September, 1944
.
INDUSTRIAL AND ENGINEERING CHEMISTRY
H1 = partial heat of solution of component 1 Ha = partial heat of solution of component 2 K1 = y,/zl or equilibrium constant for component 1 Ks = us/xa or equilibrium constant for component 2 L = molal latent heat of compound in question L' = molal latent heat of reference compound L1 = molal latent heat of component 1 from solution LI = molal latent heat of component 2 from solution L: = molal latent heat of pure component 1 I,; = molal latent heat of pure component 2 La = molal latent heat of liquid in equilibrium with vapor of composition yl L, = molal latent heat of vapors in equilibrium with liquid of composition 2 1 N = valence number pl = partial pressure of component 1 a t given temp. p2 = partial pressure of component 2 at given temp. p," = vapor pressure of pure component 1 at given temp. p i = vapor pressure of pure component 2 a t given temp. P = total pressure a t given temperature P' = total pressure of reference substance a t given temp. R = gas constant T = absolute temperature 21 = mole % of component 1 in liquid 21 = mole % of component 2 in liquid y1 = mole yo of component 1 in vapor y2 = mole % ' of component 2 in vapor 01 = relative volatility = KI/K2 y1 = activity coefficient of component 1 y2 = activity coefficient of component 2 LITERATURE CITED
(1) Akerlaf, G.,and Kegeles, G . , J. Am. Chem. SOC.,62,620 (1940). (2) Akerlaf, G.,and Teare, J. W., Ibid., 59, 1855 (1937). (3) Buffington, R. M., Servel, Inc., private communication.
865
(4) Gamont, R., and Othmer, D. F., IND.ENQ.CHEM.,to be published. (5) International Critical Tables, Vol. 111, p. 301, New York, McGraw-Hill Book Co., 1928. (6) Keyes, D. B., IND.ENGI. CHEM.,25,569 (1933). (7) Othmer, D.F.,Ibid., 20,743 (1928). (8) Ibid., 32, 841 (1940). (9) Ibid., 34,1072 (1942). (IO) Ibid., 36,669 (1944). (11) Othmer, D.F.,and Sawyer, F. G., Ibid., 35,1269 (1943). (12) Othmer, D.F.,and White, R. E., Ibid., 34,952 (1942). (13) Payn, R. C., and Perman, E. P., Trans. Faraday SOC.,25, 599 (1929). (14) Rossini. F. D..B u r . Standards J. Research. 9.679 (1932). (155 Scatchard, G.; and Raymond, C. L., J . ' A m . Chem. SOC.,60, 1278 (1938). PRESENTED before the Division of Industrial and Engineering Chemistry a t the 107th Meeting of the AMERICAN CHEMCAL SOCIETY in Cleveland, Ohio.
Correlating Vapor Pressure and Equilibrium Constant Data-Correction The author wishes to call attention to an unfortunate error which he has just discovered in Figure 3 of this paper which appeared in the July issue of INDUSTRIAL AND ENGINEER~NG CHEMISTRY, pages 669-72. The calibrations of the middle scale, for butane, should all be divided by 10. That is, the top of the scale starts at 0.4 and the bottom ends a t 10.0. D. F. OTHMER POLYTBCHNIC INSTITUTB BROOKLYN, N. Y.
SPECIFIC HEATS AT LOW TEMPERATURES OF
Titanium and Titanium Carbide K. K. KELLEY S. Bureau of Mines, Berkeley, Calif.
Pacific Experiment Station, U.
Low-temperature specific heat data are reported for titanium metal and titanium carbide in the temperature range 51 O to 298 O K. The specific heat curves of both substances are normal. The entropies of the metal and carbide have been computed as S ~ s s . t s= 7.24 * 0.07 and S2sr.,s = 5.8 * 0.1, respectively.
T
HE determination of low-temperature specific heats and entropies of titanium-containing compounds is a field that has been neglected. Only two compounds have been studied directly, titanium dioxide (rutile) by McDonald and Seltz (7) and titanium tetrachloride by Latimer (6). The entropy of titanium gas was obtained by Kelley (4) from spectroscopic data, and that of titanium tetrachloride gas by Yost and Blair (8) from molecular constant data. The only previous value for the entropy of solid titanium is the result calculated by Lewis and Gibson (6) from a single low-temperature specific-heat measurement. As a first step toward remedying this condition, determinations of the specific heats of titanium metal and of titanium carbide have been conducted throughout the temperature range 51 't o 298' K. The results obtained and the entropies computed from them are the subject of the present paper. The titanium and titanium carbide were furnished by the Titanium Alloy Manufacturing Company. The titanium, made by sodium reduction of the tetrachloride, was malleable and con-
sisted of spheroidal particles with diameters up to 4 mm. According to analyses furnished by the company, the purity was 98.75%, the principal impurities being 0.50% silicon, 0.27% iron, and 0.15% vanadium. Spectrographic analyses for other metals increased the total to 99.83%. The sample used in the present measurements contained 241.74 grams. The titanium carbide was made from rutile of 99% purity and petroleum coke in a resistance furnace, the final temperature being near 3000" C. The purity of the carbide was 96.080j0. This is not as high as would be desirable, but it was the most suitable sample available. Spectrographic analyses for impurities raised the total constituents accounted for to 99.25%; the remainder was presumably combined oxygen and nitrogen. For the present purpose it was assumed that the material contained 1.820j0 titanium dioxide and no nitride. This assumption brings the total accounted for t o 99.94%. A 370.65-gram sample was used in the specific heat measurements. Specific Heat Measurements. The apparatus employed has been described (8). The results are expressed in defined calories (1 calorie = 4.1833 international joules) per gram molecular mass of material. I n accordance with 1941 International Atomic Weights, the atomic weight of titanium is taken as 47.90 and the molecular weight of titanium carbide as 59.91. The specific heat results were corrected for the impurities present on the assumption that the specific heats are additive. This correction ranged from 0.08 t o 0.20% for the titanium, depeud-
INDUSTRIAL AND ENGINEERING CHEMISTRY
866
Vol. 36, No. 9
The results of entropy calculations follow: Gal./' K./Mole Ti Tic 0.401 0.08 6.844 5.71 7 24 * 0 . 0 7 6 . 8 =k 0 1. ~
-
0 60.12" K.,extrapolated 50.12' 298.16' K.,graphical
-
Slo8.18
Ii:xtra allowance of error has been made in the entropy of titanium carbide t o account for possible uncertainty in the correction for impurities. The entropy of titanium previously in use is 6.6 (4, 6). 'rliis figure is based upon a single mean specific heat measurement made thirty years ago and deserves no weight in compariml with the present result. No previous low-temperature specific heat or entropy ditta are available for titanium carbide, but an e3tirnate of Szss.,~= 5.5 had been made (3) by analogy with silicon carbide. The present result, of cotirpe, rests upon firmer ground. LITERATURE CITED I 0
100
FIGUEE1.
I
I
I
I
I
380
200
T OK.
SPECIFIC HEATOF TITANIUM (A) TITANIUM CARBIDE (B)
AND
ing an the temperature, and from 0.23 to 12.97% for the titanium carbide. The corrected specific heat values are given in Table I and graphically in Figure 1. No irregularities were found in the specific heats of either substance. The specific heat per mole of titanium carbide is lower than that per gram atom of titanium metal at temperatures below 189' K. This decrease in the specific heat of a carbide below that of the corresponding metal is noted also in the data for silicon carbide (2) and tantalum carbide ( I ) . Entropies at 298.16' K. The entropies were rornputed kq gaphically integrating under Cypvs. log T curves between the limits of 50.12' and 298.16"K., and adding the portions obtained by extrapolating the measured specific heats below 50.12" KIi.. In the case of titanium the Debye function, D(358/T), was found to fit the measured results t b 120' K. and was employed in thp extrapolation. For the titanium carbide the specific heat a t the lowest temperature studied is so low that no significant error c a n be introduced by employing the T3 law for extrapolation
TOLE
I. SPECIFICHEATSOF TITANIUM AND
T, K. 53.6 57.1 61.4 65.9 70.5 75.1 80.1 83.8 92.7 102.9 55.1 58.6 62.3 65.9 69.8 14.2 81.2 86.5 95.7 105.3 5
CP
T, K.
T ,'? IC
CP
Titai?ium" (Atomio 'u'eight = 47.9 Grama) 1.278 112.7 3.765 214.6 128.2 4.081 224.9 1.464 133.3 4.306 236.0 1.679 143.4 4.516 244.9 1.915 154.0 4.707 255,5 2.142 163.9 4.878 265.7 2.357 2.682 174.3 5,015 276.1 184.2 5.142 285,8 2.737 5,259 295.1 3.101 194.4 3.460 204.7 5.355 Titanium Carbideb (Molecular Weight 115.6 2.389 0.312 2.789 0.384 125.7 3.190 0.473 135.6 3.606 146.0 0.571 4.010 0.686 156.2 166.5 4,402 0.821 176.2 4.750 1,055 186.3 5.113 1.242 5.474' 1,587 196.8 1.960 206,5 5.778
C p expressed as calories per gram atom. expressed as calories per gram molecule.
b Cp
OF
CARBIDE
=
( I ) Kelley, I
