THE UNIVERSITY OF MICHIGAN RESEARCH INSTITUTE ANN ARBOR, MICHIGAN Final Report DETERMINATION OF THE LOW-TEMPERATURE HEAT CAPACITY AND THERMODYNAMIC PROPERTIES OF CERTAIN SUBSTANCES Edgar F. Westrum, Jr. George Grenier Norman E. Levitin UMRI Project 2751 CALLERY CHEMICAL COMPANY CALLERY, PENNSYLVANIA July 1958

TABLE OF CONTENTS Page LIST OF TABLES v LIST OF FIGURES vi ABSTRACT vii OBJECTIVE vii INTRODUCTION 1 THE CRYOSTAT AND CALORIMETER 1 THE HEAT CAPACITY OF A STANDARD SAMPLE OF BENZOIC ACID 8 DETERMINATION OF THE LOW-TEMPERATURE HEAT CAPACITY OF ANHYDROUS SODIUM METABORATE 8 Preparation of Anhydrous Sodium Metaborate 8 Hygroscopicity of Sodium Metaborate 9 Results of Heat-Capacity Measurements on Anhydrous Crystalline Sodium Metaborate 9 DETERMINATION OF THE LOW-TEMPERATURE HEAT CAPACITY OF ANHYDROUS CRYSTALLINE SODIUM TETRABORATE 12 Preparation and Analysis of Crystalline Sodium Tetraborate 14 Results of Heat-Capacity Measurements on Anhydrous Crystalline Sodium Tetraborate 15 DETERMINATION OF THE LOW-TEMPERATURE HEAT CAPACITY OF VITREOUS SODIUM TETRABORATE 19 Preparation and Purity of Vitreous Sodium Tetraborate 19 Results of Heat-Capacity Measurements on Vitreous Sodium Tetraborate 19 Discussion 22 THE LOW-TEMPERATURE HEAT CAPACITY OF SODIUM METHOXIDE 22 Preparation and Purity of Sodium Methoxide 22 Results of Heat-Capacity Measurements on Sodium Methoxide 25 DETERMINATION OF THE LOW-TEMPERATURE HEAT CAPACITY AND THERMODYNAMIC PROPERTIES OF AMMONIA TRIBORANE 26 Preparation of Ammonia Triborane 30 The Results of the Heat-Capacity Measurements on Ammonia Triborane 31 iii

TABLE OF CONTENTS (Concluded) Page DETERMINATION OF HEAT CAPACITY OF SODIUM HYDRIDE 35 Preparation and Purity of Sodium Hydride 35 Results of Low-Temperature Heat-Capacity Determination on Sodium Hydride 36 REFERENCES 42 iv

LIST OF TABLES No. Page I. The Molal Heat Capacity of Sodium Metaborate 11 II. Molal Thermodynamic Functions of Sodium Metaborate 13 III. The Molal Heat Capacity of Crystalline Sodium Tetraborate 17 IV. Molal Thermodynamic Properties of Crystalline Sodium Tetraborate 18 Vo The Molal Heat Capacity of Vitreous Sodium Tetraborate 20 VI. Molal Thermodynamic Properties of Vitreous Sodium Tetraborate 21 VIIo Molal Heat Capacity of Sodium Methoxide 28 VIII. Molal Thermodynamic Functions of Sodium Methoxide 29 IX. Molal Heat Capacity of Ammonia Triborane 33 X. Molal Thermodynamic Functions of Ammonia Triborane 34 XIo Molal Heat Capacity of Sodium Hydride 38 XII. Molal Thermodynamic Functions of Sodium Hydride 41 v

LIST OF FIGURES No. Page 1. Cross-sectional schematic view of cryostat. 3 2. Cross-sectional schematic view of calorimeter W-6. 6 3. Molal heat capacity of sodium metaborate as a function of absolute temperature (6-350~K). 10 4. Molal heat capacity of crystalline anhydrous sodium tetraborate. 16 5. Comparison of the heat capacities of anhydrous crystalline vitreous sodium tetraborate. 23 6. Deviation plot for the heat capacities of sodium tetraborate forms. 24 7. Molal heat capacity of sodium methoxide. 27 8. Low-temperature heat capacity of ammonia triborane. 32 9. Molal heat capacity of sodium hydride. 37 10. Comparison of heat capacities of sodium hydride with results of Sayre and Beaver. 40 vi

ABSTRACT This report summarizes the heat-capacity measurements on vitreous and crystalline sodium tetraborate, on sodium metaborate, on sodium methoxide, on sodium hydride, and on ammonia triborane. Most of these measurements were made over the range of from 5 to 350~C by the adiabatic technique in a high-precision low-temperature calorimeter. The thermodynamic functions and thermal properties of these materials have been summarized in tabular and graphical presentation and the interpretation of the data has been made. Most of these details have been submitted from time to time in the technical reports under the above contract. OBJECTIVE The objective of this project was to obtain chemical thermodynamic data and thermal measurements on certain compounds over the low-temperature range. vii

INTRODUCTION Because the several compounds which were studied have no immediate scientific relation to each other and were of interest to the sponsor primarily for technical reasons, this report is essentially a summation of the data on the individual substances presented in the separate sections of this report. These compounds are also of considerable scientific interest. The comparison of the thermal properties of the vitreous and crystalline forms of the sodium tetraborate shows an unusual effect. Data on the heat capacity of sodium hydride (and deuteride) have long been proposed to test the relative merits of heat-capacity theories. The study of the changes in the thermodynamic functions at the transformation in ammonia borane is of considerable interest in its own right. But apart from the scientific interest, the evaluation of the thermodynamic functions provide data useful in the design of production apparatus and in evaluating the potentialities of the material for applications. THE CRYOSTAT AND CALORIMETER The Mark I cryostat and electrical circuits employed for the heat capacity measurements are very similar to the equipment described by Westrum, Hatcher, and Osborne. Figure 1 is a cross-sectional view of the cryostat with the calorimeter in place. The adiabatic determinations of heat capacity were made by measuring the temperature rise produced by a measured input of electrical energy. Current and potential measurements were made on the electrical heater during the energy input and on the capsule-type platinum resistance thermometer during drift periods. These measurements were made with an autocalibrated White double potentiometer used in conjunction with a galvanometer having a rated sensitivity of 0.04 Qiv/mm at 1-m distance. The platinum resistance thermometer (laboratory designation A-3) was calibrated at the National Bureau of Standards by measuring its resistance at the boiling point of oxygen, the ice point, the steam point, and the boiling point of sulfuro The constant in the Callendar-Van Dusen equation, which relates resistance to temperature, were evaluated from these measurements made at the fixed points on the International Temperature Scale. In the region from 10 to 90~K, the resistance was measured at 19 different temperatures given by the Bureau's standard thermometer. Between 4 and 10~K we established a provisional temperature scale2 from the value of dR/dT at 10~K, the resistance of the thermometer at 10~K, and the resistance at the boiling point of helium, by evaluating the constants in the equation R = A+BT2+CT5, It is believed that the temperature scale agrees with the thermodynamic scale within 0,1~ from 4 to 14~K, within 0.02~ from 14 to 90~K, and within 0o04~ from 90 to 373~K. Essentially adiabatic conditions were achieved by surrounding the calorimeter 1

Figo 1. Cross-sectional schematic view of cryostat. Legend: 1. Helium exit connector 2. Helium transfer tube 3. Nitrogen inlet and outlet connector 4. Sleeve fitting to helium transport Dewar 5. Nitrogen filling tube 6. Helium transfer-tube extender and cap 7. Screw fitting at inlet of helium transfer tube 8. Brass vacuum can 9. Outer "floating" radiation shield 10. Nitrogen tank 11. Helium exit tube 12. "Economizer" (effluent helium vapor heat exchanger) 13. Nitrogen radiation shield 14. Helium tank 15. Bundle of lead wires 16. Adiabatic shield 17. Helium radiation shield 18. Ring for block and tackle 19. Windlass 20~ Vacuum seal and terminal plate for leads 21. Head plate 22. O-ring gasket 23. Coil spring 24. Supporting string 25. "Floating" ring 26. Calorimeter

with a shield that was maintained at the same temperature as the calorimeter. Energy input and drift periods were timed with clocks driven by an electrical timing circuit. Solid nitrogen, at reduced pressure, was used as a refrigerant for temperatures as low as 50~K and liquid helium for temperatures down to about 5~K. The calorimeter (laboratory designation W-9) used on most of the compounds herein, with 0.0001-in. gold plating on the exterior surfaces, is similar in design and dimensions to W-6, which is shown in Fig. 2 with the two exceptions that the inside was gold-plated (0.001-in.) to protect the calorimeter from possible corrosion by the sample, and the number of vertical conduction vanes was reduced from eight to four. Reducing the number of vanes permitted easier loading and unloading of the sample, had no adverse effects on the attainment of temperature equilibrium in the calorimeter, and facilitated the gold-plating procedure. The top of the calorimeter made a snug fit in the monel neck and the poor thermal conductivity of monel permitted the top to be soldered in place easily and without appreciably heating the calorimeter and contents, thereby avoiding possible thermal decomposition of certain samples. The calorimeter had a measured interior volume of about 92 ml and a calculated exterior volume of about 102 mlo The weight of the calorimeter, helium, and solder (as run) was approximately 90 g. The calorimeter (laboratory designation W-17), constructed especially for ammonia triborane and trimethylamine triborane, has very thin gold plating on the exterior and interior surfaces. It, too, is similar in design to calorimeter W-6, except that the inside was gold plated to protect the calorimeter from possible corrosion by the sample and that the number of vertical conduction vanes was reduced from eight to four. This calorimeter also had a monel neck, which permitted the top to be soldered in place easily and without appreciably heating the calorimeter and contents. This avoided possible thermal decomposition of the sample which takes place at temperatures above 320~K at an appreciable rate. The calorimeter had an interior volume of about 60 ml and weighed (including helium and solder) approximately 33 g. After the calorimeter was filled, weighed, and its top sealed in place with Cerroseal-35 solder,* it was quickly transferred from the dry box to a vacuum line and evacuated for several hours through a pinhole in the helium seal-off tube. Following evacuation, 1- to 2-cm pressure of very pure helium gas was admitted through the pinhole which was then sealed with Cerroseal solder. A glass apparatus contained a small electric soldering iron fitted to the vacuum chamber through a ground-glass ball and socket joint so that the pinhole could be sealed off under reduced helium pressure. The amount of solder was carefully adjusted so that the weight of the empty calorimeter was maintained the same in all heat-capacity determinations. Since the heat-capacity measurements were made up to 350~C, the conduction grease used in the thermometer well and thermocouple sleeve was Apiezon T stopcock grease, Grease corrections were made negligible by reproducing, to within a few tenths of a milligram, the weight of the grease on the calorimeter for each heat-capacity determination, *Low-melting solder (m.p. 117~C) 50o Sn + 50% In by weight. 5

Fig. 2. Cross-sectional schematic view of calorimeter W-6. Legend: 1. Thermal-conductivity cone 2. Monel neck 3. Monel helium seal-off tube 4. Apiezon T stopcock grease 5. Leeds and Northrup platinum resistance thermometer 6. Glass-fiber-insulated No. 40 advance (constantan) wire 7. Formvar varnish 8. Gold-plated copper heater sleeve 9. Gold-plated copper vane 10. Gold-plated copper heater well 11. Differential thermocouple sleeve 12. Spool to bring leads into thermal equilibrium with calorimeter 6

S-uZ-I N3r t-96S-g OC16 - -2 3 INSERT 11ff - 5 4 3 CM 2 — 12 C |2 0 W-6 CALORIMETER Fig. 2 7

THE HEAT CAPACITY OF A STANDARD SAMPLE OF BENZOIC ACID To verify the overall accuracy of our technique, measurements were made on the heat capacity of pure benzoic acid made available by the National Bureau of Standards in conjunction with the program of the Calorimetry Conference.3 The heat capacities measured in our apparatus agree excellently with the values reported by the National Bureau of Standards.4 DETERMINATION OF THE LOW-TEMPERATURE HEAT CAPACITY OF ANHYDROUS SODIUM METABORATE* PREPARATION OF ANHYDROUS SODIUM METABORATE Anhydrous sodium metaborate (NaBO2) is a hygroscopic crystalline solid and melts at about 966~C to a viscous liquid which does not yield a vitreous (glassy) phase. Data from the chemical literature on the physical properties of anhydrous sodium metaborate pertain almost exclusively to melting points,57 sublimation pressures,8 phase equilibria on the Na2O-B203 system,5 optical properties,5-7 and structural studies and densities based on fragmentary X-ray diffraction data.6 79, 10 A very pure sodium metaborate tetrahydrate was used as the starting material. This substance is sold commercially (Eastman Kodak Co.) under the trade name of "Kodalk." On the advice that the compound might contain a trace of calcium, a purification of the material was accomplished by recrystallization from distilled water. Most of the water of hydration was removed by pumping on the sample in a vacuum dessicator with a hyvac pump for three days. Then the sample was heated to 100~C and evacuation was continued with a high-speed diffusion pump to remove the balance of the water. This method effectively removed the water contained in the sample. It is essential that almost all the water be removed before the substance is placed in the furnace because the evolution of water vapor causes a large increase in volume of the sample. Since most of the water had been removed as previously described, the sample was placed in a platinum dish and was heated gradually in a furnace 966~C, the melting point of anhydrous sodium metaborate. The material was allowed to cool gradually to 200~C; then it was transferred from the furnace to a dessicator containing P205. White crystals of acicular habit were formed during the slow cooling. The best crystals from the various batches were removed in a dry box, combined, fused again, and recrystallized slowly to insure purity, homo*By George Grenier and Edgar F. Westrum, Jr. 8

geneity, and good crystal development of the calorimetric sampleso* Determination of water was made by loss in weight on fusiono11,2 The usual Karl Fischer reagent is unsatisfactory because complicating reactions are involved with borates. No water was detected within ~ 0.01.o The NaO2 content of the sample was determined by carefully evaporating the sample to dryness in hydrochloric acid and titrating the residual chloride with standardized silver nitrate solution using dichlorofluorescein as an indicator,'1l15 The B203 content of the sample was obtained by first neutralizing a sample of the metaborate with hydrochloric acid, then adding mannitol and titrating the boric acid potentiometrically.16-19 The percent by weight of sodium as Na2O was 47.11, 46o91, 47.30; average, 47.11 ~ 0.20C%, in accord with the claimed ~ 0.2% reliability of the method. (Theoretical Na2O: 47ol10%o ) The percent by weight of boron reported as B203 was 52.77, 52o84, 53012; average, 52.91 ~ 0.135. (Theoretical B203: 52o90%.) The material, therefore, is stoichimometrically anhydrous sodium metaborate. HYGROSCOPICITY OF SODIUM METABORATE Although the anhydrous material used in this investigation was handled in an anhydrous chamber, it was desirable to know the rate of adsorption of water from the ambient air at 40% relative humidity and 25~C. For this purpose a 2.0-g sample was fused, crystallized, and cooled in a dessicator in a platinum crucible and weighed at various times at room temperature in the ambient laboratory atmosphere. At 30 min after exposure, the increase in apparent sample weight was 0.24%, at 100 min, 0.77%, and after 11 hr, 352%. The necessity of handling this material in an anhydrous atmosphere is readily apparent. RESULTS OF HEAT-CAPACITY MEASUREMENTS ON ANHYDROUS CRYSTALLINE SODIUM METABORATE The original experimental values of the molal heat capacity of sodium metaborate at the mean temperature of the runs are given in Table I and Fig, 35 A column also gives the temperature increments, AT, of the individual determinations. Small corrections have been made for these finite temperature increments and for the slight differences in the amounts of helium and solder in the measurements on the empty and on the full calorimeter. The results are expressed in terms of the defined thermochemical calorie equal to 4.1840 absolute joules. The analyses of product material were performed by Lynn Jo Kirby of this laboratory. 9

SODIUM METABORATE Li.J.^12 0 0 0 8 Fig. 3. Molal heat capacity of sodium metaborate as a function of absolute temperature (6-350~K).

TABLE I THE MOLAL HEAT CAPACITY OF SODIUM METABORATE T, ~K AT, ~K cPa l T, ~K AT, OK Cp cal deg-1 _ _ cal deg 5.48 6.68 7.83 9.08 10.38 11.72 13.06 14.40 15.74 17.14 18.69 20.53 22.74 25.15 27.64 30.36 33.41 36.89 40.89 45.57 50 72 55.96 60. 88 64.98 71.20 77.18 77.94 84.46 91.34 99.00 1.252 1.213 1.255 1o557 1o337 1,349 1.382 1.360 1.342 1.363 1.443 1.674 2.003 2.423 2.404 2.578 2.858 3.243 3.717 4.282 5.082 5.218 5.268 4.564 6.425 6.015 5.945 6.447 6.594 7.153 8,166 0.003 0.005 0.010 0.017 0.027 0.o4o 0.057 0.078 0.105 0.139 0.185 0.253 0.354 0.487 0.652 0.859 1.125 1.464 1.883 2.405 2.997 3.598 4.152 4.604 5.244 5.839 5.908 6.515 7.099 7.674 107.29 115.59 123.94 132.48 140.98 149.44 158.07 167.33 177.16 187.21 197.36 207.75 215.06 225.14 235.23 245,47 255.80 265.98 276.10 286.16 296.22 306.34 316.45 326.55 336.56 346.49 8.402 8.207 8.489 8.594 8.402 8.426 8,824 9.704 9.954 10.142 10.177 10.172 10.112 10.059 10.113 10 380 10.287 10.078 10o.158 9.970 l. 141 10.102 10.128 10.092 9.944 9.924 8.257 8.796 9.310 9.797 10.25 10o.66 ll. 06 11,48 11.88 12.28 12.66 1.302 13.28 13.62 13594 14.27 14.58 14.88 15.16 15.45 15.71 15.99 16.24 16.48 16.73 16.96 11

The ice point was taken to be 273.16~K9 and the gram molecular weight of sodium metaborate (NaBO2) was taken as 65.811 g. A calorimetric sample of 133-6378 g (2.03061 moles) was employed for these determinations. The molal heat capacity and the thermodynamic functions derived from the heat capacity are listed at rounded temperatures in Table IIo These heat-capacity values were read from a smooth curve through the experimental points, and they are estimated to have a probable error of 0l1% above 25~K, 1.0% at 140K, and 5o0% at 5~Ko The heat capacity was extrapolated below 10~K with a Debye function, The effect of nuclear spin is not included in the entropy and freeenergy function. The estimated probable error in the entrophy2 heat content, and free-energy function is 0.1% above 1000K, but to make the table internally consistent and to permit accurate interpolation, some of the values are given to one more figure than is justified by the estimated probable error. Small corrections have been made for the finite temperature increments and for the slight differences in the amounts of helium and solder in, the measurements on the empty and on the full calorimeter. The results are expressed in terms of the defined thermochemical calorie equal to 4o1840 absolute joules. The ice point was taken to be 273.16~K. The molal heat capacity and thermodynamic functions (in calories per degree) may be extrapolated to higher temperatures by the following three formulas predicated on the method described by Shomate.20 C = 10.23 + 0.0212 T - 7,02 x 104 T-2 P (Ho - H~o)/T = 10.23 + 0.0106 T + 7.02 x 104 T2 - 1447.9 T1 S~ = 23.58 log T + 0.0212 T + 3o51 x 104 T-2 - 47~44 These formulas should be used with caution as they are an approximation justified only by the absence of experimental determinations. However, no thermal transformations or anomalies were detected by Morey and Merwin5 by thermal analysis between 3500K and the melting point. DETERMINATION OF THE LOW-TEMPERATURE HEAT CAPACITY OF ANHYDROUS CRYSTALLINE SODIUM TETRABORATE* Despite the use of borax and related materials in ceramic technology for many centuries and their widespread utilization in current chemical technology, reliable thermodynamic data on alkali borates are relatively rare. Data in the By Edgar F. Westrum, Jro, and George Grenier. 12

TABLE II MOLAL THERMODYNAMIC FUNCTIONS OF SODIUM METABORATE ~~~T,~0~K ca 0 0 c ( c s, H - HO, -(F - HO)HT,.....K.cal aeg-l cal deg'1 cal cal deg 5 10 15 20 25 0 002 0O024 0.090 0.232 0.479 30 35 40 45 50 0.830 1.276 1.788 2.341 2.913 6o 70 80 90 100 110 120 130 14o 150 4.054 5.122 6,102 6.982 7.751 8.438 9.066 9,646 10.19 10.70 o. ooo6 0.008 0o028 0.071 0.147 0.264 0.425 0.628 0.870 1,146 1.779 2',485 30234 4.005 4.781 5.553 6.314 70063 70798 8.519 90224 90914 10 588 11.246 11.891 12.521 135139 135743 14,337 14.918 15.489 16. 49 16.600 17.140 17.672 20.203 16.224 17.574 13 0.002 0.059 0.32 1.09 2.82 6.05 11.28 18.92 29023 42.36 77.22 123520 179.38 244.91 318.65 399.63 487.17 58008 680.0 784.5 893.7 1007.5 1125.4 12473. 1373.0 1502o2 1634.9 1771.0 1910.4 2052,9 2198.4 2346.9 2498.2 2652.3 2809.1 3631.0 0.0001 0.002 0.007 Oo 002 Oo 007 0.017 o 0534 00062 0.103 0.155 0.220 0.299 0.492 0.725 0.992 1.284 1.595 1.920 2 254 2.596 2.941 35289 3.638 3.988 4.336 4.681 5.026 50368 5.707 60043 65377 6.707 7.054 7o034 7.357 7.678 7.994 8,308 9.829 7.459 8.250 160 170 180 190 200 11.16 11.59 12.00 12538 12.74 210 220 230 240 250 13.10 13.44 13577 14.10 14.40 260 270 280 290 300 14,70 14 99 15.27 15.55 15.81 350 17.04 273515 298.15 15.o8 15.76 2780.0

chemical literature on the physical properties of anhydrous vitreous and crystalline sodium tetraborate are concerned primarily with melting point and phase equilibrium studies5 on the Na20-B203 systems. We use the designation sodium tetraborate to refer to the chemical composition Na2B407, although a contrary usage is occasionally found.5 Although two or possibly three distinct crystallographic phases of this material exist,5 the material prepared for this work is the ca-form and is ordinarily obtainable and commercially available. No evidence for an enantiotropic inversion between the various forms has been found,5 despite a careful search from below 500~ to the melting point. The rate of conversion of p to a is very slow and the reverse transformation has not been observed. PREPARATION AND ANALYSIS OF CRYSTALLINE SODIUM TETRABORATE The crystalline sodium tetraborate sample was prepared by crystallizing a dehydrated sample of analytical-reagent grade sodium tetraborate decahydrate from the molten state in a platinum dish under carefully controlled conditions. Since rapid cooling or prolonged periods of heating at temperatures appreciably higher than the melting point of 742.5~C5 result in glass formation, it is essential for crystal growth that the temperature does not exceed 760~C nor remain at this temperature for a period of more than about 10 min, and that a controlled rate of cooling be maintained. This was achieved by gradually decreasing the temperature in the electric muffle to about 300~C in 10-hr time. The covered platinum dish was then transferred to a dessicator over phosphorus pentoxide to cool to room temperature without adsorption of water. The resulting white crystals were shown to be free of glass particles by a careful examination of the sample under a polarizing microscope.* Determination of water was made by loss in weight on fusion.112 The usual method involving Karl Fischer reagent is unsatisfactory because complicating reactions are involved with borates. Although it is reported by Morey and Merwin5 that the crystalline material at 300~C and the molten tetraborate itself will take up water in humid weather, this is lost upon crystallization of the compound under anhydrous conditions, so the method as employed here is efficacious. Determination of water by this technique indicated O0Ol ~ Oo01l water. The Np03 content of the sample was determined by carefully evaporating the sample to dryness in hydrochloric acid and titrating the residual chloride with standardized silver nitrate solution using dichlorofluorescein as an indicator. 1"15 The B203 content of the sample was obtained by first neutralizing a sample of the metaborate with hydrochloric acid, then adding mannitol and titrating the The analyses of the final calorimetric samples were performed by Lynn J. Kirby of this laboratory. 14

boric acid potentiometrically 7 boric acid potentiometricallyo The percent by weight of sodium as Na20 was 30o80, 30.78, 30o79; average, 30.79 ~ 0.01%. (Theoretical Na2O: 30o80o.) The percent by weight of boron reported as B203 was 69~26, 69,20, 69.07; average, 69.18 ~ 0.04%. (Theoretical B203: 69.20%) The material is, therefore, stoichimometrically anhydrous sodium tetraborate, Na2B407. The mass of the crystalline sample used in the calorimeter was 79.6707 g (in vacuo). RESULTS OF HEAT-CAPACITY MEASUREMENTS ON ANjYDROUS CRYSTALLINE SODIUM TETRABORATE The experimental values of the heat capacity of crystalline sodium tetraborate are presented in Table III and Fig. 4. Small corrections have been made for the finite temperature increments and for the slight differences in the amounts of helium and solder in the measurements on the empty and on the full calorimeter. The results are expressed in terms of the defined thermochemical calorie equal to 4.1840 absolute joules. The ice point was taken to be 273.15~K. The molal heat capacity and the thermodynamic functions derived from the heat capacity of these substances are listed at rounded temperatures in Table IVo These heat-capacity values were read from a smooth curve through the experimental points, and are estimated to have a probable error of 0.1% above 25~K, 1% at 14~K, increasing to 5% at 5~K. The heat capacity was extrapolated below 10~K with a Debye function. The effect of nuclear spin is not included in the entropy and free-energy function. The estimated probable error in the entropy, heat content, and free-energy function is 0.1% above 1000K, but to make the table internally consistent and to permit accurate interpolation, some of the values are given to one more figure than is justified by the estimated probable error. Formulas for the extrapolation of the molal thermodynamic functions to temperatures above 350~K are derived by the method described by Shomate20 using 300~K as the base temperature. The equations for crystalline sodium tetraborate (in cal deg-1 mole-1)are Cp = 21.83 + 0.0850T - 2.250 x 105 T2, (H~ - Ho)/T = 21.83 + 0.0425T + 2.250 x 105 T- - 3779~8 T-" and S~ = 50.27 log T + 0.0850T +1125 x 105 T-2 - 105.70. 15

CRYSTALLINE SODIUM TETRABORATE 50 40 30 I. 0 1~T ~~30~T,K 10 0 50 100 150 200 250 300 350 T,0K Fig. 4. Molal heat capacity of crystalline anhydrous sodium tetraborate. (The centers of the open circles represent the direct experimental determinations. The diameter of the circles does not represent an estimate of precision.)

TABLE III THE MOLAL HEAT CAPACITY OF CRYSTALLINE SODIUM (Calories per degree) TETRABORATE T, ~K AT, ~K Cp T, ~K AT, K Cp SERIES I 5.82 6.60 7.81 9007 10.21 11,50 12.92 14.37 15.92 17.52 19.21 21.03 23.02 25.23 27.73 30.61 33.80 37.25 41.09 45.45 50.18 55.32 61.01 67.36 74.48 81.61 89.18 97.84 107.29 117.03 126.62 135.89 144.71 153.70 162.66 0.575 2.104 1.538 1.246 1.235 1.490 1.423 1.558 1.571 1.631 1.753 1.893 2.097 2.322 2.664 3.095 3.276 3.621 4.067 4.636 4.832 5.433 5.939 6.750 7.484 60920 8.218 9.098 9.798 9.673 9 517 9.015 8.611 8.826 9.081 0.015 0.019 0.030 0.055 0 089 172 o08 181.88 191.80 201.60 211.13 9.738 9.869 9.958 9.648 9.397 29.70 31.03 32.34 33.60 34.83 00144 0.226 05328 0.460 0.623 220.53 229.84 238.94 248.07 257.40 0.843 1.097 1.430 1.824 2.289 266.90 276.50 286.39 296.65 306.88 9.400 9.168 90020 9.242 9.428 9.558 9.622 10.171 10.15336 10o131 o10175 9.990 10,443 10o348 35599 37.12 38.17 39.22 40.32 41.36 42.36 43.41 44.47 45.52 46054 47051 48.48 49.33 317.02 327.09 337.30 347.69 2.882 3.591 4.380 5.296 6.346 SERIES II 7.506 8.746 10.11 11.59 15.15 14.70 16.27 17.89 19.60 21.28 253.26 262.55 271.91 281.41 291.36 9.136 90456 9.273 9.731 10o152 10355 10.253 10 386 11.260 10o411 39.78 40o81 41.88 42.89 43592 44.99 46.02 47.00 48.02 49.06 301.61 311 91 322.22 333.05 343597 22.91 24.38 25.73 27.08 28.38 17

TABLE IV MOLAL THERMODYNAMIC PROPERTIES OF CRYSTALLINE SODIUM TETRABORATE T, Cp, S, - H -(F~ H)/T, "K cal/deg cal/deg cal cal/deg OK~ ~~~~, cal/deg..... 5 10 15 20 25 00012 0.081 0.379 0.949 1.781 30 35 40 45 50 20751 3.861 5.036 6.238 7.462 60 70 8o 90 100 110 120 130 140 150 9.870 12.18 14o35 16.38 18.29 20 o08 21.79 23543 25.00 26.53 00004 0.027 0.108 00288 o.585 0.993 1.499 2.091 2.753 3.474 5.047 6.744 8.512 10.522 12.149 13.976 15.797 17.607 19.401 21.178 22.938 24.678 263.99 28.097 29.777 31.438 33.080 34.705 36.310 37.896 39.463 41.016 42.552 44 070 45.572 52.850 41.504 45.296 o.014 0.202 1.255 4.449 11.19 22.46 38.96 61.17 89.34 123.57 210.22 320.60 453526 607.1 780.6 972.5 1181.9 1408.1 1650.3 1908.0 218006 2467.6 2768.6 3083 0 3410,5 3750.9 4105.0 4469.4 4846.5 5235.1 5635.1 60463. 6468.4 6901.1 7344 2 9708.1 6178.6 7261.9 Oo001 0.007 0.024 o066 0.138 0.244 0.386 0.562 0.768 1.003 1.543 2.164 2.846 35576 4.343 5.135 5.948 6.776 7.613 8,458 9.309 10.163 11.018 11.871 12.725 135576 14.425 15.273 16.117 16.956 17.789 18.622 19.451 20.273 21 091 25.112 18,885 20.940 i60 170 18o 190 200 210 220 230 240 250 27099 29.41 30.77 32,10 33540 34.68 35.93 37.12 38.29 39.43 260 270 280 290 300 350 273.15 298.15 40.57 41.67 42.75 43.79 44.83 49.65 42.01 44.64

These equations should be used with caution above 3500K as they represent an approximation justified only by the absence of experimental determinations. However, no evidence for thermal transformations or anomalies was detected by Morey and Merwin5 by thermal analysis between 3500K and the melting point. DETERMINATION OF THE LOW-TEMPERATURE HEAT CAPACITY OF VITREOUS SODIUM TETRABORATE* PREPARATION AND PURITY OF VITREOUS SODIUM TETRABORATE The vitreous sodium tetraborate was prepared from the same material as the crystalline sample. The dehydrated sample was heated to 820~C for 30 min to insure glass formation. The glass was annealed for 15 min at 420~C and cooled in an anhydrous atmosphere. Analytical data by identical methods on the vitreous material indicated: water, 0.0% ~ 0.1%; Na20, 30.75%, 30.79% (theoretical, 30.800); B203, 69l16%, 69.27% (theoretical, 69.20%), in good accord with theory. The mass of the vitreous sample consisting of fragments of 2-5 mesh, was 112.6441 g (in vacuo)o RESULTS OF HEAT-CAPACITY MEASUREMENTS ON VITREOUS SODIUM TETRABORATE The experimental values of the heat capacity of this material are listed in Table V using the same conventions as previously noted. The molal thermodynamic functions are reported in Table VI; however since the third law of thermodynamics may not be assumed for the vitreous phase, the entropy increment is tabulated, and the free-energy function cannot be specified at present. Formulas for the extrapolation of the molal thermodynamic functions to temperatures above 350~K for vitreous sodium tetraborate (in cal mole"1 deg-1) are: C = 27.83 + 0.0270T - 4.320 x 105 T"2 p (H~ - Ho)/T = 27.83 + 0.0360T + 4.320 x 105 T-2 - 5819.5 T-1 and S - So = 64.09 log T + 0.0720T + 2.160 x 105 T-2 - 137,96. By Edgar F. WestrumJr., and George Grenier. 19

TABLE V THE MOLAL HEAT CAPACITY OF VITREOUS SODIUM (Calories per degree) TETRABORATE T, K AT, K Cp T, K AT, K Cp 5.31 6.68 8.09 9.22 10.32 11.54 12.82 14.13 15.59 17.21 19.01 21.08 23.41 25.95 28.71 31.69 34.85 38.23 41.92 46.13 51.00 56.39 62.26 68.55 75.01 81.43 88.o6 95.20 L03.03 L11.83 1.337 1.800 1.252 1.110 1.140 1.322 1.265 1.373 1.563 1.674 1.935 2.206 2.460 2.623 2.890 3.070 3.253 3. 508 3.873 4.546 5.176 5.605 6.116 6.468 6.455 6.370 6.885 7.395 8.270 9,324 0.015 0.027 0.057.0 99 0.150 121.62 131.54 140.88 149.95 159.04 0.217 0.305 00411 0.549 0.724 168.25 177.49 186.79 196.08 205.13 0.947 1.231 1.598 2.030 2.543 214.14 223.13 232.21 241.51 250.99 10.250 9 594 9.093 9.036 9.141 9.280 9.206 9.392 9.183 8.907 90113 8.863 9.298 9.286 9.685 9.895 9.745 9.726 9.763 10.059 10o571 10o511 10.102 14.917 21533 22.94 24.42 25.79 27.14 28.48 29.77 31.05 32.30 33.49 34.66 35.80 36.92 38.06 39.18 40.36 41.42 42.49 43.56 44.60 45.68 46.77 47.74 48.92 3.137 3.794 4.540 5.361 6.326 7.445 8.694 10.00 11 38 12.72 360.78 270.61 280.35 290.09 300,00 310.30 320.84 331.13 343.63 14.08 15.41 16.73 18.14 19.67 20

TABLE VI MOLAL THERMODYNAMIC PROPERTIES OF VITREOUS SODIUM TETRABORATE T.al dep, ~ _K _ cal deg" 5 10 15 20 25 0.013 0.134 0.490 1.078 1.866 30 35 40 45 50 2.795 3.838 4.933 6.063 7.220 60 70 80 90 100 9.499 11.69 13.78 15.77 17.60 110 120 130 140 150 19.36 21o06 22-70 24.28 25.80 0' so - O cal deg"' 0.004 0.044 0.158 0.375 0.697 1,117 1.625 2.207 2.853 3.552 5.072 6.702 8.400 10.138 11.895 13.655 15.413 17.163 18.903 20.631 22.343 24.041 250721 27. 87 29.036 30.668 32.285 33.887 35.471 37.042 38.597 40.136 41.660 43.169 44.663 51.918 40.620 44.391 - ao, cal 0, 0O16 0.334 1.795 5.635 12.92 24.51 41o04 62.93 90.40 123.61 207.30 313.32 440. 64 588.5 755.4 940.1 1142.2 1361.1 1596o0 1846.4 2111.8 2391.8 2686.0 2993.9 3315.4 3650.1 3997.7 4357.9 473005 5115.2 5511.7 5916.6 6338,7 6768.7 7209.5 9565.2 6050.9 7127.6 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 350 273.15 298.15 27.29 28.70 30 11 31.48 32.82 34.12 35.40 36.65 37.87 39.07 40.23 41.36 42.46 43.54 44.61 49.50 41.71 44.42 21

DISCUSSION A comparison of heat capacities of crystalline and vitreous sodium tetraborate is depicted in Fig. 5. It is striking that the heat capacity of the vitreous material is lower than that of the crystals above 350K, as may be seen even more clearly in the deviation plot, Fig. 6. This contrasts with data on other crystalline-vitreous pairs. For example, the heat capacity of quartz rises above that of vitreous silica only at about 2100K.21 Moreover, the heat capacity of crystalline boron trioxide21 exceeds the heat capacity of vitreous boron trioxide only at temperatures above 300~K. From the heats of solution in nitric acid of Na20, B203 and two forms of Na2B40722 and the heats of formation of Na20 and B203,23 the heats of formation of crystalline and vitreous Na2B407 are calculated as -786.5 ~ 3 and -781.5 ~ 3 kcal mole-l, respectively, at 25~. The present measurements, together with entropy data on the elements, 23s24 permit the evaluation of the free energy of formation of crystalline Na2B407 as -739.7 ~ 3 kcal mole-1 at 25~. It is not possible to evaluate the zero-point entropy of the vitreous material; however, for the devitrification reaction, H oK = -4.99 kcal moleTHE LOW-TEMPERATURE HEAT CAPACITY OF SODIUM METHOXIDE* Sodium methoxide has long been used as a laboratory reagent in the preparation of important organic intermediates. Since 1944 it has been commercially available and currently is widely used on a large scale in the manufacture of certain pharmaceuticals, dyestuffs and other important organics. There is, therefore, considerable technological interest in accurate thermal properties of this material. No previous measurements of the heat capacity of sodium methoxide have been reported in the literature. PREPARATION AND PURITY OF SODIUM METHOXIDE The reaction of sodium metal with methyl alcohol to yield sodium methoxide and hydrogen was performed in a closed Pyrex vacuum system in a nitrogen atmosphere purified by passage over hot copper to remove oxygen, over potassium hydroxide pellets to remove acid, and through two phosphorus pentoxide columns to remove the remaining traces of water. Analytical reagent grade methyl alcohol (ketone, aldehyde and organic acid content to pass ACS test) was purified by refluxing for 24 hr over magnesium methoxide25 followed by subsequent fractional distillation in the nitrogen atmosphere directly into a storage bulb connected to the reaction vessel. About 60 g of sodium metal (99.950 purity) was cut under xylene into one-cm cubes with fresh metallic surfaces and quickly transferred By Edar F. Westrum, Jr., and George Grenier. By Edgar F. Westrum, Jr., and George Grenier. 22

SODIUM TETRABORATE 50 40 I. 30 _ bJ 0 I 0 - < 20 u 1 - CRYSTALLIF --- VITREOUS 0 II 0 50 100 150 200 250 T,~K Fig. 5. Comparison of the heat capacities of anhydrous crystallne vitreous sodium tetraborate. 300 350

SODIUM TETRABORATE (VITREOUS-CRYSTALLINE) LJ I IJ LLJ T. 0 u < -0. I 5 20 50 100 200 300 T,K Fig. 6. Deviation plot for the heat capacities of sodium tetraborate forms. Cp = Cp, vitreous Cp, crystalline,

into a cylindrical receiver 4-cm diam by 25 cm in length. This receiver communicated with the spherical one-liter reaction vessel below it through a coaxial Pyrex capillary tube of 0.9-mm ID and 4-cm length. After evacuation of the sodium for 20 hr (while the alcohol was refluxing), the sodium was fused to permit possible slag to float to the surface. Five hundred milliliters of methanol were added to the reaction vessel, and molten sodium was then injected under a slight nitrogen pressure. The sodium flow into the reactor was regulated by partially withdrawing a closefitting steel twist drill from the capillary connecting the sodium cylinder to the reactor. The position of the drill was manipulated with a coaxial steel shaft which extended from the shank of of the drill up through the sodium and out of the vacuum/nitrogen space through a vacuum-tight Teflon standard taper o-ring gland. The use of a drill made possible the penetration of a tip of solid sodium methoxide which occassionally formed on the reactor side of the capillary. The rate of addition of the sodium was limited by the capability of the exit tube reflux condenser to dissipate the heat of the reaction. The hydrogen left the exit tube via a mercury-seal-bubbler. The excess methanol was removed by continuous evacuation over several days as the temperature was gradually increased to 100~ to decompose any dialcoholate (NaOCH32CH30H) present. The product was subsequently exposed only to the anhydrous nitrogen atmosphere of the dry box for as short a time as possible. Total alkali plus carbonate was determined by titration of weighed samples with standard acid to the methyl orange end-point yielding 99.87 ~ 0.02% (as sodium methoxide). Total alkali was determined on additional weighed samples to the phenolphthalein end-point as 99.72 ~ 0.01% (as sodium methoxide). The difference of the two titrations indicates the carbonate content to approximate 0.15%. No water or hydroxide was detected by high-sensitivity Karl Fischer reagent. Perhaps the best indication of the absence of traces of water or of methanol is the freedom of the heat-capacity curves of anomalous behavior near the fusion temperatures of these substances. Spectrochemical analysis confirmed the presence of less than 0.02% metallic contaminants. Attempts to obtain macroscopic crystals were unsuccessful. The NaOCH3 consisted of a fine, white powder. To increase the amount of material in the calorimeter and to improve the thermal conductivity, the material was pelleted into rods with rounded ends about 5 mm in diameter and 10 mm in length. The measurements were made on 39.8571 g (in vacuo) of sodium methoxide, the molecular weight of which was taken to be 54.026. RESULTS OF HEAT-CAPACITY MEASUREMENTS ON SODIUM METHOXIDE The heat-capacity determinations were made with the Mark I adiabatic cryostat in calorimeter W-9. The calorimeter was loaded in a dry box, evacuated under high vacuum and 2.8 cm of helium gas were added at 27~ to aid in the establishment of thermal equilibrium. The original experimental values of the 25

molal heat capacity of sodium methoxide at the mean temperature of the runs are given in Table VIIo Since the determinations are presented in chronological sequence, the approximate temperature increments can be readily inferred. Small corrections have been made for the finite temperature increments and for the slight differences in the amounts of helium and solder in the measurements on the empty and on the full calorimeter. The results are expressed in terms of the defined thermochemical calorie equal to 4.1840 absolute jouleso The ice point was taken to be 273.15~K. The molal heat capacity and the thermodynamic functions derived from the heat capacity are listed at rounded temperatures in Table VIII. These heat capacity values were read from a smooth curve through the experimental points, and they are estimated to have a probable error of 0.1% above 250K, 1% at 10 K, and 4% at 5~K. The heat capacity was extrapolated below 6~K with a T3 function. The effect of nuclear spin is not included in the entropy and free-energy function. The estimated probable error in the entropy, heat content and free-energy function is 0.2% above 100~K, but to make the table internally consistent, some of the values are given to one more figure than is justified by the estimated probable error. The measured heat capacities from 5 to 70~ are plotted in Fig. 7 together with an estimate of the "excess" heat capacity near 340 obtained by interpolating the temperature dependence of the Debye theta over the anomalous range. The molal enthalpy and entropy increments associated with this anomaly of unknown origin are 11.5 cal mole-land 0.43 cal molel' deg-1, respectively. DETERMINATION OF THE LOW-TEMPERATURE HEAT CAPACITY AND THERMODYNAMIC PROPERTIES OF AMMONIA TRIBORANE* The desirability of data on the thermal and thermodynamic properties of a material with as many technological possibilities and fundamentally interesting physical properties as ammonia triborane needs no argument. The preparation of ammonia triborane was reported by Parry and Kodama26 in 1957. It is, unfortunately, rather difficult to prepare in high purity on a fairly large scale at the present time and is sufficiently unstable to require some care in its handling. Very little information is presently available concerning the physical properties of this interesting compound. Nordman, Reimann, and Peters27 have made a single crystal x-ray diffraction study to elucidate its structural and crystallographic properties. They find that the NH3B3H7 molecule contains a triangle of boron atoms with one side only slightly shorter than the other two. By Edgar F. estrum Jr., and Norman E. Levitin. By Edgar F. Westrum, Jr., and Norman E. Levitin. 26

TK. 40 0 60 8 0. T LJ 0 1 0 2 U Cu a. 6 4 2 I ~ 00. ' 0 d T -2 o 0 _j U 0 < ou 0 10 20 30 4-0 50 T, K Fig. 7. Molal heat capacity of sodium methoxide. Experimental heat capacities are plotted and resolved into the lattice contribution (dashed curve) and the anomalous portion (inset). 27

TABLE VII MOLAL HEAT CAPACITY OF SODIUM METHOXIDE (IN CAL/DEGREE) T, ~K p T,~K Cp T,~K Cp ~.,,,,, ~ ~ ~ ~.... I,,. ~ ~,,...... t~,, ~ J,...?,. -.;.,;,.......: ~ - ~ ~ _ - 5.84 6.74 8.14 9.65 7.92 8.92 10.16 11.50 12.94 14.27 15.85 17.41 19.02 20.83 22.99 25.86 28.93 32.15 35.66 0.41 0.53 0.71 0.96 0.76 0.81 1.05 1.260 1.517 1.777 2.079 2.387 2.707 3.063 3.464 3.994 4.570 5.062 5.173 39.69 44.20 49.22 54.55 60.23 66.45 72.62 79.33 86.88 94.52 101.56 108.92 117.64 127.63 138.03 148.20 158.20 168.15 5.266 5.659 6.105 6.590 7.114 7.682 8.203 8.773 9.390 9.937 10,38 10.86 11.36 11.88 12.35 12.77 13.14 13.41 177.95 187.57 197.05 206.37 215.62 218.71 228.60 238.62 248.52 258.24 268.09 278.11 288.23 298.40 308.44 318.46 328.73 339.41 13.76 14.03 14.27 14,49 14.72 14.79 15.03 15.25 15.48 15.71 15.89 16.13 16.38 16.55 16.86 17.10 17.23 17.48 28

TABLE VIII MOLAL THERMODYNAMIC FUNCTIONS OF SODIUM METHOXIDE (. H c c _- (Fo - T S~ (HO- HO ), HOd)/T, T, O~K,cal/deg cal/deg, cal,. cal/deg 5 10 15 20 25 30 35 40 45 50 60 70 80 90 100 110 120 130 140 150 160 170 18o 190 200 210 220 230 240 250 260 270 280 290 300 350 273.16 298.16 (0o318) 1.002 10915 2.895 3.837 4.799 5.160 5.282 5.728 6.177 70091 7.977 8.831 9.615 10.305 10.925 11.489 11. 990 12.438 12.840 13.197 13.520 13.821 14.098 14.353 14.593 14.828 15.058 15.285 15.511 15.736 15.960 16.189 16.417 16.645 17.722 16.031 16.604 (0.106) 0.500 1.074 1.759 2.507 3 289 4.067 4.762 5.408 6,035 7.242 8.402 90523 0o 609 11.659 12.671 135646 14.585 15.490 16.362 17.203 18.013 18.795 19.549 20.279 20.985 21.669 22.333 22.979 23.608 24.220 24.818 25.403 25.975 26.536 29.185 25.004 26,433 (0.40) 3050 10.73 22.75 39.60 61.13 86.38 112.40 139.87 169.63 235.96 311.32 395539 487.7 587.4 693.5 805.6 923.1 1045.2 1171.7 1301.9 1435.5 1572.2 1711.8 1854.1 1998.8 2145.9 2295.4 2447.1 2601.1 2757.3 2915.8 3076.5 3239.5 3404.9 4264.5 2966.3 3374.3 (0.026) 0.150 0.359 00621 0.923 1.251 1.599 1.952 2.300 2.642 3.309 3.954 4.581 50190 5.785 6.366 6,932 7.484 8.024 8.551 9.066 9.569 10.o60 10 539 11.009 11.467 11.915 12,353 12.783 135204 13.615 14.019 14.415 14 804 15.186 17.001 14.145 15.116 29

The NH3 group is attached to the boron atom opposite the shortest boron-boron bond and is pointed at about a 65~ angle out of the plane of the boron atomso They also found evidence of a structural transformation taking place below room temperature, but were not able to establish the temperature of the transition. We find that the transition takes place at 297,10~K and that it is an unusually entropic one. PREPARATION OF AMMONIA TRIBORANE The ammonia triborane was prepared by the method of G. Kodama.26 Tetraborane and tetrahydropyran were reacted at a temperature of about -120~C to moderate the reaction: 2 B4H1o + 2 CH2(CH2)40 -- 2 CH2(CH2)40:B3H7 + B2HE. After excess tetrahydropyran was removed, the tetrahydropyran triborane was then reacted in ethyl ether with ammonia at -78~C. CH2(CH2)49:B3H7 + NE3 - NI3B3H7 + CH2(CH2)4 The excess ammonia, ethyl ether, and displaced tetrahydropyran were removed at room temperature. The product was dissolved in benzene and removed from the reactor. It was subsequently precipitated by addition of methylcyclohexane to the solution and was filtered under a nitrogen atmosphere. Further purification of the product was achieved by dissolving it in benzene, filtering the solution, and precipitating the ammonia triborane with a large excess of methylcyclohexane. The product was then dissolved in toluene and recrystallized at -95~C. The product was filtered again in an anhydrous nitrogen atmosphere, and the adsorbed toluene was removed by evacuating for two hours under high vacuum. The sample was stored under vacuum at -196~C until it was used. The yield of crude ammonia triborane was between 70 and 80% of the theoretical based on the tetraborane used. The yield of the finally purified product was approximately 50% of theoretical. Chemical analyses for nitrogen, boron, and active hydrogen were made with the following results: N2, 24.8% (theoretical, 24o9%); B, 57.4% (theoretical, 57.2%); and active H2, 12.47% (theoretical, 12.46%). There is every indication then that the product was 99.8% pure. The absence of the toluene used as a recrystallizing solvent is established by the absence of a hump in the heat capacity curve at or near the melting point of toluene. The preparation was made by J. Carter and analyzed by him. The details of the large scale preparation will be presented elsewhere.28 30

THE RESULTS OF THE HEAT-CAPACITY MEASUREMENTS ON AMMONIA TRIBORANE The original experimental values of the molal heat capacity of the sample of ammonia triborane weighing 15.085 grams (vacuo) are presented in chronological sequence together with the mean temperature of the individual runs in Table IX 2nd in Figo 8. These data have been corrected to represent true heat capacities by applying a curvature correction for the finite temperature increments actually used in the measurements. The size of these temperature increments can be inferred in general from the mean temperatures of the adjacent data points. The results are expressed in terms of a defined thermochemical calorie equal to 4.1840 absolute joules. The ice point was taken to be 273.15~K and the gram formula weight of ammonia triborane was taken to be 56 548 g. The molal heat capacity and the thermodynamic functions derived from the heat capacity data are listed at rounded temperatures in Table X. These heatcapacity values were read from a smooth curve through the experimental points and they are estimated to have a probable error of approximately 0.1% above 25o, 1% at 14~K increasing to about 5% at 5~Ko The heat capacity was extrapolated below 5~K using a Debye function. The effect of nuclear spin and of mixing of isotopes is not included in the entropy and free-energy function. The estimated probable error in the entropy, heat content, and free-energy function is 0.1% above 1000K, but to make the table internally consistent and to permit accurate interpolation, some of the thermodynamic values are given to one more figure than is justified by the estimated probable error. In addition to the numerical quadrature of points read from the smooth curve, the data of Table IX were fed into a program On the IBM 650 calculator which independently evaluated the heat capacity at rounded temperatures, and which performed the integration leading to the thermodynamic functionso In this manner a completely independent check has been obtained on the numerical values, within the precision indices indicated in the above paragraph. Because of the slow rate of achievement of temperature equilibrium in the transition region, it was not possible to delineate heat capacity as a function of temperature with great exactitude. To evaluate more precisely the thermodynamic functions, therefore, a number of energy inputs of varying magnitude were made in the transition region to obtain the enthalpy and entropy increments. We have designated the form of the material stable below the 297.10~K transition temperature as the a-form and that stable above this temperature as the 3-form. It will be noted in Table IX that the heat capacity near the transition temperature approximates 3 x 103 cal mole-1 deg-l suggesting very strongly that the transition is indeed a first-order one. However, there is a considerable pre-transitional rise in heat capacity. This fact makes rather difficult the evaluation of the entropy and enthalpy increments on transition. To obtain these values it is necessary to obtain a "normal" heat-capacity curve for the substance in the absence of the aforesaid transition over a rather broad range. As a zeroth approximation to this "background" heat capacity, we have simply 51

Cp, CAL. MOLE-I 0 0 DEG.' 0 Oc 0c 0 0 0 K M aN - I ' I 'I ' I CtCO CD CD I crt', CD f 0 C4C 0 0 — I 0 0 ro 0 to 0;K ( 0 tO 0 0 0 M (A) Cp, CAL. MOLE ` I DEGO'

TABLE IX MOLAL HEAT CAPACITY OF AMMONIA TRIBORANE ToK Cp T~K Cp T,~K Cp Cp~~~~~r. Series I 147.26 172.38 181.38 174.40 183.09 192.18 201.77 211.04 219.92 229.26 230.71 239.61 249.06 258.44 267.76 276.85 286.03 293.84 297.03 18.81 21.09 21.96 21.27 22.15 23.03 23.97 24.94 25.96 27.06 27.20 28.36 29.76 31-36 33.35 35.63 38.62 (84. (2130 I I 295-20 297.00 297.20 298.87 302.36 43.17 (2660 (2660 (72. 37.81 ) ) ) Series IV Series II 53557 56.07 60.63 66.06 71.45 1 77.20 1 83.50 1 90.49 1 97.71 1 102.34 1 109.99 1 118.11 1 126.66 1 ) 134.87 1 ) 143.03 1 151.59 1 160.51 169.54 2 178.63 187.68 ) ) Series V 5.49 3 66.80 7.35 6.38 7.16 8.03 8.76 9.57 6.13 4.79 7.743 8.185 8.962 9.831 L0.595.1.388 L2.291 3. 162 35.969 L4.465 -5.266 L6.09 L6.92 17.68 L8.42 L9.20 DO. 01 0. 82,1l66 ~2 57 5.47 6.06 6.72 7.52 8.40 9.25 10.21 11.72 13554 15.20 16.71 18.16 19.82 21.84 23595 26.14 28.52 29.44 32.49 35574 39.34 43.19 47.19 51.49 56.09 86.56 153.87 241.15 297.51 0.011 0.017 0.021 0.035 0. o66 0.116 0.195 0.199 0.306 0.453 0.609 0.790 1.024 1.351 1.741 2.170 2.656 2.847 3.500 4.185 4.974 5.771 6.569 7.385 8. 18 (12 ) (19 (26 ) (107 ) 282.75 288.93 294.46 298.23 303.26 308.78 314.95 37.70 39.86 (69. (400 37.86 38.54 39, 5 Series VI Series III 283.79 288.27 291.79 37.78 39.62 41.27 0.012 0.026 0.033 00018 0.028 o048 0.082 0.140 0.019. o008 250073 260.05 269.49 278.69 287.35 292.57 298.74 296.38 297.09 297.20 30.02 31.59 33~59 35.98 39.13 41.51 (148 ) (213 ) (2270 (3150 ) 33

TABLE X MOLAL THERMODYNAMIC FUNCTIONS OF AMMONIA TRIBORANE T,~K Cp S~ H~-Ho He-Ho -(F~-H) cal cal cal. cal cal deg mole. deg mole deg mole deg mole deg mole 5 10 15 20 25 (0.009) 0.176 0,435 1.052 1.946 30 35 40 45 50 2.967 4.027 5.109 6.135 7.102 60 70 80 90 100 80857 10.412 11.820 13. o80 14.215 110 120 130 140 150 15.27 16.27 17,23 18.15 19.06 (ooo00) 0.036 0.140 0.342 o0668 1.112 1.649 2.258 2.919 30616 5.070 6.551 8.035 9.502 10. 940 12.344 13.716 15.056 16.367 17.650 18.909 20.146 21.365 22.571 23.767 24.953 26.133 27.313 28.494 29.683 30.888 32.120 333.96 34.740 35.451 39.895 32.516 (0.01) 0.29 1.60 5.19 12.59 24.83 42 33 65.18 93031 126.43 206.41 302.9 414.2 538.8 675.3 822.8 980.5 1148.0 1324.9 1510.9 1706.0 1910.1 2123.4 2346.6 2579.7 2822.8 3076.7 3342.0 3619.6 3911.0 4218.3 4544.6 4895.5 5278.4 5486.6 6807.8 4652,2 (0.002) 0.029 0.107 0,260 0,504 0,828 1.210 1.629 2.074 2.529 3.440 4.327 5.177 5.986 6.753 7.480 8.171 8.831 9.464 10o073 10.662 11.236 11.797 123551 12.898 13.442 13.985 14,530 15.082 15.644 16.224 16.832 17.484 18.202 18.598 22.693 17.032 (0o001) 0.007 0.033 o 082 0,164 0.284 0.439 0.629 0.845 1. 87 1.630 2.224 20858 3.516 4.187 4,864 5.545 6.225 6.903 7.577 8.247 8.910 9.568 10.220 10.869 1.511 12.148 12.783 13.412 14.039 14.664 15.288 15.912 16.538 16.853 17.202 160 170 180 190 200 210 220 230 240 250 19.96 20.86 21.82 22.82 23.80 24.83 25.95 27.12 28.41 29.90 260 270 280 290 295 300 273.15 31.57 33.76 36,52 40.24 43.01 38.22 34.55 298.15 (50) (39.627) (6727) (22-562) (17-065)

interpolated a smooth curve which is tangent to the observed heat capacities at 250~K and again at 310~Ko The difference in the integral of the enthalpy along the observed curve minus that along the interpolated curve from 250 to 310~K indicates an enthalpy increment of transition of 1233 cal mole-1 and the corresponding transitional entropy increment is 4.15 cal mole1 deg.o It is interesting to note that the transitional entropy increment approximates rather closely the value R In 8 = 4.13 cal mole-1 deg'-o This increment is consistent with a tentative interpretation of the possible configurations of the ammonia triborane molecule in the p-form. The temperature of the a-5 transformation was determined as 2.97O10 ~ 0o04~ after a drift toward equilibrium of several hours duration. Attempts to establish the transition temperature by cooling curves were unsuccessful; the sample usually supercooled as much as 5~ before undergoing the: * a transition and failed to reach the equilibrium temperature. A thermal anomaly of unknown origin was also observed in the vicinity of 11~K. This appears to be a rather broad transformation with an entropy increment of about 001 cal mole'l deg - and is thus quite insignificant. DETERMINATION OF HEAT CAPACITY OF SODIUM HYDRIDE PREPARATION AND PURITY OF SODIUM HYDRIDE Although for the study of the thermodynamic properties of sodium hydride, as with any other substance, it would be desirable to have macroscopic crystals, we were unsuccessful in preparing macroscopic crystals in sufficient yield to make heat-capacity measurements possible on them. Several attempts to prepare sodium hydride by direct combination between hot sodium at 400 to 550~C were unsuccessful. And after considerable study and analysis, it was decided to take advantage of commercial preparations of the highest quality available and to purify these further. Although approximately seven samples of sodium hydride from several suppliers were tried, the sample actually used in the calorimeter was obtained from a sodium hydride dispersion of claimed 99.9+% purity obtained from Metal Hydrides, Inc., at Beverly, Massachusetts. This material was obtained in the form of a 25% dispersion in a mineral oil designated at Bayol 85. To refine the sodium hydride and separate it from the oil in which it was dispersed, extraction with rather volatile solvents such as hexane and normal pentane was used repeatedly. Research-grade, carefully dried Phillips Petroleum Co.hydrocarbons were used in a special, enclosed, fitted glass-funnel — drying-chamber similar to one shown by Sayre and Beaver.29 The sodium hydride dispersion was placed in the funnel within the nitrogen atmosphere of the dry box, and all possible filtrate was drawn off by mechanical evacuation through the fitted glass plate. The funnel with its standard taper connections was then connected to a high-vacuum line; 35

the anhydrous solvents were added, and the stopcocks were closed, isolating the funnel-drying chamber which was then removed and shakeno The glass balls in the drying chamber effectively broke up any packed hydride allowing effective washing of the hydride. The hexane was then removed on the vacuum line by flushing with a slight pressure of anhydrous nitrogen. Repeated washings, shakings, and reattachment of the funnel-drying chamber were made until no further mineral oil was obtained in the washings. The last traces of hexane and pentane were removed by evacuation under high vacuum. Following analysis, the sample was transferred in the anhydrous nitrogen atmosphere of the dry box to the calorimeter with as much dispatch as possible and the small calorimeter cover sealed into place. The calorimeter was then transferred to the usual loading-highvacuum line, the requisite amount of helium added after evacuation, and the calorimeter sealed as previously described. We determined the purity of the resultant sodium hydride by chemical analysiso The sodium-to-hydrogen ratio was determined by decomposing a sample in water within a hydrogen atmosphere. The amount of hydrogen liberated was compared to the basicity of the resulting solution. Sodium metal was used in checking the effectiveness of this procedure. Inert contaminants were proved to be absent by decomposing the sample in water and titrating the resulting alkalinity. Determination of free sodium was made by method of Eddy, Messner, and Weber30 and carbonate was determined by a modification of the method of Frazer and Schoenfeldero31 Neither sodium nor carbonate were present to the extent of more than a few hundredths of one percent. The absence of any mineral oil in the resultant product was established by dissolving large quantities of the hydride and examining the resultant solution for the oily layer. A further proof of the absence of hydrocarbon contaminants, both mineral oil and hexane, may be argued from the absence of anomalies at the melting temperatures of these substances in the final heat capacity measurements. RESULTS OF LOW-TEMPERATURE HEAT-CAPACITY DETERMINATION ON SODIUM HYDRIDE The results of the low-temperature heat-capacity determinations are presented in Table XI and shown also in Fig. 9- The same conventions and conditions apply to these data as have been used generally throughout this reporto It is interesting to note that there is no evidence of any thermal anomaly over the entire temperature range of the measurements, nor are there small humps indicating contamination of the sample by hydrocarbon solventso It is interesting to compare these results of considerably higher precision with those of Sayre and Beaver over the rather limited temperature range from 60 to 90~K which they measured. We find that our heat capacities differ from theirs on the average by approximately 3%, but the trend at the upper end of their range is somewhat different. The trend of our curve is indeed more consistent with their theoretical calculation but both sets of data are approximately 20% lower than their theoretical curve. This suggests the desirability of re-examining the bases of their theoretical calculations and also of extend ing the work on sodium deuterides over a much larger temperature range than 36

TEMPERATURE, 0 100 200 300 10 8 I. LJ 0 I LJ J 0 J I) 6 4 0.4 I - 0.2 0 IJ 0.2 0 J < U L. U 2 0 0.1 a 0.0 0 10 20 30 TEMPERATURE, Fig. 9. Molal heat capacity of sodium hydride.

TABLE XI MOLAL HEAT CAPACITY OF SODIUM HYDRIDE (in cal mole"1 deg-1) T, ~K Cp T, ~K Cp T, ~K Cp Series I 216.35 226.05 236.45 246.68 256.75 266.68 276.44 286.29 296.25 306.21 326.01 335.81 345.62 Series II 6.54 7.62 8.51 8.31 9.36 10.61 12.01 7.130 7o346 7.556 7.759 7.967 8,143 8.328 8.492 8.668 8.848 9.182 9.326 9.528 13.52 15.02 16.45 17.89 19.22 20.61 22.40 24.45 26.59 28.92 31.40 34.08 36.67 39.04 41.55 44.60 48.26 46.29 49.93 54.30 59.41 65.06 71.48 o48 O.0o6 0.077 0.099 0.123 0.152 0.199 0.264 0.344 0.447 0.570 0.722 0.874 1.026 1.186 1.389 1.634 1.502 1.745 2.028 2.346 2.679 3.025 78.57 86.15 94.04 103.10 112 22 122.69 132.57 142.11 151.83 161.81 171.82 181.88 191.87 201.69 211.52 200 00 209.42 221.22 238.01 313.09 318.70 324.27 331.94 341.68 3.361 3.691 5.985 4.280 4.552 4.841 5.100 55337 5.572 5.809 6. o66 6.333 6.557 6.789 7.014 6.737 6.953 7.232 7.583 8.960 9. 42 9.133 9.254 9.412 0.009 0.012 0.015 0.020 0.028 0,036 38

they did. (A comparison of our results with theirs is shown in Fig. 10 ) The thermodynamic functions of sodium hydride have been computed by a numerical quadrature of the heat-capacity data as previously described in this report and tabulated in Table XII. 39

4.5 4.0 (50+ LI. / / O / 0 / x+ -/ / I / A 3.5 // >J // // 0 / x o o / / 3.0 / BEAVER AND S/ e / vx/ - THEORY u // x + EXPERIt |,'+/ THIS RESEARC~ EXPERI 2.5 -/+ 01 I I I l I 60 70 80 TEMPERATURE, K Fig. 10. Comparison of heat capacities of sodium hydride with results of Sayre and Beaver. \YRE VENT MENT 90 40o

TABLE XII MOLAL THERMODYNAMIC FUNCTIONS OF SODIUM HYDRIDE T~, K C (S~ - So) (Ho - H) (H - Ho)/T -(F~ - H)/T cal/deg cal/deg cal cal/deg cal/deg 10 0.0240 15 o. o6o4 20 o0.1386 25 0.2830 30 0.4991 35 0.7752 40 1.o87 45 1,416 50 1.750 60 2.382 70 80 90 100 110 120 130 140 150 16o 170 18o 190 200 210 220 230 240 250 260 270 280 290 300 350 2,944 3.432 35839 4.182 4.488 4.769 5.033 5.286 5.528 5.766 6.013 6.262 6.509 6.748 6.980 7.202 7.418 7.624 7.825 8.019 8.206 8.387 8.561 8.732 9.541 o.oo8o 0.0240 o.05o8 0.0959 0.165 0.262 0.386 0.5533 0.700 1.075 1.486 1.912 2.540 2.763 3.176 3.579 35971 4.353 4.726 5.091 5.448 5.798 6.143 6.483 6.818 7.148 7.473 7.793 8.109 8.419 8.725 9.027 9.325 9.618 11.026 8.821 9.564 o.060 0.263 0.739 1.764 3.692 6.861 11.506 17.753 25.669 46.369 73.074 105.01 141.44 181.59 224.95 271.25 320.27 371.88 425.95 482.42 541.3 602.7 666.6 732.8 801.5 872.4 945.5 1020.7 1098.0 1177.2 1258.3 1341.3 1426.0 151205 1969.6 1284.3 1496.4 o. oo60 0.0175 0.0369 0.0706 0.123 0.196 0.288 0.395 0.513 0 773 1.044 1.313 1.572 1.816 2.0045 2.260 2.464 2.656 2.840 3.015 3.184 30348 3.508 3.664 3.817 3.965 4.111 4.253 4.392 4.528 4.661 4.790 4.917 5.042 5~628 4.702 5.019 0,442 0.599 o.768 0,947 1.131 1.319 1.507 1.697 1.886 2.076 2.264 2.450 2.635 2.819 3.001 3.183 3.362 3.540 30717 3.891 4.064 4.237 4.408 4,576 5.398 4.119 4.545 0.0020 0.0065 0.0139 0.0253 0.042 o066 oo098 o0138 o,187 0.302 273.15 8.264 298.15 8.700 41

REFERENCES 1. Westrum, E. F,, Hatcher, J. Bo, and Osborne, Do W., Jo Chemo Physo, 219 419 (1953), 2. Hoge, Ho J., and Brickwedde, Fo G,, Jo Res,o Natl. Buro Stdso, 229 351 (1939). 3. Ginnings, D, C,, and Furukawa, Go T., J. Amer. Chem. Soc 9 75: 522 (1955). 4o Furukawa, G. To. McCoskey, Ro E., and King, G. Jo, J. Res. Natl, Bur. Stds., 47, 256 (1951). 5. Morey, G. W,, and Merwin, Ho E., Jo Amero Chemo SoCo., 58, 2248 (1936), 6. Cole. S. S., Scholes, S. R., and Amberg, Co Ro J. AmerO Ceramic Soco 18, 58 (1935)o 7. Cole, S. S. Taylor, No W., and Scholes, S. R,, Jo Amero Ceramic Soco. 18, 79 (1935). 8. Cole, So S., and Taylor, No W., J. Amero Ceramic Soc., 18 82 (1935)o 9. Fang, Ssu-Mien, J. Amero Ceramic Soc., 20, 214 (1937)o 10. Cole, So S., Scholes, S. R., and Amberg Co Ro., J Amero Ceramic Scc,. 20, 215 (1937). 11. Menzel, H., and Schulz, Ho, Zo Anorgo Chem., 2453 157 (1940)o 12. Menzel, Ho, and Schulz, Ho, Z. Anorgo Chem., 251, 167 (1943). 13. Reinbach, Eo., Bero, 26, 164 (1893). 14. Ramsay, W., and Aston, E., Chem. News, 66, 92 (1892)o 15. Willard, H. Ho, and Furman, N. H., Elementary Quantitative Analysis, D. Van Nostrand Co., Inc., New York, 1946o 16. Briscoe, Ho Vo A,, Robinson, P. Lo, and Stephenson, J., J. Chemo Soc,, 127, 150 (1925). 17. Furman, No H., Editor, Scott's Standard Methods of Chemical Analysis, Do Van Nostrand Co., Inc., New York, 1950. 18. Wherry, Eo T., and Chapin, Wo Ho, J. Amero Chemo Soc., 30, 1691 (1908)o 19. Wilcox, Lo Vo, Ind. Eng. Chemo and Edo, 2, 358 (1930). 42

REFERENCES (Concluded) 20. Shomate, C. H., J. Phys. Chem., 58, 368 (1954)o 21. Westrum, E. F., Jro, forthcoming publication. 22. Shartsis, L., and Capps, Wo, J. Am. Ceram. Soc., 37, 27 (1954). 23. Contributions to the Data of Theoretical Metallurgy, XII. Heats and Free Energies of Formation of Inorganic Oxides, Bulletin No 542, Bureau of Mines, Uo So Govt. Printing Office, Washington, D. C., 1954. 24. Selected Values of Chemical Thermodynamic Properties, National Bureau of Standards Circular No. 500, U. S. Govto Printing Office, Washington D. C., 1950. 25. Vogel, A. I., Practical Organic Chemistry, 2nd edition, Longmans, Green, New York, 1951. 26. Parry, Ro W., and Kodama, G., Transactions XVIth Congress, Int. Union Pure and Applied Chemistry, Paris, June 1957. 27. Nordman, C. E., Reinmann, C., and Peters, C. Ro, Abstracts of Papers, 133rd Meeting of the American Chemical Society, San Francisco, California, p. 46L, Abstract No. 109 (1958). 28. Parry, R. W., private communication. 29. Sayre, E. V., and Beaver, J. J., J. Chem. Phys., 18, 587 (1950). 30. Eddy, L. B., Messner, A. E., and Weber, A. E., Determination of Free Sodium in Sodium Hydride, Report CCC-1024-TR-186, May 23, 1956, Callery Chemical Company, Callery, Pa. 31. Frazer, J. W., and Schoenfelder, C. Wo, Determination of Lithium Carbonate in Lithium Hydride, Report UCRL-4918, March 12, 1957, University of California Radiation Laboratory, Livermore, California. 43

UNIVERSITY OF MICHIGAN Illl3 90 5 03527 499llll 3 9015 03527 4995