INDUSTRIAL A N D ENGINEERING CHEMISTRY
June 1952 log y1
=
-
S”‘
XZ
52
=0
d log
SIR: I am indebted to Dr. Gilmont for pointing out, in his fore-
0121
and (3)
Substituting Equation 2 in 3 and integrating, one obtains In yl = A In
A fBIn-A - XP B
B
+ xz
and In yz = ( A
- 1) In AA2-
- 1
+ ( B + 1) In -B-++ xz
(4)
which may be written in exponential form to yield
and (4)
Equation 4 may be combined with the expression for ideal relative volatility, namely,
This last equation is a thermodynamic test of the constants determined from the data by Prahl’s correlation, and is analogous t o Equation 25 of Gilmont et al.(1). This test was applied to the example given by Prahl, namely for the system carbon tetrachloride-methanol a t 35’ C. with the following excellent results: a;% =
1451
0.798 (0.018)0~013 (1.166)1.166- 1.173 (1.018)1.018 (0.166)0.166
-
which deviates less than 21/2% from the actual value calculated from vapor pressures.
going interesting study, the theoretical thermodynamic significance of my correlation. I want to take exception, however, t o some of his conclusions as to its practical applicability. 1. “It cannot be extended to more than two parameters.” The mathematical formula itself is, of course, limited to two parameters. That does not imply, however, a limitation to the physical systems to which it can be applied. For the acetic acidbenzene system, for instance, Rosanoff @)had to go to the fourth power of x. Gilmont says about the same system (1): “For the 37 three-parameter systems, agreement. . . .appeared excellent. , . . , the one serious exception being the acetic acid-benzene system,. . . I ’ It was shown in the paper (3) that this system can be represented very well with the two-parameter correlation. 2. “The nature of the equation rules out the correlation of those systems, which give a maximum or minimum point in the 0 1 2 ~ us. xz curve.” This statement is correct only with the implication-correlation by one set of constants. My method of correlation, however, includes the use of more than one set of constants for different ranges of one system. By this means, it permits correlation of systems as defined above, within any range of experimental accuracy. It uses different constants for difference ranges of x in much the same way, as for instance, different sets of constants in the Clausius-Clapeyron equation are used to describe vapor pressures of one substance in different temperature ranges. 3. “For systems which approach ideality, inordinately high values of m or Y will be obtained.” It is correct that for systems approaching ideality, values of m or Y approach infinity. Cases in which numerical values of m or Y become so large that it is inconvenient t o handle them are so close to ideality, or more likely can be represented so closely by a .linear equation, that there is no reason to go to a twoparameter equation. The best procedure to follow in order to avoid unnecessary calculation is to calculate the 01 values for the experimeatal x - y points. Plot CY us. x. If the 01 us. x plot is a horizontal straight line, 01 = c, use y = 1-
cx
x 3. cx
If the (Y vs. x plot is an inclined straight line, LY = ar Thus, the algebraic expression for relative volatility employed in the Prahl correlation is equivalent to exponential expressions for the activity coefficients, and a combination of these yields a thermodynamic test of the data in terms of the correlation coefficients. The limitations of the method are now clearly seen-it cannot be extended to more than two parameters and the nature of the equation rules out the correlation of those systems which give a minimum or maximum point in the 0121 us. x2 curve, such as the ethanol-chloroform system a t 35” C. In the latter respect it is similar to the Van Laar equation. I t should also be noted that the equation reduces to Raoult’s law (ideal system) only if m or Y in Prahl’s Equation 4 goes to infinity; thus, in order to approach ideality one must approach a discontinuity. For nonideal systems this is no drawback, but for systems which approach ideality, inordinately high values of m or Y will be obtained. LITERATURE CITED (1) Gilmont, R., et al., IND. ENC.CHEM.,42,120 (1950). (2) Prahl, W., Ibid., 43, 1767 (1951).
ROGER GILMONT
Exm. GREINER Co. 20-26 N. MOORE ST. NEWYORK13, N. Y.
+ b, use
If the 01 us. x plot is not a straight line, proceed as described in my paper. LITERATURE CITED
(1) Gilmont, R., et al., IND. ENCI. CHEM.,42, 120 (January 1950). (2) Prahl, W. H., Ibid., 43, 1767 (August 1951). (3) Rosanoff,M. A., and Easley, C. W., J . Ant. Chem. Soc., 31,953-87 (1909).
WALTERH. PRAHL DUREZ PLASTICE & CHEMICALS, INC. N. Y. NORTH TONAWANDA,
Correction In the article “Heats O? Combustion of Some Nitro Alcohols” [R. M. Currie, C. 0. Bennett, and Dysart E. Holcomb, IND. ENO. CHEM.,44, 329 (1952)1, parts B, F, and G of the subcaption of Figure 2 are in error and should read as follows: B. Telescope, F. Galvanometer, and G. Constant-level controller. R. M. CURRIE
