -- -- I -- -.0c.o _ 0 30 60 90 120 150 MIN. Figure 31.

-119 014.012.010 AAM^ RUN * 67 - I x 10 GM MOL CuSO4/t / / ao w CD 0 U) 0.w CD / /.Ooe.006.004.002 0 ir /7 0 3 0 60 0 120 15C MIN. Figure 32. I' -' RUN *68 I x10GM MOL.,CuS zz <L, u m i i iii i mmu 012 a.010 sG:o 0 >.006 4.004 0.006 m 0 w.002 0 0 30 60 90 MIN. Figure 33. 120 150

-120-.020.018.016.014 LJ (0 I x:.l012 Go n 0.010,.00..008.006.004.002 0 I f RUN * 69 16'GMMOL/e CuS04 - -- /-/ ^I/1 1 Ie u: 0 30 60 90 120 150 K 0 210 240 MIN. Fiw 534.

.0012.0010 co.008 D.006 0 L&.004.002 0 RUN * 70 I 10 GM MOL CuS04/t __ /' z.~,i / [11 i 0 30 60 90 MIN. Figure 35. 120 150.016.014.012 Ca (/, Cl 008 Q o.010.006.004.002.ooe 0 I-1 RUN i# 71 3X10 Gl MOL CuSO4/ / I0 - __ -- I... v~~~~~~~~~~~~i,.. 0 30 60 90 MIN. Figure 36. 120 150

.020.018.016 ca,.014 0 (/). I I.._ RUN # 72 4xlO GM MOL CuSO4/t or[X/' RUN 473.022 4 xl0 GM MOL CuS04' -.020.018.016 D 14.012 f~f\ __ _ _ i- _ - - NCM 0 a I.uI -.010 -.008.006.004.002 A - - - - O CD:) ao 4o cu 0 I i\) o 0.008.006.004.002 0 / 4 (. r I I I 0 30 60 90 120 150 180 MIN. 0 30 60 90 120 150 180 MIN. Figure 37. Figure 38.

-123-.020.018.016.014.012 0. to e.010 0 O.006.006 P~fJ I RUN # 74 / 8xlO GM MOL CuSCQ/t j. I /1.002 / / V 0 30 6 B0 90 MIN. Figure 39. 120 150 180 Io 0 u1 GO 9 (DE J.IO -.008.006 -f'" iL'Ii i.vv-v.002 0 RUN *75 Ix 10 GM MOL CuSO I I I 0 30 60 90 120 150 MIN. Figure 40. 180

-124-.012. l - I IRUN# 76 I x10 GM MOL CoCf/t J.4.(.4.4 fAoIa 306 002 0 30 60 90 120 150 MIN. Figure 41..012 o.010 Lo 0 *008 0.008 m 4 0.006.004.o9e 0 30 60 90 MIN. Figure 42. 120 150

GM EQUIV. 02 ABSORBED a o ii 8 cD 8 e IZJ. xZ m. GM EQUIV. 0z ABSORBED 8 ~ 8. 8 i2 o —0 —--------- Of's —o _ 0- -'..... 0'NII-N~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~, FP - -- - I - I - r I

.016.014.012 0 Ial m.006.004.002 RUN # 80 I IO GM MOL CoC(l / __ -.', /.._..../.. /n 0 ( 3 30 60 90 MIN. Figure 45. 120 150.012.010 a o.008 2 o,*< o.006 3.004 002.00 I/ /0 RUN # 81. _ _0i GM MOL CoCIt/t,_ x..... / 0 30 60 90 120 150 MIN. Figure 46.

-127-.012.010 a w a:.008 0 Cn m N.006 0 O.004 LJ.002 0.016.014.012 0 o.010 cn t) m N.008 0 X)006 CJ Io.004.002 0 I I RUN # 82 _ 2x i GM MOL CoCf2/t 0/ 0 30 60 90 120 15 0i 0 MIN. Figure 47. 30 60 90 MIN. Figure 48. 120 150

a to Lii O U) m 4 0 0 N 2 O.02, I I -I RUN #84.0 22,10GM MOL CoC I /t.020 -C.oie I'018.016.014.012.010 -.008.006.004 nflt, _____ F / i.018.016.014 C w a.012 o 0 c) m a.008 S 0 D.008 L 0.006.004.002 RUN # 85 2x C GM MOL CoCI2/t / 0 0 / I /,,,....= IA I ro I l0 0 t^mi o 30 6o0 90 iu iou MIN. Figure 50., FW 1/ 30 60 90 120 150 I80

-129 a go 0.2 02.006.004 --- RUN* 866 3 x 107GM MOL CCy/t O K, I I I,, 0 30 60 90 120 1C MIN.?igure 51. /.01.0o1.oge.... 8.o co c.010 0 (a o" 0 5.006.004.002 I (, /- II - RUN # 87- /xlO'GM MOL CoCt/t _ _, 1,! / 0 0so 60 90 MIN. Figure 52. 120 1I0

-130-.021.02t m.024 0 o).01 0.00O 2 0 00'.0.h 0 6 RUN 88 / RUN # 88 5 xlO M MOL CoCI/ 30I 60 I 0 30 60 90 MIN. Figure 53. 120 150 0 Lo o aC N 0 w:: 150 MIN. Figure 54.

.04.04 AfW 0 CL 0 o (n 0 0) cD 0 Cl 0D.036.032...028.024 --.020...012 n f' ---- -- I ---- - --- /00 f.036 032. 028 O.024 Cn N4.020 0 3.016 CD Z.012.00.00S.004 0 I \-' I.0o,I RUN # 90 4 / Ix 10- GM MOL CoCG2/t06 90 /1' 1 1 1~~~~~~~~ ^. ~ ~ ~~~, I.0'r _. - - - 0 30 60 90 MIN. Figure 56. 120 150 0 30 60 90 Fi e N. Figure 55. 120 10

-132-.032.028 m.024 0 U) in i.020 N 0:,:.oa0.012.0 0.008.004.012.010 Qa O 0) 0 X.006;.004 a.002 2 0 60 90 MIN. Figure 57. 150 60 90 MIN. Figure 58. 150

-133 CD X.006 0 0 m.004 5.002 a0 i o 09 Q w m do hD 0 bJ cr.010.008.006.004.002 0.oo MIN. Figure 59. RUN #95 A-IO' GM MOL MANNITOLB 1~ ___ ___ ___ ___ ___ 0 30 60 90 MIN. 120 IS0 180 Figure 60.

.010 C QC at 0 co o) 0 w.UU.006 - di --.A8........ ____ \tL ___ ------ ----- - n00& 4 r.00 j-I I _ 6_ RUN' 96...._ xlO eGM MOL MANNITOL./ a / I' I I I CD 0 w o cn 0 m a 9 2 0.00-4 ~O.0028 YO.oo.00o % "I I I I I RUN # 97 -IXIO GM MOL MANNITOIt —i i/ 0 o0 sO 90 O10 1G0 MIN. Figure 61. - 0 30 60 90 120 10o MIN. Figure 62..041 -- - __.. _ - w c /, / 0.01 -— / --- RUN* 98.006 00-w4 - 2,x,'IO Q,.0O.. MANNitoI./f 0 s0 90 90 Ito 10 MIN. Figure 63..00 t.00 0 U) N 0 3.oo LLJ RUN# 99 i- 5xlO GM MOL MANNITOL/o 0 s0 so 90 MIN. Figure 64. 120 160

C C C 4 4 L ~1.008.u RUN' 100 z0 006-5x510 GM MOL MANNITOL/t n) 0 D ".004.. — 0 30 60 90 MIN. Figure 65. 120 150 IS0 0 (D 0 a 3 CJ 0 30 60 90 1 120 150 MIN. Figure 66. 180

0 0 co 4t N 0:0 (0.016 ~ bdA I RUIN l102 5xI GM MOL I - ENZYL ALCOHOL/tC K::::A I' _l0 I I --.0. A —..d- l II. < I -10 1fiS / 0 s0 60 90 MIN. Figure 67. 120 0 U) o ON 0,056,.04 -.040.032 int' InO -" /l.012.010 0 co'U - r.008 0 Co OQ.006 0 2.004:: 0.002 0 I I RUN * 103.Ix16lM MOL BENZYL - ALCOHOL/t LI 0.016.008 0 o a / RUN# 104 25Sx 10 GM MOL BENZ'L~/ I I iALCOHOL/e _. ) 30 60 90 I10 MIN. Figure 69. 190 _ i,..._... _ v 0 0 30 60 90 MIN. Figure 68. 120 160

-137 b, cu o" -in to 0 U) CD.048 -9. -.044.040.036 - - -1-.032.028.024.020...016.0 a12 — _ — - - -.008./ -- -- RUN# 105 5xl( GM MOL BENZYL ALCOHOL/P.004..... o. _ -0 30 60 90 120 150 180 210 Figure 70.

-138 a W co 0 o W. 0 L 0.006 9%OA4I RUN # 106 | A1xi0GM MOL BENZYL ALCOHOL / -.004.-.. 00- - 30t.i 60,0 U) m.o 0 0 (.01 o 2.0( 03 l16 I RUN * 107 1.5xlO GM MOL BENZYL ALCOHOL / e I 1 1. 1 1~ 12 -- ^^ 0 04 30 6 90i 0 0 30 60 s90 MIN. Figure 71. 120 150 0 30 60 90 MIN. Figure 72. 120 150 180 Q'I w m 0. u) =>.:. a ww0 006 I I RUN# 108'qxlCOGM MOL BENZYL ALCOHOL /t - I —-__ ____[I____ IC& m 0.( (n 0.(: C 0 w co 0J "- I %FI I RUN# 109 II2'xlO2GM MOL BENZYL ALGOHOL/I 008 - D04 _ ~ L""' ""I r" D1R 0V 04 00 20 150 1I0 O A u 30 60 90 1 MIN. Figure 73. 0 30 60 90 120 150 MIN. Figure 74.

-139 a w Uo 0 0 o" 0 w.*00 4 RUN# 110 rt104 GM MOL CATECHOL/ t.006 i -.004 Aha I I 0a w o CD 0 0 a RUNN #lil I Ix6 6GM MOL CAT CHOL/t.006..004.002'00, 0C 0 )......... - J - I. w - 0 50 60 MIN. 90 120 150 30 60 90 MIN, 120 ISO Figure 75, Figure 76..010 cw od d006:.004 w.002.002 RUN # 112 - NO CATALYST ADDED - __I 1__ I__.01( A% 7 0.00 o 4. 0.00 0 2.O C3 RUN #I 113 )9-NO CATALYST ADDED 6 )2 r / 0 30 60 90 120 Is0 MIN. 0 30 90MI MIN. 120 150 Figure 77. Figure 78.

APPENDIX V DATA AND CALCULATIONS OF k WITH DIFFERENT STIRRER SPEEDS L

-141 TABLE 10 Calculations of k from data in Figures 79-103 L CAi = 10.54 x 10-4 gm equiv./a; Catalyst concetration = 2 x 1 gm mol C / added Catalyst concentration = 2 x 10 6 gm mol CoC12/1 added C N' Stirrer Bo A speed gm equiv. gm equiv. Run # RPM 1 cm2 x min ft/hr..........:-;:~ ],,,,,,,,,L, _ _,,, ~.......................~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 35:40 41 45:, 52 60 62 76 80 80 85 85 90 100 100 120 125 140 150 165 175 180 200 200 210 0.126 0.216 0.156 0.200 0.156 0.276 0.340 0.244 0.380 0.276 0.444 0.352 0.432 0.344 0.352 0.424 0.240 0.460 0.164 0.520 0.252 0.288 0.324 0.406 0.411 2.34 2.64 2.58 2.46 2.30 2.70 2.97 2.91 2.80 2.96 3.93 3.76 2.86 3.70 3.62 2.92 2.54 3.91 2.91 3.29 3.40 3.70 3.90 3.33 3.54 x 10-6 X 10-6 x 10-6 x 10-6 x 10-6 x 10-6 x 10-6 x 10-6 x 10-6 x 10-6 x 10-6 x 10-6 x 10-6 x 10-6 x 10-6 x 10-6 x 10-6 x 10-6 x 10-6 x 10-6 x 10-6 x 10-6 x 10-6 x 10-6 x 10-6 4.37 4.92 4.80 4.59 4.29 4.92 5.55 5.43 5.22 5.51 7.34 7.03 5.34 6.83 6.75 5.41 6.22 7.30 5.51 6.14 6.34 6.89 7.27 6.23 6.64

FIGURES 79 THROUGH 103 REPRESENT THE RATE DATA FOR VARIOUS STIRRER SPEEDS

0..020 CD. o.012.0o0e - RUN I.004 1 EFF'EC OF,35 1.rM. 0 30 so 90 120 10 MIN. Figure 79. Qt 0 CD o u, S. 9;.049 -.o0..040- - -.056- --.032 - --.024.020-.012.001 RUN# e.004 ^y- EFFECT OF NM 40 R.RM. o 30 60 90 MIN. 120 150 Figure 80.

-144 C C < d 0 af.04 -..044 --.040........036 --- -- -.039 - ---- 024.020 i.o02 16.012 RUN# 3.008 — - EFFECT OF N, 41 R.P.M..004.... o0 0 30 60 90 MIN. 120 150 180 Figure 81.

-145 a w 0c 0 V) 4 m 0 w z.024 -. - -.020,.0 16.012 a —.,004.004 RUN# 4 EFFECT OF N, 45 R.P.M. 30 60 90 MIN. 120 150 Figure 82..032 /.028 / at c) 0 u) t) o 4n 0 0 O AI.020.016.012 -.008 RUN # 5.004 /EFFECT OF N, 52 R.P.M. o0 I 0 30 60 MIN. 90 120 150 Figure 83.

044 -.040.032 —.036.028.032.024 o.028 w I J.J ~ ilJ, a: /ir.020 O.024 o 0) 0 N ".016 o0.020 0 0 0.012 --:::)- -__ w 0.016 - / w 2 00/0.012 I.008 RU N #7.008 _____ ____ ____ /~~~.004.008 -- EFFECT OF N RPM RUN#6 0 <.004 -RUN60 30 60 90 120 EFFECT OF RPM, 60ORPM 0 ___________________ MIN. 0 30 60 90 120 150Figure 85. MIN. Figure 84.

.040.036 __I I /.040 -..-. ---.036.032.028 I a3 GI 0: 0 oV co 0 D a 0.03Z.028.024.020.016.012 rnon I I I I CD La 0 U) CD m 0 so un C) C9.3 /.024.020.016.012.008.004 0 RUN#8 EFFECT OF N, 76RPM i ii 1,1 I I -pI.004 0 RUN #9 EFFECT OF NI 80 RPM I I1 0 30 60 90 120 0 150 MIN. Figure 86. 3C 60 90 MIN. Figure 87. 120 150

-148-.064.060 / ).040.036.032 non I --- I.UZU a w 0.024 (/).04,.020 0 D.016 0 I (D.012.008 / RUN#10.004 - EFFECT OF N, 80RPM 0 0 30 60 90 120 150 MIN. Figure 88. a w m Or 0 o <c 0 o J 0.056 R.052.048.044 040.036.032.028 024.020.016.012.00- I.004 o1 i RUN II EFFECT OF N, 85 RPM v 0 30 60 90 120 150 180 MIN. Figure 89.

. /' CL O co m 0:) so 0 0 w 0 C3 068 - 064.060 -.056 D522.062.048.044.040.036.032.028.024.020.0126.006 RUN #12 EFFECT OF N, 85RPM.004 - Ok- --- ---- ---- ---- ---- --- 0 30 60 90 MIN. Figure 90. 120 150 180

-150 n.40 r 0 m co 4 0 0.036.032.028.024.020.016.012.008.004 0, I I / a I I I.048 044.040.036.032 0 m o.028 4 m O.024 w.020 0.016.012.008.004 0 4 I RUN # 13 EFFECT OF N j 90RPM, I I i I/ I RUN # 14 EFFECT OF N, 100 RPM 0 30 60 MIN. Figure 91. 90 120 Ira 0 30 60 90 120 MIN. Figure 92.

(n 0 0 w 2 CD o u..052 __..048.044.040.036 --.032.028.024.020.016.012.008 /~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.040 -. -.036.032 ~.028 0 X24 oJ 0?.020 Z.016.012.008.004 RUN # 16~ EFFECT OF,120 RPM 0 30 60 90 90 120 MIN. Figure 94..004 n RUN#15 EFFECT OF N 0 IOORPM l! l l I I v 0 30 60 90 120 0 50 MIN. Figure 93.

-152 N a Lu.048.044.040.036.032.028.024.020.016.012.008.004 ( C~~~~~~~~~~~~~~~.068.064.060.056.052.048.044 v.040.036 5.032 a a.028.024.020 3 I RUN 7 * 7 EFFECT OF N'125 RPM 20.016.012.008.004 ) 30 60 90 MIN. Figure 95. I O O MIN. Figure 96.

-153-.040.040.036 I I I,036.032.0 - 90 1 032 -.028.028 C0 _~.ozo: F.97. $.024.0- 24 - ).020.020 0 04.012 --- -- -.012-.008 --- -- -.008 RUN* 2.004.004 RUN 19 EFFECT OF N, EFFECT OF N /50 RPM 0 30 6 90 120 0 30 60 MIN. MIN. Figure 97. Figure Fiaure 98.

-154 a w co 0 m 4:) 0 0 CD LJ.040. - 1 -:036..032...^.028 -- 24 - -.020.016..012. - --.008. — - -.044.040.036.032 o.028 0 4 el.024 o.020 L.0.016.012.008.004 0 I I RU.N# 21.004 EFFECT OFN, 175RPM 0 30 60 91 12 0 30.60 90 120 MIN. 0 30 60 90 120 MIN. Figure 100. Figure 99.

-155 X)72.052'.060.048 -.056.044.052.040.048.036.044 cn.032 S.040 0 0n 4 4 c-:.026 - -.036.024 0.032 0.020 ___- - u.028.016 -- -- -- —.024..012 -.020.008 -.016.00 23.012 EFFECT OF N, 200 RPM 00 0 —-- I-I.006 0 30 60 90 120 MIN. RUN* 24 F 0004 EFFECT OF N7 200 RPM Figure 101. 0 30 60 90 120 150 MIN. Figure 102.

-156-.048.044.040.036.032 CD o.028 (I) 0D24 0.020.016.012.008. RUN#25.004 EFFECT OF N, 210 RPM 0 30 60 90 120 MIN. Figure 105.

APPENDIX VI DATA AND CALCULATIONS OF k FOR HE EFFECT OF XYEN CONCENTRATION FOR THE EFFECT OF OXYGEN CONCENTRATION -157

TABLE 11 Calculations of kL with 99.5% O1, Data from Figures 104-110 Amount of N' A catalyst CBo C Catalyst added gm equiv Run # used gm mol/2 gm equiv/i gm equiv/ cm2 x min kL, ft/hr 26 CO CCl 1 x 10-10 0.216 1.27 x 10-3 2.28 x 106 0.88 27 CO Ci2 1 x 10- 0.225 1.27 x 10-3 2.35 x 10-6 0.91 28 CO Cl2 1 x 108 102.24 x 106.86 29 CO Cl2 1 x 10-X 0.220 11.27 x 103 3.66 x16 1 141 30 CO Cl 1 x 10-6 0.198 1.27 x 10 6.4 0-6 j 2.47 31 CO Cl 2 106 0.248 1.27 x 103 839 x 6 3.24 32 CO C21 2 x 0.17 1.27 103 8.24 106 3.18 __ _ _..11 b __....... H \J1c00 I

FIGURES 104 THROUGH 110 REPRESENT THE RATE DATA WITH 99.5 PER CENT 02 FOR VARIOS C++ CONONS FOR VARIOUS Co CONCENTRATIONS -159

0 U) an a (D.044.040.036.052 0 CIl uJ n.028 o at.024 N > 020 0 LI (o.012.008.004 0 RU *27 EFFECT OF Po, GM MOL CoCt/t,' -/ XW 1~~~~~~ jra,.JI=C Oi= l raw~P~ L... I o0 I 1 0 30 60 90 MIN. Figure 104. 120 _ 0 30 60 90 MIN. Figure 105. 120 150

0 LJ C) 0: 0 n1 0 V) vi CM 0 w CD m a 0 tU 0 a 0.044.040.036.032.028 - D24.020.016.012.008 I I HJ )-J 004 0 I RUN#29 EFFECT OF P02 IO GM MOL COCt2/1 I I 1I i 0 30 60 90 MIN. Figure 106. 150 0 30 60 90 MIN. Figure 107. 120 150

-162-.112.104.096.088.080 a.072 In u1 m.064.0 0 0 J6 2.048 0.040.032.024.016.008 0 0 30 60 90 120 150 MIN. Figure 108.

a w Im a: 0 0) m o 0 0 w 0 30 60 90 120 150 I80 MIN. Figure 109.

-164-.080 072 064.056 Q: o.048 en 0 -::: 0.032 to.024.016.008 0 XIj I RUN #32 EFFECT OF P02 2x166GM MOL COCt2/t Ik LJI I 0 30 5 0 90 120 150 MIN. Figure 110.

APPENDIX VII DATA AND CALCULATIONS OF kL WITH VARIOUS SODIUM SULFITE CONCENTRATIONS WITH AND WITHOUT CATALYST -165

TABLE 12 (a) Calculations of kL and y with Data from Figures 112-136 and CAi from Figure 111 ko = 0.118 ft/hr (Appendix III) L DB/DA = 0.546 (Appendix VIII) B A Catalyst Concentration: 2 x 10-6 gm mol CoC12/2 CBo gm equiv/1 CAi gm equiv/2 N A gm equiv cm2 x min kL ft/hr C8o CAi DB CBo A Ai kL y =L k - 1 L Run # 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 0.00270 0.00470 0.00656 0.00714 0.00764 0.01160. 0.0172 0.0182 0.0196 0.0238 0.0344 0.0426 0.0490 0.0616 0.0716 0.0926 0.143 0.197 0.348 0.530 0.664 0.914 1.350 1.720 1.782 1.788 10.54 x 10-4 10.54 x 10-4 10.54 x 10-4 10.54 x 10-4 10.54 x 10-4 10.40 x 10-4 10.40 x 10-4 10.40 x 10-4 10.40 x 10-4 10.00 x 10-4 9.8 x 10-4 9.8 x 10-4 9.6 x 10-4 9.4 x 10-4 9.4 x 10-4 9.0 x 10-4 8.8 x 10-4 8.4 x 10-4 7.6 x 10-4 6.8 x 10-4 6.0 x 10-4 5.44 x 10-4 5.12 x 10-4 5.00 x 10-4 5.00 x 10-4 5.00 x 10-4 2.76 x 10-7 3.04 x 10-7 3.32 x 10-7 3.40 x 10-7 3.72 x 10-7 6.40 x 10-7 8.0 x 10-7 13.32 x 10-7 8.88 x 10-7 5.2 x 10-7 8.08 x 10-7 15.2 x 10-7 17.28 x 10-7 18.60 x 10-7 17.0 x 10-7 22.1 x 10-7 30.24 x 10-7 30.8 x 10-7 24.0 x 10-7 19.3 x 10-7 16.0 x 10-7 12.0 x 10-7 10.0 x 10-7 1.25 x 10-7 3.08 x 10-7 2.88 x 10-7 0.513 0.565 0.613 0.630 0.692 1.210 1.515 2.48 1.68 1.02 1.62 3.05 3.54 3.89 3.55 4.83 5.84 7.22 6.21 5.78 5.04 4.32 3.84 0.495 1.210 1.130 2.56 4.45 6.21 6.75 7.22 11.15 16.50 17.20 18.85 23.80 35.20 43.5 51.0 65.6 76.2 103.0 162.0 234.0 458.0 780.0 1106.0 1675.0 2640.0 3420.0 3564.0 3576.0 1.40 2.43 3.40 3.69 3.95 6.09 9.02 9.40 10.30 13.00 19.20 23.80 27.9 35.9 41.6 56.4 88.6 128.0 251.0 426.0 602.0 913.0 1440.0 1870.0 1945.0 1955.0. 3.35 3.78 4.13 4.34 4.86 9.20 11.85 20.00 13.20 11.10 12.70 24.80 29.00 32.00 29.10 39.9 48.4 60.2 51.6 48.0 41.6 35.6 31.5 3.18 9.25 8.57 (b) Calculations of kL and y for Reaction without Catalyst (Data from Figures 137-143) 114 115 116 117 118 119 120 0.0685 0.0577 0.0295 0.0162 0.1966 0.6011 0.280 9.4 x 10-4 9.5 x 10-4 10.0 x 10-4 10.4 x 10-4 8.4 x 10-4 6.4 x 10-4 8.0 x 10-4 3.44 x 10-7 2.85 x 10-7 2.60 x 10-7 1.55 x 10-7 4.11 x 10-' 1.26 x 10-7 2.81 x 10-7 0.729 0.594 0.515 0.295 0.97 0.39 0.639 5.16 4.03 3.36 1.50 7.2 2.3 4.85

FIGURES 111 THROUGH 143 REPRESENT THE SOLUBILITY OF 02 IN AQUEOUS Na2SO4 [SEIDEL (36) ] AND THE RATE DATA FOR VARYING SODIUM SULFITE CONCENTRATIONS

-1 I0 N os 0 1J -4 o 10 =E CD I _____I___________I__ I _ _ I+II 0I.1 2.3.4.5.6.7.8.9 l II I- I I L I.1.2.3.4.5.6.7.8.9 1. I H 0'\! I 0 v..._ GM MOL Na2SO4/t Figure 111. Solubility of 02 in aqueous Na2S04, Seidel.(7)

-169-.0010.0008 0 w CD Iz o.0006 C) O.0004 0.0002 w 2 f I/ 0 o.0024.0020 m.0016 o N DON >.0012 5.0008.0004 10 20 30 40 50 MIN. Figure 112. 0 30 60 90 120 MIN. Figure 113.

-170-,0052 -. /.0048 - - 04 --.00 44.0044. -0040.0040.. 1.0036.0036 -.0032 n-.0032 W.002 8.0028 -:.0024 0 D.0024 - igr.0020.0020 — 2 001.0016 -/.0012 / 0012RUN#36 EFFECT OF Co0.0008 / -.0004 CBO: 0.00 714 RUN #35 0004 EFFECT OF C —- 0 ~~80 O ~0 30 60 90 120 150 C o=0.00656 80 I I M IN 0 30 60 90 120 MIN. Figure 115. Figure 114.

-171-.0o.0.0018.0016 0 Q ~.0014 0 () co 2 D.0010 0.0008.0006 no/lA I l/ NOTE: SAMPLES TAKEN /4 AT 5 MIN. INTERVALS I I I 0O02 0 RUN # 37 EFFECT OF CBo C80 ca00764.012 0'.010 Im <.008 -.006 004.002 0 10 20 30 MIN. Figure 116. 40 50 / Ll a 0 U) <: o" LL /.0080.0060.0040.0020 0 *11 RUN 38 / -- EFFECT OF Co8 Co =0.0116, I I I1 I 0 30 60 90 120 MIN. Figure 118. m 0 30 60 90 MIN, Figure 117. 120 150

-172 to a: 0 e) 0 1%1 0 to w 03.020 S.016 m.012 S" cr a.008 (.004 0 RUN# 41 EFFECT OF C90 Co= 0.0196..... I I 0 30 60 90 12O 10 MIN Figure 120. MIN. Figure 119.

-173-.0056.0052 0048.0044 w.0040 m 0 () m.0036 <1 0 > 0032 o I.J 2.0028.0024.016 0 Z.012 0 U, oC0.008 S.004 g / 0 30 -_/ 7/ / RUN#43 -- EFFECT OF CC8o-0.034 4 2 I -I. 60 90 120 MIN Figure 122. 0 30 60 90 120 15( MIN Figure 121.

-174-.020 S.016 Im m 0 0.012 0 >.008 2.004 0.024.- -. —.020 cc.016 0 V) <[ / N.012 o.008 S / RUN# 46 0 04 EFFECT OF CBO 004 C8o 0.0616 0 - 30 60 0 12 0 30 60 90 12' 30 60 9 MIN. Figure 123. 0 MIN. Figure 125. - I - I IF I i - 0 0 CID 0 a 0.020.016.012.008.024 / / a.020 Lu ax 0 Cfl.016 c oo a o L&J 2.008.004 0 / ) /.004 0 0 RUN 45 EFFECT OF C8_ C80=0.0490 I I /zz RUN #47 EFFECT OF CBo_ C80 = 0.0716 1 1 -~~~~~~~~~ 30 60 90 120 MIN. 0 30 60 90 120 MIN. Figure 124. Figure 126.

-175-.020 I/ a 0.016 0 e.012 D / o.00 I co_ / RUN 48.004 EFFECT OF CBO C =0.0926 0 --- I o I.096 I I RUN #49.088 -EFFECT OF CE Co0:O.1426 080.072 0t.048 X- - --.064 m 0 m.048 w.032.024.016.008 0 0 30 60 90 ~101 — /-/ ffi t- c F 0 30 60 90 MIN Figure 127. 120 120 150 180 210 MIN. Figure 128

036.032.028.024 W 00 m.020 N 0.016.012.008 004 0 i i -7RUN # 50 EFFECT OF CBo - CBo=O. 197 w m co 0 U, N 0 w 0 30 60 90 120 MIN. Figure 129. MIN. Figure 130.

-177 C m to O., I ___ RUN * 52.036 EFFECT OF C 8.052 C8o: 0.530.__.048 -.....044 4 _____-.040.036.032.028.024 ____.020 --.016 / -.... -- -.012.008 p~f\A............. ___ ___ _.uq u.036.032.028 a w m 024 r 0 C,, m a,,.020 N X.012.008.004 0 0 - -RUN#S53 EFFECT OFCB CB 0.664 I J / I 30 60 90 120 150 180 MIN. Figure 132. 0.v O L 0 30 60 90 120 MIN. Figure 131. 150 180 210

-178-.032.028.024 Q w I, n.020 0') en m,.016 0 3.012 0.008.004 0 I I' RUN 54 / -EFFECT OF Cgo / CSo O. 914 / / ^^-F~.l~ i I I I 1 i I I 1 a 0 30 60 90 120 150 180 MIN. Figure 133. 0 to Uc 0 n W 0 o.040 RUNS #55 /.036 EFFECT OF CBo C0o= 1.350.032 - D28.024- -/...020.016.012 frn a _ _____.4 0 30 60 90 120 150 180 210 MIN. Figure 134. 240

-179-.010 CJ L33 0 m U) N 00 0 L3 a 2 CD.008.006.004 RUN # 56 EFFECT OF Cso8 C8o = 1.720 —, (NOTE THE LONG DURATION OF _THE RUN) ____ I L I I/ 0 r, I I I I 0 60 120 180 _ 240 300 360 420 480 MIN Figure 135.

.040.036.032.028 0 w cr. o.024 C) m o.020 a.016 0.012.008.004 0 I 0 60 120 180 240 300 360 420 480 540 MIN. Figure 136. 600

-181 0.007 0.006 / a ID ct 0 u) o 0 CD 0.005 0.004 0003 Q.9 i I I i i i CL co o 4 0 LI C u.u, -- -'' 0.005. 0.00. -... — -- / / 1 i i i / 0.001 0 / -EFFECT OF Cao ( NO CATALYST) C o 0.0685 I I _ RUN # 114 0.001 A-h RUN# 116 EFFECT OF CBo(NO CATALYSIT CBs. 0.0295 I & I I I 0.001 a000o 0n 30 6 90 12 1250 MIN. Figure 137. 6 5 4 3 2 RUN # 115: __ / EFFECT OF Cso( NO // CATALYST) Co-= 0.0577 III 30 60 90 120 O 30 60 90 120 MIN. Figure 139. 150 O0 a. 0'0 C) 4 N 0 a CD,., 0.00 aL 0 0 0 C 0E 0.002 -- o.00o -- -- oo/ 0.00 Qoc i RUN 117 EFFECT OF CB0(NO CATALY ST)CBgO.O 162 I I I 0 30 60 90 120 150 ( 0 30 60 90 120 150 MIN. MIN. Figure 140. Figure 138.

-182 n, o0:3 O; MIN. 0 u) 4 N 0 0 w, Figure 141..006 RUN # 119 _ EFFECT OF CSo (NO CATALYST) C = 0.6011.004.002 —... J...... 0 ^ ~ - --- ---- --- --. --- --- --- -0 60 120 MIN. Figure 142. 180 240 0 w co N a o ot:g (3.006 I RUN # 120 EFFECT OF Co / -(NO CATALYST) - CaB 0.280.004 - I.002 0 -0 60 MIN. Figure 143.!20

APPENDIX VIII CALCULATIONS OF -7 FROM VARIOUS MODELS -183

-184DA = 1.56 x 10 3 cm2/min, Sherwood and Reid CAi = 10.54 x 104 gm equiv 02 /. TABLE 13 Calculation of the Diffusivity of Na2SO3 at 25~C DB Using the conductivity Na \2so (1/n + (l/\ + convention = 50 = 57.4 l/n ) RT 1/A_) F2 Table 3 Table 3 (17) n + = n = 1 DB 2 x 8.318 x 298 (1/50.1 + 1/57.4)(96,500)2 = 1.422 x 10-5 cm2/sec = 8.532 x 10-4 cm2/min

TABLE 14 Calculation of y for Hatta, Kishinevskii, Danckwerts and Higbie Models According to Table 1 Run # 90 91 89 88 92 1 x 10-6 1 x 10-6 7 x 10-7 5 x 10-7 2 x 10-6 Amount of catalyst gm mols CoCl2/9 CBo gm equiv/1'Kishinevskii 0.10598 0.09930 0.09232 0.08598 0.07989 0.07351 0.08078 0.07346 0.06787 0.06143 0.05504 0.05009 0.06975 0.06371 0.05801 0.05297 0.04802 0.04272 0.11964 0.11444 0.10885 0.10370 0.09826 0.09331 0.05173 0.04435 0.03703 0.03079 0.02500 0.01980 100.55 94.21 87.59 81.58 75.80 69.74 76.64 69.69 64.40 56.27 52.22 47.53 66.18 60.46 55.00 50.25 45.59 40.80 113.50 108.57 103.28 98.35 93.22 88.51 48.50 43.56 35.12 29.20 23.72 18.79 ~Hatta 54.89 51.44 47.83 44.54 41.39 38.08 41.85 38.05 35.16 31.82 28.51 25.95 36.14 33.01 30.03 27.44 24.89 22.28 61.97 59.28 56.39 53.69 50.89 48.33 26.46 23.79 19.18 16.00 12.95 10.25 |B1, Boa DA I CAi YHigbie and YDanckwerts 74.40 69.72 64.82 60.36 56.10 51.60 56.72 51.57 47.65 43.12 38.64 35.17 48.97 44.74 40.70 37.18 33.73 30.20 83.99 80.35 76.43 72.77 68.98 65.50 35.89 32.24 25.99 21.60 17.55 13.90 73.40 68.72 63.82 59.36 55.10 50.60 55.72 50.57 46.65 42.12 37.64 34.17 47.97 43.74 39.70 36.18 32.73 29.20 82.99 79.35 75.43 71.77 67.98 64.50 34.89 31.24 24.99 20.60 16.55 12.90 I O *I fe

Calculations of -y = (kL/kL - 1) for Sherwood and Wei Model using Equations 63 and 57, Appendix I, ii. D = 1.56 x 10-3 c; C = 10.54 x 10-4 gm equiv ~2 A min Ai - q n gm equiv SO, gm equiv Na+ m = (n - 0.281 nq)% 9600 x m Run # nq I 0.281 nq n + m 6000 x n 6000n + 9600m 78(n + 356 q 60007800(n + ) - 1356 q 7800(n + m) - 1356 q 9.16 x 10-4 DA CAi L/k - 1 90 91 89 88 92 0.10598 0.09930 0.09232 0.08598 0.07989 0.07351 0.08078 0.07346 0.06787 0.06143 0.05504 0.05009 0.06975 0.06371 0.05801 0.05297 0.04802 0.04272 0.11964 0.11444 0.10885 0.10370 0.09826 0.09331 0.05173 0.04435 0.03703 0.03079 0.02500 0.01980 0.10492 0.10387 0.10284 0.10181 0.10079 0.09978 0.07998 0.07917 0.07839 0.07760 0.07682 0.07606 0.06906 0.06836 0.06766 0.06700 0.06634 0.06567 0.11844 0.11726 0.11609 0.11493 0.11378 0.11264 0.05173 0.05122 0.05070 0.05020 0.04970 0.04920 0.01101 0.01079 0.01058 0.01036 0.01015 0.00995 0.00639 0.00627 0.00614 0.00602 0.00590 0.00588 0.00477 0.00467 0.00458 0.00449 0.00440 0.00431 0.01403 0.01375 0.01348 0.01321 0.01295 0.01269 0.00267 0.00262 0.00257 0.00252 0.00249 0.00242 0.01112 0.01031 0.00949 0.00875 0.00805 0.00734 0.00646 0.00581 0.00532 0.00477 0.00423 0.00361 0.00481 0.00436 0.00392 0.00354 0.00318 0.00280 0.01417 0.01342 0.01263 0.01192 0.01118 0.01051 0.00267 0.00227 0.00188 0.00154 0.00124 0.00098 0.00312 0.00290 0.00266 0.00246 0.00226 0.00206 0.00182 0.00164 0.00149 0.00134 0.00119 0.00107 0.00135 0.00122 0.00110 0.00099 0.00089 0.00078 0.00398 0.00377 0.00355 0.00335 0.00314 0.00295 0.00075 0.00063 0.00053 0.00043 0.00035 0.00027 0.08882 0.08301 0.08898 0.08888 0.08882 0.08884 0.06759 0.06805 0.06819 0.06841 0.06863 0.06934 0.05848 0.05872 0.05900 0.05916 0.05923 0.05943 0.10006 0.09988 0.09965 0.09922 0.09904 0.09872 0.04383 0.04462 0.04516 0.04571 0.04647 0.04636 0.19374 0.18688 0.19182 0.19069 0.18961 0.18862 0.14757 0.14723 0.14658 0.14601 0.14545 0.14540 0.12754 0.12708 0.12666 0.12616 0.12557 0.12510 0.21850 0.21714 0.21574 0.21415 0.21282 0.21136 0.09556 0.09584 0.09586 0.09591 0.09617 0.09556 629.5 623.2 617.0 610.5 604.8 598.7 479.8 475.0 470.0 465.6 460.9 456.4 414.4 410.2 406.1 402.0 398.0 394.0 710.6 703.6 696.6 689.6 682.7 675.8 310.3 307.3 304.2 301.2 298.2 295.2 852.7 796.9 854.2 853.3 852.7 852.9 648.8 653.3 654.6 656.7 658.8 665.7 561.4 563.7 566.4 567.9 568.6 570.5 960.6 958.8 956.6 952.5 950.8 947.7 420.8 428.3 433.5 438.8 446.1 445.0 1511.2 1457.7 1496.2 1487.4 1478.9 1471.2 1151.0 1148.4 1143.3 1138.9 1134.5 1134.1 994.8 991.2 987.9 984.0 979.4 975.8 1705.0 1700.0 1682.0 1672.0 1660.0 1620.0 746.0 748.0 750.0 750.0 752.0 745.0 143.0 134.5 125.2 116.5 108.5 100.0 109.5 99.5 92.0 83.3 74.6 69.0 94.5 85.5 78.7 72.0 65.2 58.0 162.2 155.2 147.5 141.0 133.2 126.5 70.1 60.1 50.2 41.7 33.9 26.8 1482 1419 1471 1463 1457 1450 1129 1128 1124 1121 1118 1121 975 973 972 969 966 964 1671 1661 1652 1641 1632 1623 731 735 737 739 744 740 1368 1323 1371 1371 1370 1371 1042 1049 1051 1055 1060 1065 900 906 909 912 914 917 1543 1545 1535 1531 1527 1524 676 688 700 708 718 719 1.082 1.070 1.070 1.065 1.070 1.054 1.082 1.074 1.070 1.062 1.052 1.051 1.080 1.075 1.072 1.050 1.060 1.050 1.080 1.072 1.072 1.072 1.070 1.065 1.035 1.028 1.021 1.018 1.015 1.012 58.1 55.4 51.5 48.0 44.6 41.0 45.1 41.0 37.9 34.3 30.7 29.9 38.9 35.6 32.4 29.5 26.8 23.8 66.7 64.0 60.8 58.0 54.8 52.0 28.8 24.8 20.6 17.2 13.9 11.1 62.7 58.4 55.2 51.2 47.8 43.3 48.6 44.0 39.8 36.4 32.4 31.5 42.0 38.2 34.8 31.0 28.4 25.0 72.0 68.6 65.2 62.2 58.6 55.4 29.8 25.5 21.0 17.5 14.1 11.2 I 03 I

TABLE 16 Reaction Rates Without Catalyst Runs # A-I with 1300 RPM; 0.5 SCFM Air Run # J with 4GG RPM; 0.25 SCFM Air A(S03) A(S03) At At | Time/.|gm equiv/| Time, m quequv Time, equiv euiv Run#.nin SO. min Run m inSOS m A 00.2810 0.0158 F 0 0.00335 0.0007 1 0.2664 1 0.00215 2 0.2520 2 0.00130 3 0.2343 3 0.00070 4 0.2166 4 0.00037 5 0.2009 5 0.00024 B 0 0.1460 0.0146 G 0 0.03565 0.01 1 0.1305 1 0.0256 1 2 0.1166 2 0.0166 C0 3 0.1053 3 0.00835 4 0.0920 4 0.00300 5 0.0732 5 0.00115 C 0 0.1365 0.0157 H 0 0.0195 0.0057 1 0.1183 1 0.0138 2 0.1030 2 0.0051 3 0.0885 3 0.00066 4 0.0734 4 0.00016 D 0 0.0814 0.0113 I 0 0.0306 0.0083 1 0.0704 1 0.0223 2 0.0597 2 0.0144 3 0.04763 0.0066 4 0.0359 4 0.00037 5 0.0242 E 0 0.01551 0.0050 J 0 0.148 0.0064 1 0.00989 1 0.1425 2 0.00565 20.1374 3 0.00291 3 0.1290 4 0.00175 4 0.1236 5 0.00106 5 0.1161 I I

APPENDIX IX DATA AND CALCULATIONS FOR CHEMICAL KINETIC COEFFICIENTS

TABLE 17 Recalculation of ku+ from Fuller-Crist Data from Equation 25 using Constants from Latimer from Equation 25 using Constants from Latimer ++ Cu added gm mol/Q Time, sec Conc. of SO3 gm mol/I Calculated ++ Cu conc. gm mol/i k(Cu++) min x mol 3(CU++) min x mol 1 x 1 ~4 1 x 10 —4 1 x 10-6 1 x 10-, 1 x 108 1 x 109 X 1O 0 20 40 60 0 20 40 60 0 20 40 60 0 20 40 60 0 20 40 60 0 20 40 60 0.0143 0.0086 0.0041 0.0008 0.0125 0.0072 0.0025 0.0002 0.0131 0.0082 0.0039 0.0008 0.0135 0.0088 0.0045 0.0014 0.0127 0.0080 0.0039 0.0016 0.0150 0.0122 0.0094 0.0072 0.0699 x 10-9 0.1163 x 10-9 0.2430 x 10-9 1.250 x 10-9 0.0800 x 10-9 0.1389 x 10-9 0.4000 x 10-9 5.00 x 10-9 0.0763 x 10-9 0.1219 x 10-9 0.2564 x 10-9 1.250 x 10-9 0.0740 x 10-9 0.1136 x 10-9 0.222 x 10-9 0.714 x 10-9 0.0787 x 10-9 0.1250 x 10-9 0.2564 x 10-9 0.625 x 10-9 0.0665 x 10-9 0.082 x 10-9 0.1062 x 10-9 0.139 x 10-9 1.378 x 108 1.438 x 108 1.341 x 108 1.376 x 108 1.734 x 108 0.981 x 108 I Ix I 1.081 1.377 1.254 x 108 x 108 x 108 0.915 x 108 1.299 x 108 1.176 x 108 1.039 x 108 1.290 x 108 0.800 x 108 negative 0.00 0.04 x 108

TABLE 1I Calculations of k3(Co++) from Equation 27 Co+ added gm mol/a Time, min Conc. of so0 gm mol/a Calculated Co conc. gm mol/A ++ Co added gm mol/A Conc. of SO3 gm mol/S Calculated ++ Co++ conc. gm mol/a k ) mol x min 3(Co+ )' mol x min Time, min i k3(Co*4)' mol x min Run # Run # a b c d 1 x 101 x 10-7 1 x 101 x 10 0 1 2 3 4 5 0 1 2 3 4 5 6 0 1 2 3 4 5 0 1 2 3 4 5 0.0483.u443 0.0352 0.0292 0.0210 0.0127 0.0566 0.0498 0.0417 0.0336 0.0251 0.0161 0.0550 0.0508 0.0436 0.0364 0.0292 0.0223 0.0625 0.0548 0.0470 0.0399 0.0325 0.0248 3.23 3.52 4.44 5.35 7.42 10.0 2.75 3.13 3.74 4.65 6.21 9.80 1 1 1 1 1 1 1 1 1 1 1 1 x 10-8 x 10-8 x 10-8 x 10-8 x 10-8 x 10-8 x 10-8 x 108 x 10-8 x 10-8 x 10-8 x 10-8 x 10-8 x 10-8 x 10-8 x 10-8 x 10-8 x 10-8 x 10-8 x 10-8 x 109 x 10-o x 10-9 x 10-9 x 10-9 e negative 0.034 x 106 0.012 x 106 0.050 x 106 0.062 x 106 f negative 0.016 x 106 0.026 x 106 0.043 x 106 0.012 x 106 1 x 101 x 10-6 2 Y 10 5 x 10-7 0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5 0.0593 0.0495 0.0396 0.0303 0.0208 0.0120 0.0777 0.0681 0.0582 0.0489 0.0393 0.0297 0.0806 0.0704 0.0605 0.0418 0.0331 0.0502 0.0416 0.0334 0.0252 0.0168 0.0092 I 2.63 x 3.15 x 3.93 x 5.14 x 7.48 x 12.95 x 2.0 x 2.29 x 2.68 x 3.19 x 3.96 x 5.25 x 10-8 10-8 10-8 10-8 10-8 10-8 10-8 10-8 10-8 10-8 10-8 10-8 0.018 0.034 0.043 0.060 0.068 x 106 x 106 x 106 x 106 x 106 negative 0.004 x 106 0:013 x 106 0.031 x 106 0.047 x 106 I 0! g negative 0.0 0.013 x 106 0.024 x 106 0.032 x 106 1.93 x 10-8 2.22 x 102.58 x 108 3.72 x 10-8 4 70 x 10-8 3.10 x 10-8 3.74 x 10-8 4.66 x 10-8 6.18 x 10-8 9.25 x 10-8 16.95 x 10-8 negative negative 0.012 x 106 0.033 x 106 h negative 0.002 x 106 0.006 x 106 0.021 x 106 0.036 x 106 0.019 0.027 0.040 0.056 0.060 x 106 x 106 x 106 x 106 x 106

TABLE 19 Reaction Rates with Cu Catalyst Runs # I-IV with 1300 RPM; 0.5 SCFM Air Run # V with 400 RPM; 0.25 SCFM Air Amt of catalyst gm mol/a A( So3) At gm equiv. - min A(so3) At Time, min gm equiv/1 SO3 Run # I II 5 x 10-7 5 x 10-6 0 1 2 3 4 5 0 1 2 3 4 5 0.1286 0.1163 0.1033 0.0887 0.0752 0.0608 0.1170 0.1039 0.0886 0.0728 0.0568 0.0041 0.0136 0.0156 I H t

TABLE 20 gn Run # a Reaction Rates with Co Catalyst Data from Table 18 1300 RPM; 0.5 SCFM Air A (SO3) A(SO3) At | Amt of At 1 equiv/ g equivcatalyst Time, gm equiv/| gm euiv SO 3. min Run # gm mol/2 min SOs |. min 0.0966 0.0164 e 1 x 10-6 0 0.1186 0.0187 0.0886 1 0.0990 0.0703 2 0.0792 0.0583 3 0.0606 0.0420 4 0.0417 0.0254 5 0.0240 0.1132 0.0164 f 1 x 10-6 0 0.1550 0.0190 0.0997 1 0.1362 0.0834 2 0.1164 0.06770 3 0.0978 H 0.0503 4 0.0785 IO _~~- _-~~ _-5 0.0594 0.0322 0.1100 0.0141 g 2 x 106 0 0.1612 0.0194 0.1017 1 0.1408 0.0873 2 0.1210 0.0728 3 - - 0.0583 4 0.0835 0.0447 5 0.0661 b c d 0.1250 0.1095 0.0940 0.0798 0.0649 0.0497 0.0150 h 0.1005 0.0833 0.0669 0.0504 0.0337 0.0184 0.0166

TABLE 21 Data for the Determination of kT a' Ai(Literature) = 10. C. = 10.54 x 10-4 gm equiv 02/2 Ai(Liter ature) Duration of a run sec mis of N/200 Thiosulfate for 100 ml sample No. 1 2 3 4 5 6 7 0 5 15 22 300 300 720,000 Average of # 5-7 1.21 12.24 18.16 18.34 18.95 18.67 18.39 18.67 H \O I ~1 0 o aI1 Slope of the curve, Figure 14 = 5.28 1 k a' = 2.303 x 5.28 12.2 mmn L min

TABLE 22 Data Obtained from Figure 11 for the Determination of k' from ko. a' nd. a' for Reaction without Catalyst Time, min Run # D E G H I 0 1 2 3 4 5 0 1 2 0' 1 2 3 4 0 1 2 1 2 3 Bo gm equiv 0.081~ 0.0704 0.0590 0.0476 0.0369 0.0246 0.0160 0.0094 0.0054 0.0356 0.0256 0.0166 0.0083 0.0030 0.0200 0..0138 0.0070 0.0306 0.0223 0.0144 0.0066 A C. Bo At gm equiv'-. min 0.0111 0.0114 0.0114 p.0116 0.0114 1 Bo (average) 0.0066 0.004P.oio010 0.0090 0.0083 0.0053 1 CAai \' CB o/^t H' Bo 12.3 14.2 16.7 21.0 28.0 62.5 106.5 28.0 39.5 60.0 119.0 50.0 72.5 32.5 44.8 69.5 0.0950 0.0925 0.0925 0.0905 0.0925 I 4= 0.160 0.264 0.105 0.117 0.127 0.191 0.170 0.155 0.127 0.133 0.137 0 J062 0.0068 0.0083 0.007c 0.007E

TABLE 23 Calculation of y from Equation 33 for k = 1100 e = 0.613 min C Bo B BO, M M2M gm equiv = I- -- 1M M- - M =- k' C D C 2 -0 4 Bo IDA. CAi'a 2a a 0.02 10 63 14 0.757 0.378 0.142 2.01 0.03 15.95 21 0.757 0 378 0.142 2.74 0.04 21.25 28 0.757 0 378 0.142 3.32 0.06 31.-90 42 0.757 0 378 0.142 4.37 0.08 42.50 56 0.757 0.378 0.142 5.20 I V\ I

TABLE 24 Estimation of k' from k for reaction without catalyst L Data from Figures 77 and 137-140 e = 0 613 min C Bo D 2 C k' gm equiv + H - -1 liters Rubn # _ _ ft/hr y +1 Ai (7+1) 2 7.. M gm equiv min a 1 112 000812 0.76 6.45 5.45 56.0 41.5 50.5 46.0 1170 114 0.0685 0.729 6.16 5.16 47.0 38.0 42.0 42.5 1275 11'5 0.0577 0.594 5.03 4.03 39.5 25.4 35.5 28.3 1020 116 0.0295 0.515 4.36 3.36 19.7 19.0 16.3 23.0 1620 117 0.0162 0.295 2.50 1.50 10.35 6.25 8.9 7.28 930 ^7kT>aT ^ - "=1liters AX79=-r —-A =~ Wnl J.L. Jf - L' H I —!\ J-,V % —L CL' c v V C -I U V- u A -L Zu a gm equiv min

TABLE 25 Estimation of k' from k for reaction with Cu catalyst = 0.613 min e = 0.613 min gm mol Cu SO4 ~ CBo gm equiv Q Calculated Cu++ Cugm mol gm mol & kL, ft/hr y+ 1 (kL/L) L L'Ya B C Aj Ai Run #'Y (Y + 1) 2 ya -y liters gm equiv. min M 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 4 x 10-9 4 x 10-9 4 x 10-s 4 x 10-8 4 x 10-8 1.5 x 10-7 4 x 10-4 4 x 10-4 1 x 10-6 1 x 10-6 1 x 10-6 1 x 10-6 3 x 10-6 4 x 10-6 4 x 10-6 8 x 10-6 1 x 10-5 0.097 0.070 0.090 0.066 0.062 0.086 0.080 0.072 0.063 0.062 0.086 0.088 0.084 0.077 0.112 0.074 0.048 2.06 x 10-11 2.86 x 10-11 2.22 x 10-l 3.03 x 10-11 3.22 x 10-11 2.32 x 10-l 2.50 x 10-11 2.78 x 103.17 x 10-11 3.22 x 10-1 2.32 x 10-1 2.27 x 10-1 2.38 x 10-11 2.59 x 10-1 1.78 x 10-11 2.70 x 10-11 4.16 x 10-11 0.602 0.756 0.891 0.600 0.697 0.783 0.891 0.826 1.137 0.657 0.917 1.023 1.131 1.171 1.330 1.378 1.496 5.1 6.41 7.55 5.09 5.92 6.63 7.55 7.00 10.15 5.57 7.77 8.67 9.60 9.94 11.25 11.70 12.70 4.1 5.41 6.55 4.09 4.92 5.63 6.55 6.00 9.15 4.57 6.77 7.67 8.60 8.94 10.25 10.70 11.70 67.0 48.2 62.3 45.5 42.6 59.4 55.2 49.5 43.5 42.5 59.5 60.8 58.0 53.2 77.0 51.0 32.9 26.0 41.0 57.0 26.0 35.0 44.0 57.0 49.0 103.0 31.2 60.5 75.2 92.5 98.5 127.0 113.0 162.0 62.9 42.8 55.8 41.4 37.7 53.8 48.7 43.5 34.3 38.0 52.8 53.1 49.4 44.3 66.7 40.3 21.2 27.8 46.2 63.6 28.6 39.6 48.5 64.5 55.6 130.2 34.9 67.8 85.8 108.0 117.0 147.0 143.0 251.0 593 1,370 1,470 900 1,330 1,170 1,680 1,610 4,250 1,170 1,640 2,030 2,670 3,160 2,660 4,010 10,900!

-198 TABLE 26 Estimation of k' from kL for reaction with Co++ catalyst 8 = 0.613 min Calculated a = gm mol Bo Cos+ D C k' CO C2 gm equiv gm mol k ft/hr 1 liters Run* y+ [1DA CAi (Y + 1) a M gmequiv min 76 1 x 10-11 0.096 0.775 6.55 5.55 66.5 43 61.0 47 1,010 77 1 x 110 0.112 0.793 6.72 5.72 77.6 45 72.0 48 900 78 1 x 10-9 0.158 0.836 7.08 6.08 110 0 50 104*0 53 700 79 5 x 10-9 0.168 0.944 8.00 7.00 117.0 64 110.0 68 840 80 1 x 10-8 0.158 1.340 11.38 10.38 110.0 129 99.6 142 1,870 81 1 x 10-8 0.150 1.200 10.15 9.15 104.5 103 95.3 107 1,480 82 2 x 10-8 0.106 1.030 8.70 7.70 73.5 75 66.8 83 1,620 83 5 x 10-8 0.082 3.8 x 10-8 1.385 11.75 10.75 56.5 138 45.7 171 4,320 84 1 x 10-7 0.170 1.83 x 10-8 1.490 12.62 11.62 118.0 159 106.4 176 2,150 85 2 x 10o7 0.070 4.45 x 10-8 1.627 13.80 12.80 48.2 190 35.4 259 7,660 86 3 x 10-7 0.100 3.12 x 10-8 2.400 20.35 19.35 69.2 413 49.9 573 11,900 87 5 x 10-7 0.081 3.86 x 10-8 2.100 17.80 16.80 55.8 316 39.0 453 11,650 88 5 x 107 0.01196 2.6 x 10-8 3.155 26.70 25.70 83.0 712 57.3 1030 17,900 89 7 x 10-7 0.06975 4.46 x 10-8 3.620 30.70 29.70 48.0 940 18.3 2460 73,000 90 1 x 108 0.106 2.91 x 10-8 4.120 39.9 38.9 73.5 1590 34.6 3380 66,000 91 1 x 108 0.0808 3.86 x 108 3.940 33.4 32.4 55.8 1056 23.4 2520 64,000 92 2 x 10 0.052 6.00 x 10-8 4.790 40.6 39.6 35-5 1600 negative 33 2 x 10- 0.00270 4.35 3.35 0.8 negative 34 2 x 10- 0.0047 4.78 3.78 2.3 negative 35 2 x 10" 0.00656 5.13 4.13 3.6 negative 36 2 x 10- 0.00714 5.34 4.34 4.02 negative 37 2 x 106e 0.00764 5.86 4.86 4.35 negative 38 2 x 10- 0.0116 10.20 9.2 8.05 negative 39 2 x 106 0.0172 12.85 11.85 11.1 negative 40 2 x 10- 0.0182 21.0 20.0 11.7 negative 41 2 x 10o 0.0196 14.2 13.2 12.8 negative 42 2 x 10-" 0.0238 13.2 x 10-8 12.1 11.1 15.7 146 4.6 497 4.35 x 104 43 2 x 10"e 0.0344 9.06 x 108 13.7 12.7 23.2 188 10.5 415 2.5i x 104 44 2 x 10e 0.0426 7.3 x 10-8 25.8 24.8 29.0 665 4.2 4580 2.24 x 105 45 2 x 10e 0.0490 6.35 x 10-8 30.0 29.0 33.5 900 4.5 6700 2.84 x 105 46 2 x 10e 0.0616 5.06 x 108 33.0 32.0 42.3 1043 10.3 4280 1.44 x 105 47 2 x 106 0.0716 4.35 x 10-830.1 29.1 49.5 905 20.4 2180 6.3 x 105 48 2 x 10- 0.0926 3.37 x 10-8 40.9 39.9 64.0 1670 24.1 4430 1.0 x 105 49 2 x 10" e 0.1426 2.19 x 10 8 49.4 48.4 99.0 2440 50.6 4770 6.95 x 104 50 2 x 10-6 0.197 1.57 x 10-8 61.2 60.2 137.0 3730 77.0 6600 6.95 x 104 51 2 x 10- 0.348 8.8 x 10-9 52.6 51.6 243.0 2760 192.0 3490 2.08 x 104 52 2 x 10-6 0.530 5.9 x 10-9 49.0 48.0 371.0 2400 323.0 2760 1.08 x 104 53 2 x 106e 0.664 4.7 x 10-9 42.6 41.6 465.0 1820 424.0 1990 6,230 54 2 x 10 0.914 3.42 x 109 36.6 35.6 641.0 1340 606.0 1420 3,200 55 2 x 10-e 1.315 2.37 x 10-9 32.6 31.6 914.0 1060 883.0 1095 1,730 56 2 x 10-" 1.72 1.82 x 10-9 4.18 3.18 1210.0 1750 1207.0 1755 2,120 57 2 x 10- 1.782 1.75 x 10-9 10.25 9.25 1250.0 1050 1241.0 1055 1,220

TABLE 27 Estimation of k' from Fuller and Crist Data 1 kl = 0o78m min CAi = lo27 x 10-3 gm equiv/1 k k. - -— k k=C. k= CAi ++) kl + ks(Cu lit liters gm mol (Cu ) /2 k3 x (Cu ) min-1 gm equiv min 3 (original) x 1 x 1011 56 x 10 3 0.165 614 -8 1 1x 10-1~ 1.56 x 10-2 0.178 626 1.6x01 x 10-9 1.56 x 10 - 0.318 736 liters 1 x 10-8 1.56 x 100 1.723 1,845 mol o min 1 x 10-7 1.56 x 101 15.763 12,880 II k - (corrected) 1 10 x 10 7 10 0.233 669 7 0 9 1 x 10-~1 7 x 10-1 0.863 1,168 1 x 10-9 7 x 100 7.163 6,120 liters 1 x 10-8 7 x 101 70.163 55,600 mol o min x 10- 7 7 102 700.163 551,000 I \O O

TABLE 28 Calculation of k' for Mannitol from k and from Equation 34 L Amount of Mannitol gm mol/a CBo gm equiv/i kL t/h ft/hr kn L =, — -1 kL a a I %Ai (Y + 1) 2 k' liters gm equiv x min k from Eq. 34 minl k k' = k CAi liter gm equiv x min Ya -Y M I.I I 4 5 x 10-7 5 x 10-6 1 x 10-5 5 x 10-5 1 x 10-4 2.5 x 10-4 5 x 10-4 5 x 10-3 1 x 10-2 0.086 0.097 0.130 0.090 0.116 0.092 0.048 0.068 0.156 0.776 0.685 0.646 0.622 0.532 0.440 0.228 0.187 0.157 5.58 4.80 4.47 4.27 3.50 2.73 0.93 0.585 0.330 47.0 53.0 71.0 49.2 63.2 50.2 26.2 37.1 85.0 43.2 33.5 30.0 27.7 20.2 13.9 3.72 2.50 1.77 41.4 48.2 66.5 45.0 59.7 47.5 25.1 36.5 84.7 49.2 36.9 32.1 30.3 21.4 14.7 3.88 2.54 1.78 1160 791 512 700 383 333 168 77.5 23.8 0.155 0.108 0.081 0.027 0.0147 0.0063 0.0032 0.00033 0.000163 147 102 76.7 25.6 13.8 5.97 3.02 0.309 0.154 I O! TABLE 29 Calculation of k' for Benzyl Alcohol from k and from Equation 35 L Amount of Benzyl Alcohol gm mol/Q CBo gm equiv/A k L ft/hr k L 1 |D|% 1 D [i c-i k' k zero liters from gm equiv x min Eq. 35 k - zero CAi - CBo (y + 1) 2 a -Y M 5 x10-7 1 x 10-6 2.5 x 10-6 5 x 10-6 1 x 10-5 5 x 10-5 1 x10-4 1 x 10-2 0.100 0.124 0.092 0.096 0.136 0.124 0.152 0.146 0.629 0.642 0.590 0.275 0.266 0.098 0.114 0.0256 4.33 4.44 3.82 1.33 1.26 __ 54.7 63.9 47.2 49.2 70.0 28.3 29.5 14.6 5.4 5.1 50.4 59.5 43.4 47.9 68.75 30.8 31.7 15.9 5.55 5.18 640 532 359 120 79.5 0.016 0.016 0.016 0.016 0.016 152 122 165 158 112