I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
2808
differences are probably due in part to the fact that the quantities A and B in the van Laar equations, which were assumed t o be constant, vary somewhat over the temperature range involved. Equation 1, also, is strictly applicable only a t constant temperature. As a further test of Lecat's azeotropic data, the constants A and B were obtained using the azeotropic composition of 75.0y0carbon tetrachloride and the boiling point of 73.1 ' C. Values of the activity coefficients were then calculated from the van Laar equations, using these values of A and B. The results, plotted in Figure 4 for comparison, show poor corrcspondence with the experimental coefficients. The vapor-pressure data used in evaluating Equation 1 were taken from the International Critical Tables (5)over the range 70" t o 110" C., inclusive. The experimental and theoretical values of the activity coefficients are given in Table 111.
IO
8 6 4
3 2
I
0
0.6
0.4
0.2
XI,
MOLE FRACTION
CCI,
0.8
1.0
IN LIQUID
---
72.
TABLE 111. ACTIVITYCOEFFIC-IENTS Computed from Experimental Data XI
Figure 4. Natural Logarithm of the Activity Coefficient against Mole Fraction Carbon Tetrachloride in Liquid 0 yr, experimental data 0
experimental data
Van Laar, A and B from these data .Van Laar, A and B from Lecat's azeotrope
0.000 0.058 0.141 0.300 0.441 0.522 0.683 0.818 0.851 0.950 1.000
Furthermore, after the azeotrope had been located, its composition was checked twice by runs lasting over 4 hours, with identical results. In Figure 4 the logarithm of the activity coefficient for each Component is plotted against the mole fraction of carbon tetraohloride in the liquid. Under the conditions prevailing in these experiments the activity coefficient may be computed with negligible error from the equation Y =
Log,
71
(1
Log,
YZ
(1
From van Laar, Lecat's Data
Y1
Y2
Y1
1.00
3.22 2.94 2.59 2.03 1.65 1.48 1.22 1.08 1.05 1,006 1.00
1.00 1,003 1,02 1.09 1 23 1.37 1.84 2.68 3.00 4.50 5.75
5.38 4.56 3.66 2.46 1.82 1.57 1.23 1.08 1.05 1.006 1.00
1.03 1.06 1.15 1.29 1.40 1 . 84 2.73 3.05 5.54
Y2
1.00
1.005 1.03 1.15 1,38 1.58 2.28 3.45 3.84 5.72 7.13
ACKNOWLEDGMENT
The authors wish to thank C. C. Winding of Cornel1 University for his steady interest in the work and for his many helpful suggestions. LITERATURE CITED
Carlson, H. C., and Colburn, A. P., IND. ENQ.CHEM.,34, 581
Ibid., pp. 215, 218, 240, 245. Ibid., 1'01. V I I , p. 12. Jones, C. A , , Schoenborn, E. *M., and Colburn, A. P., IND. Exc,. CHEM..35. 666 (1943). Laar, J. J. van, Z.'physkk. Chem., 7 2 , 7 2 3 (1910) : 83, 599 (1913) : 137, 421 (1928). Lecat,, M., R ~ ctrav. . chim., 45, 620 (1926). Ibid., 47, 13 (1928). Schicktanz, S. T., Etienne, A. D., and Steele, W. I., IND.ENG. CHEM.,ASAL. ED., 11, 420-2 (1939). Tomonari, T., 2. physik. Chent . , B32, 202-21 (1936). RECEIVED February 21, 1949.
+ gy B
=
2: 90 2.51 2.00 1.64 1.50 1.24 1.10 1.07 1.013 1.00
Calculated from van Laar Equation8
YZ
"International Critical Tables," Vol. 111, p. 68, New York, McGraw-Hill Book Co., 1929.
A
=
Yl
(1942).
PI/
pTz
where y = the activity coefficient; P = the total pressure of the vapors, in this case 760.0 mm. of mercury; P o = the vapor pressure of the pure component a t the solution temperature, mm. of mercury; y = the mole fraction of the component in the vapor phase; and x = the mole fraction of the component in the liquid phase. The values computed from the experimental data according to Equation 1 have been compared with values calculated from the van Laar solutions of the Gibbs-Duhem equation ( 1 , 6 ) , which are given below in the form presented by Carlson and Colburn:
+
z)2
(3)
where A and B are the values of log, y1 and log, y~ for XI = 0 and = 0, respectively; the values giving very nearly the best fit of the data are A = 1.170 and B = 1.750. The subscripts 1and 2 denote carbon tetrachloride and n-propyl alcohol, respectively, in this instance. Of the several proposed solutions to the Gibbs-Duhem equation, the van Laar equations have been found t o fit more systems better than the others (f), although their theoretical validity is questionable. Figure 4 shows that the observed data are in close agreement with the theoretically predicted values. The z2
Vol. 41, No. 12
Correction. In a recent article by D. S. Carr and B. L. Harris [IKD. ENG.CHEhf., 41, 2014 (1949)] the transition of sodium di-
chromate from the dihydrate was reported as 74.8" C. This was ascribed to W. H. Hartford [ J . Am. Chem. Soc., 63, 1473-$ (1941)l and is in error. The value reported by Hartford is 84.6 C., which was erroneously reported in Chemical Abstracts [35, 4272 (1941)]. The erroneous value was corrected in Chemical Abstracts [35,5769 (1941)l. The paper by Carr and Harris observed a transition as judged by aqueous tension studies "at about 75"," obtained by observation of the slope of the Clausius-Clapeyron plot of the data. The slopes of the curves above and below the intersection are nearly equal, so that an appreciable error could have occurred in reading the temperature owing to minor error in constructing the curves. Even so, it is not understood why so large a difference from the correct value of 84.6" C. obtained.
B. L. HARRIS
