ENGINEERING RESEARCH INSTITUTE THE UNIVERSITY OF MICHIGAN ANN ARBOR Technical (Third Quarterly) Report DETERMINATION OF THE LOW-TEMPERATURE HEAT CAPACITY OF ANHYDROUS AND VITREOUS SODIUM TETRABORATE George QrWnier, Edgar F. Westrum,. -jr (Associate. Professor.of Chemistry) Project 2223 CALLERY CHEMICAL COMPANY CALIERY, PENNSYLVANIA May 1955

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN TABLE OF CONTEaTS page LIST OF TABLES iii ABSTRACT iv OBJECTIVE iv INTRODUCTION 1 PREPARATION AND ANALYSIS OF CRYSTALLINE SODIUM T'ETRABORATE 1 PREPARATION AND PUIITY OF VITREOUS SODIUM TETRABORATE 2 CALORIMETRIC TECHNIQUE 3 EXPERIMENTAL RESULTS 5 BIBLIOGRAPHY 10 FIGURES 12 ii

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN LIST OF TABLES page I. THE MOLAL HEAT CAPACITY OF CRYSTALLINE SODIUM TETRABORATE 4 II. THE MOLAL HEAT CAPACITY OF VITREOUS SODIUM TETRABORATE 5 III. MOLAL THERMODYNAMIC PROPERTIES OF CRYSTALLINE SODIUM TETRABORATE 7 IV. MOLAL THERMODYNAMIC PROPERTIES OF VITREOUS SODIUM TETRABORATE 8 V. EXTRAPOLATED MOLAL THERMODYNAMIC FUNCTIONS OF CRYSTALLINE SODIUM TETRABORATE 9 VI. EXTRAPOLATED MOLAL THERMODYNAMIC FUNCTIONS OF VITREOUS SODIUM TETRABORATE 9 iii

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN ABSTRACT We have prepared samples of high-purity anhydrous crystalline and vitreous sodium tetraborate (Na2B407) and determined their heat capacity from about 6 to 3500K by adiabatic calorimetry. Values of the heat capacity and the derived thermodynamic functions have been computed and tabulated. Molal values at 298.160K of the heat capacity at constant pressure, entropy, enthalpy increment (HT - Ho) and free-energy function are: 44.64 cal deg-1 45.30 cal deg-1, 7262 cal, and -20.94 cal deg-l, respectively, for the crystalline modification. For the vitreous modification, the molal values at 298.160K of the heat capacity at constant pressure, the entropy increment (So - SO). and enthalpy increment (Ho - Ho), are: 44.42 cal deg-1, 44.39 cal deg-l, and 7127 cal, respectively. OBJECTIVE To obtain chemical thermodynamic data and thermal properties on certain compounds over low- and high-temperature ranges. iv

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN INTRODUCTION Despite the use of borax and related materials in ceramic technology for many centuries and widespread utilization in current chemical technology, reliable thermodynamic data on alkali berates are relatively rare. This report presents low-temperature heat-capacity data on both crystalline and vitreous sodium tetraborate and the derived thermodynamic functions and thermochemical quantities computed therefrom. PREPARATION AND ANALYSIS OF CRYSTALLINE SODIUM TETRABORATE We use the designation sodium tetraborate to refer to the chemical composition Na2B407, although a contrary usage is occasionally found (e.g., cf. Ref. 1). Data in the chemical literature on the physical properties of anhydrous and crystalline sodium tetraborate are concerned primarily with melting-point and phase-equilibrium studiesl on the Na2O-B203 systems. Two and possibly three distinct crystallographic phases of this material have been claimed.1 The material prepared for this work is the alpha-form and is that ordinarily obtained and commercially available. No evidence for an enantiotropic inversion between the various forms has been found,1 despite a careful search from below 5000C to the melting point. The rate of conversion (beta to alpha) is very slow below these temperatures, and the reverse transformation has not been observed. 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 con —. trolled conditions.2 Since rapid cooling or prolonged periods of heating at temperatures appreciably higher than the melting point of 742.5~C1 result in glass formation, it is essential for crystal growth that the temperature does not exceed 7600C nor remain at this temperature for a period of more than about ten minutes, 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 ten-hours time. The covered platinum dish was then 1 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 1 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN 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. The analyses of the final calorimetric samples were performed by Lynn J. Kirby of this laboratory. Determination of water was made by loss in weight on fusion.3S4 The usual method involving Karl Fischer reagent is unsatisfactory because complicating reactions are involved with borates. Although it is reported by Morey and Merwinl that the crystalline material at 3000C 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 0.01 + 0.01% water. The Na20 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,3,4,5,6,7 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.78,9l The percent by weight of sodium as Na20 was 30.80, 30.78, 30.79; average, 30.79 + 0.01%. (Theoretical Na20: 30.80%.) 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, stoichiometrically anhydrous sodium tetraborate, Na2B407. The mass of the crystalline sample used in the calorimeter was 79.6707 g (in vacuo). PREPARATION AND PURITY OF VITREOUS SODIUM TETRABORATE The vitreous sodium tetraborate was prepared from the same material as the crystalline material. The dehydrated sample was heated to 820~C for thirty minutes to insure glass formation. The glass was annealed for 15 minutes at 4200~C and cooled in an anhydrous atmosphere.

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN Analytical data by identical methods on the vitreous material indicated: water, 0.0% + 0.1%; Na20, 30.75%, 30.79% (theoretical, 30.80*); B203, 69.16%, 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). CALORIMETRIC TECHNIQUE The adiabatic calorimeter, cryostat, and method of operation have been described previously.~0 The calorimeter was loaded in a dry box and after evacuation 2.0 cm of helium gas at 3000K were added to aid in the establishment of thermal equilibrium. Temperatures were measured with a capsule-type platinum resistance thermometer (laboratory designation A-3) contained in a re-entrant well in the calorimeter. A 160-ohm constantan heater was wound on a cylindrical copper tube surrounding the resistance thermometer. The thermometer was calibrated on the temperature scale of the National Bureau of Standards,10 from 14 to 3730K. Below 140K, the scale was obtained by fitting the equationll R = A + BT2 + CT5 to the resistance at the boiling point of helium and to the resistance and dR/dT at 140K. It is believed that our temperature scale agrees with, the thermodynamic scale within 0.10 from 4 to 140K, within 0.03~0 from 14 to 900K, and within 0.050 from 90 to 373~K. The thermometer resistance and the power input were measured with a calibrated White double-potentiometer., calibrated resistances, and a calibrated standard cell. An electric timer operated by a calibrated tuning fork and amplifier was automatically started at the beginning of the heating period and stopped at the end. EXFERIMENTAL RESULTS The experimental values of the heat capacity of crystalline sodium tetraborate are presented in Table I and Fig. I, those for vitreous sodium tetraborate in Table II. 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*.16 0K. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN TABLE I THE MOLAL HEAT CAPACITY OF CRYSTALLINE SODIUM TETRABORATE (Calories per degree) T, oK AT, K Cp T,.K - AT,.K Cp SERIES I 172.08 9.738 29.70 181.88 9,869 31.03 5.82 0.575 0.015 191,80 9.958 32.34 6.60 2.10o4 0.019 201.60 9,648 33.60 7.81 1,538 0.030 211.13 9,397 34.83 90O7 1.246 o,o055 10.21 1.235 o.o89 220.53 9.400 35.99 229.84 9-168 37*12 11.50 1.490 0,144 238.94 9.020 38.17 12.92 1.423 0.226 248.07 9.242 39*22 14,37 1*558 0.328 257.40 9.428 40,32 15.92 1.571 0.460 17-52 1.631 0,623 266.90 9,558 41.36 276.50 9,622 42.36 19.21 10753 o.843 286.39 10,171 43.41 21.03 1.893 1.097 296.65 10.336 44.47 23.02 2,097 1.430 306.88 10.131 45.52 25.23 2.322 1.824 27.73 2.664 2.289 317.02 10,175 46.54 327,09 9.990 47.51 30.61 30095 2,882 337.30 10,443 48,48 33.80 35276 30591 347.69 10,348 49.33 37.25 35621 4.380 41.09 4.067 5-296 SERIES II 45.45 4,636 6.346 253,26 9.136 39.78 50.18 4,832 7,506 262.55 9.456 40o81 55.32 5.433 8~746 271.91 9.273 41.88 61,01 5.939 10.11 281.41 9.731 42,89 67036 6.750 11,59 291.36 10.152 43,92 74.48 7.484 13.15 301.61 10,355 44.99 81.61 6.920 14.70 311.91 10,253 46.02 89.18 8,218 16.27 322.22 10.386 47,00 97.84 9,098 17.89 333.05 11,260 48.02 107,29 9.798 19.60 343.97 10,411 49.06 117*03 9.673 21,28 126.62 9.517 22.91 135.89 9.015 24.38 144.71 8.611 25.73 153.70 8.826 27,08 162.66 9.081 28.38 ____ ___ ___ ____ ___ ___ ____ ___ ___4

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN TABLE II THE MOLAL HEAT CAPACITY OF VITREOUS SODIUM TETRABORATE (Calories per degree) T, OK AT, OK Cp T, OK AT, ~K Cp 5.31 1.337 0.015 121.62 10.250 21-33 6.68 1.800 0.027 131.54 9.594 22.94 8.09 1.252 0.057 140.88 9.1093 24.42 9.22 1.110,o099 149,95 9-036 25.79 1032 1.140 0.150 159.04 9.141 27.14 11.54 1.322 0.217 168.25 9.280 28.48 12.82 1.265 0,305 177.49 9.206 29.77 14.13 1.373 0o.411 186,79 9-392 31.05 15.59 1,563 0.549 196.08 9.183 32*30 17.21 1,674 0.724 205.13 8.907 33.49 19 L01 1Q935 0.947 214.14 9-113 34.66 21.08 2.206 1.231 223.13 8.863 35.80 23.41 2.460 1.598 232.21 9.298 36.92 25.95 2.623 2.030 241.51 9.286 38.o6 28~71 2.890 2.543 250.99 9.685 39.18 31.69 3.070 3.137 260.78 9.895 40,36 34,85 3.253 3.794 270.61 9*745 41.42 38.23 3.508 4.540 280.35 9.726 42.49 41.92 3.873 5~361 290.09 9.763 43.56 46.13 4.546 6.326 300.00 10.059 44,60 51.00 5.176 7'.445 310.30 10.571 45.68 56-39 5.605 8.694 320.84 10.511 46.77 62.26 6.116 10.00 331.13 10.102 47.74 68.55 6.468 11.38 343.63 14.917 48.92 75.01 6.455 12.72 81.43 6.370 14.08 88.06 6.885 15.41 95.20 7.395 16.73 103.03 8.270 18.14 111.83 9.324 19.67 5

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN The molal heat capacity and the thermodynamic functions derived from the heat capacity of these substances are listed at rounded temperatures in Tables III and IV. These heat-capacity values were read from a smooth cuve through the experimental points, and they are estimated to have a probable error of 0.1% above 25~K, 1% at 140K, increasing to 5% at 50K. 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 in order 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. Since the third law of thermodynamics may not be assumed for the vitreous phase, the entropy increment is tabulated, and the free-energy functirn cannot be specified at present. The high precision of the data can be seen best in Fig. 2, in which the deviation of the direct experimental values from the smooth-curve values are presented. This precision is also typical of the crystalline data. A comparison of the heat capacities of crystalline and vitreous sodium tetraborate is depicted in Fig. 3. 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. 4. This contrasts, for instance, with data on the heat capacities of vitreous silica and quartz as determined by Westruml2. Here the quartz Cp curve rises above the vitreous silica Cp curve only at about 2100K. In another example, the heat capacity of crystalline boron trioxidel2 exceeds the heat capacity of vitreous boron trioxide at a temperature of about 2850K. The molal thermodynamic functions extrapolated to the sodium tetraborate melting point, 742.50~C (1015.660K), are listed at rounded temperatures in Tables V and VI. The formulae for the extrapolation of these functions are derived on -the basis of the method described by Shomate.13 UTsing 300~K as the base temperature, the equations for crystalline sodium tetraborate are Cp = 21.83 + 0850T - 2.250 x 105- THo - Ho = 21.83T +.0425T2 + 2.250 x 105 T-1 - 11,124.0, and S = %0.27 log T +.0850T + 1.125 x 105 T-2 - 105.70.

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN TABLE III MOLAL TKERMODYNAMIC PROPERTIES OF CRYSTALLINE SODIUM TETRABORATE - CsO, ~sH0 - H, (F - o)/T | OK cal/deg cal/deg cal cal/deg 5 o.012 o.oo4 0.014 0.001 10 0.081 08027 0.202 0.007 15 0.379 0.108 1.255 0.024 20 0.949 0.288 4.449 0.066 25 1.781 0.585 11.19 0.138 30 2.751 0*993 22.46 0.244 35 3.861 1.499 38.96 0.386 40 50o36 2.091 61.17 0.562 45 6.238 2.753 89.34 0.768 50 7.462 3.474 123.57 1.003 60 9.870 5.047 210.22 1.543 70 12.18 6.744 320.60 2.164 80 14.35 8.512 453.26 2.846 90 16.38 10.322 607.1 3.576 100 18.29 12.149 780.6 4.343 110 20.08 13.976 972.5 5-135 120 21.79 15.797 1181.9 5.948 130 23.43 17.607 1408.1 6.776 140 25.00 19.401 1650.3 7.613 150 26.53 21.178 1908.0 8.458 160 27.99 22.938 2180.6 9.309 170 29.41 24.678 2467.6 10o163 180 30.77 26.399 2768.6 11o 018 190 32.10 28.097 3083~0 11.871 200 33540 29.777 3410.5 12.725 210 34.68 31.438 3750.9 13.576 220 35.93 33.080 4104.0 14.425 230 37.12 34.705 4469.4 15.273 240 38.29 36.310 4846.5 16.117 250 39.43 37.896 5235.1 16.956 260 4057 39.463 5635.1 17.789 270 41.67 41.016 6046,3 18.622 280 42*75 42*552 6468.4 19.451 290 43*79 44.070 6901.1 20.273 300 44.83 45.572 7344.2 21.091 350 49.65 52,850 9708.1 25.112 273.16 42.01 4'1.504 6178.6 18.885 298.16 44.64 45.296 7261.9 20.940 7 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN TABLE IV MOLAL THERMODYNAMIC PROPERTIES OF VITREOUS SODIUM TETRABORATE TY Cp SO -SO Ho -HO9 ~K cal deg cal deg-1 cal 5 0o013 0.004 0.o16 10 0.134 0.044 0.334 15 0.490 0.158 1.795 20 1,078 0.375 5.635 25 1.866 0.697 12.92 30 2.795 1.117 24.51 35 3.828 1.625 41.04 40 4.933 2.207 62.93 45 6.0o63 2.853 90.40 50 7,220 3.552 123.61 60 9.499 5.072 207.30 70 11.69 6.702 313.32 80 13.78 8,400 440.64 90 15.77 10.138 588.5 100 17.60 ll.895 755.4 110 19.36 13.655 940.1 120 21.06 15.413 1142.2 130 22.70 17.163 1361.1 140 24.28 18.903 1596.0 150 25.80 20.631 1846.4 160 27.29 22.343 2111.8 170 28.70 24.041 2391.8 180 30.11 25.721 2686.0 190 31.48 27.387 299359 200 32.82 29.036 3315.4 210 34.12 30.668 3650.1 220 35 40 32.285 3997*7 230 36.65 33.887 4357.9 240 37.87 35.471 4730.5 250 39.07 37.042 5115.2 260 40.23 38-597 5511.7 270 41.36 40.136 5916.6 280 42.46 41.660 6338.7 290 43.54 43.169 6768.7 300 44.61 44.663 7209.5 350 49.50 51.918 9565.2 273.16 41.71 40.620 6050.9 298.16 44.42 44.391 7127.6

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN TABLE V EXTRAPOLATED MOLAL THERMODYNAMIC FUNCTIONS OF CRYSTALLINE SODIUM TETRABORATE C' -.........0 Io T. C I S, HO - How -(Fo - 0)/T,.K caldeg cal/deg kcal cal/deg 400 54.4 5948 12,31 29.01 450 59.0 6605 15o15 32.81 500 63.4 72.9 18.21 36.51 550 67.8 79.2 21.49 40,08 600 72.2 85.3 24.99 43,60 650 76.6 91.2 28*71 47o05 700 80.9 97*0 32.65 50.41 750 85.2 102,8 36.80 53.o71 800 89,5 108.4 41*17 56.95 850 93.8 114,0 45.75 58.13 900goo 98.0 119.4 50-54 63.28 950 102.3 124,9 55.55 66.39 1000 106,6 130.2 60.78 69.44 1015.16 107.9 131.9 62.40 70.39 TABLE VI EXTRAPOLATED MOLAL THERMODYNAM[C FUNCTIONS OF VITREOUS SODIUM TETRABORATE T. Cp, S~ - s8, H~ - HO, ~K cal/deg cal/deg kcal 400 53.9 59.0 12.15 450 58,1 65.5 14*95 500 62,1 71.9 17.96 550 66,0 780O 21.16 600 69.8 83.9 24,56 650 73.6 89.6 28.14 700 77.4 95*2 31,92 750 81.1 100.7 35*88 800 84,8 106.0 40.40 850 88.4 111.3 44.35 900 92.1 116.4 48.87 950 95,8 121.5 53.56 1000 99.4 126*5 58.44 lO15 o16 100o5 128.1 59.96 9

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN Those for vitreous sodium tetraborate are: Cp = 27,a83 + w0720T - 4.320 x 105T-2, H - H0 = 27,83T +.0360T2 + 4,320 x 105T-1 - 13,029.0, and S~ - S0 = 64.09 log T +.0720T + 2.160 x lo5T-2 - 137.96. The extrapolated values have an estimated error of 0.4% below 6000K and 2,0% at the melting point.: As with all extrapolations, considerable uncertainty as to the validity of the extrapolation procedure is involved. These values, therefore, should be used with due caution as an approximation justified only by the absence of experimental determinations, This limitation is particularly serious here because the extrapolation extends over a long range. However, no evidence for thermal transformations or anomalies were detected by Morey and Merwin1 by thermal analysis between 3500K and the melting point. BIBLIOGRAPHY 1. G. W. Morey and H. E. Merwin, J. Amer. Chem. Soc., 58:2248 (1936). 2. Lo G. Black, U*S. Patent, 2,064,337 (Dec. 1936). 3. H. Menzel and H. Schulz, Z. Anorg. Chemo, 245:157 (1940). 4. H. Menzel and H. Schulz, Z. Anorg. Chem., 251:167 (1943)* 5 E. Reinbach, Ber., 26:164 (1893). 6. W. Ramsay and E. Aston, Chem. News, 66:92 (1892) 7. H. Hw Willard and N. H. Furman, Elementary Quantitative Analysis. New York: D. Van Nostrand Co., Inc., 1946. 8* H, V. A. Briscoe, P. L. Robinson, and J. Stephenson, J. Chem. Soc., 127:150 (1925)..9g N. H. Furman, Editor, Scotts's Standard Methods of Chemical Analysis, New York: D. Van Nostrand Co., Inc., 1950. 10. Edgar F. Westrum, Jr., and George Grenier, Second Quarterly Technical Report on Sodium Metaborate. Project 2223 (Feb. 1955). 11. H. J. Hoge and F. G. Brickwedde, J. Res. Natl. Bur. Stds., 22:351 (1939). 12. Edgar F. Westrum, Jr. Unpublished data. 13. C. H. Shomate, J. Phys. Chem., 58:368 (1954).

Fig. 1. 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,)

CRYSTALLINE SODIUM TETRABORATE 50 40 I. T 30 IJ 0;[ < 20 0~ 10 0 50 100 150 200 250 300 350 T,~K Fig. 1

Fig. 2. Deviation of the Direct Experimental Points on Vitreous Sodium Tetraborate from the Smoothed Curve. (The precision of the data is indicated by dashed lines representing + 0.1% deviation )

VITREOUS SODIUM TETRABORATE.04 +0.1 7 0 5 o0 5 0 00 3 I, o 0 — ~~~~00 0 o o U-.02 -0.1 %~,N -.04 5 20 50 100 200 300 T,~K Fig. 2

Fig. 3. Comparison of the Heat Capacities of Anhydrous Crystalline Vitreous Sodium Tetraborate.

SODIUM TETRABORATE 50 40 T.30 ~ ~ <720 10 — CRYSTALLINE 0 I ~/'.~ —- VITREOUS 0 50 100 150 200 250 300 350 T,~K Fig. 3

Figw 4. Deviation Plot for the Heat Capacities of Sodium Tetraborate Forms. Cp = Cp, vitreous p, crystalline

SODIUM TETRABORATE (VITREOUS-CRYSTALLINE) 0.2 K IFig T. -0.2.j u -0.4 — 0.6 5 20 50 100 200 300 T,~K Fig., 4