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INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 44, No. 6
Baur ( 1 ) for 104" C. and 2iO" C. are given in Figure 2 ; the value for 270" C . is in good agreement (SiF4 ( g ) + 2Hz0 (9) = 4 H F (9) + Si02 (8)) wit,h t,he results of the present work, but t,he value Constants in Thermodynamic Functions for 104" C. is incorrect. Temp. Range, F o r m of Si02 (s) K. a b c x 103 d x 10-6 i Ryss (6) calculated equilibrium constant,sfor the Vitreous 298-2000 26,220 -6.470 0.41 -1.08 -1.x1 reaction from thermodynamic data. His calculaa-Quartz 298-848 -1.497 tions mere based upon data for amorphous silica 2 4 , 1 6 5 -8.842 @Quartz 848-2000 a-Cristobalite 298-523 26,810 14.483 -8.28 -2.80 -68.20 and 6-quartz at several temperatures between 25" 2 4 , 3 2 0 -8.819 1.23 -2.80 4.91 6-Cristobalite 623-2000 a-Tridymite 298-390 27,150 16.809 -10.1,j -2.80 -64.02 and 330" C., a range in which P-quartz is not a 6-Tridymite 390-2000 2 4 , 8 3 0 -7.069 0.93 -2,80 -0.52 stablephase. Theconstantsdeterminedin thepresa T h e functions ent experiments fall between those calculated by A H o (calcd.) = a - 0.4343 bT - cT? f 2 dT-1 Ryss for amorphous silica and quartz. AFO (calcd.) = a + bT log T + c T 2 + d T - 1 4- iT 106 K (atm.) = -0.2186 (aT-1 + b log 2' + c T + d T - ? + i) The results of calculations based upon more rewere derivezfrorn entropies a n d heats of formation given, b y the National Bureau of Standards (6) a n d heats of transition and heat capacity equat:ons given by.Kelley (41, with t h e cent and more complete thermodynamic data (,$, 5 ) assumptions t h a t Si02 has unit activity, t h e total equilibrium pressure IS 1 atmosphere, a n d are shown in Table 111. The logarithms of the t h e gaseous components behave ideally. equilibrium constants for reaction 1 with vitreous silica and with a- and P-cristobalite are plotted in Figure 2. The equilibrium constants for a-quartz, a-cristobalite, and a-tridyniite are practically the same, as are tube then was heated a t 350' C. and flushed Tvith dry nitrogen t o those for P-quartz, 8-eristohalite, and 8-tridymite. The fact constant weight. From the weights of the absorption tubes the t h a t t,he experimental line in Figure 2 crosses both the vitreous amounts of hydrogen fluoride, silicon tetrafluoride, and water in silica line and the 6-cristobalite line indicates that equilibrium the effluent gas n-ere obtained. in the system silicon tetrafluoride-water is influenced by the The measured volume of carrier gas was corrected to standard form of the solid silica. The agreement of the experimental conditions, and partial pressures of the reactants were calculated. data with the vitreous silica line a t low temperatures and with The equilibrium constant, K , was expressed as the P-cristobalite line a t high temperatures indicates that Equation 7 is of practical utility over the temperature range from 100" t o 1 i O O " C. When the apparatus was opened a t the conclusion of the study, where the p terms are partial pressures in atmospheres. a small amount of finely divided silica was found among the silver helices in the bottom of the equilibration tube. This silica EVALUATION O F RESULTS n-as identified as cristobalite by microscopic and x-ray examinaThe experimental data and the logarithms of the equilibrium tion. The silica in the main portion of the equilibration chamber constants calculated therefrom are shown in Table 11. The equiwas largely cristobalite with some unchanged silica gel. librium constants are plotted in Figure 2. The results obtained LITERATURE CITED at 200' C. are erratic, but those for higher temperatures are reasonably consistent. The absence of a systematic variation in (1) Baur, E., 2.physik. Chem., 48,483-503 (1904). K p with variation in pHPoindicates that equilibrium was attained (2) Froning, J. F., Richards, M. X., Stricklin, T. W., and Turnbull, S.G., IND.EKG.CHEM.,39, 275-8 (1947). and that the variations in K , are due to inherent analytical errors. (3) Hantke, G., 2. angew. Chem., 39, 1065-71 (1926). The equation (4) Kelley, K. K., U. 8.Bur. Mines, Bull. 476 (1949). ( 5 ) Kational Bureau of Standards, "Selected Values of Chemical log K p ( a t m . ) = 5.547 - 6383/T (7) Thermodynamic Properties," Sei-. I, 1947-48. (6) Ryss, I. G., J . P h y s . Chenz. (U.S.S.R.), 14, 571-81 (1940). represents the experimental data for 300 400 ', 600 ', and 800' C. (7) Wartenberg, H. v., and Bosse, O., 2. Elektrochenz., 28, 384-7 with a maximum deviation of 4.6%. The average experimental (1922 j values for the four temperatures and the values calculated from RECEIVED for review December 3, 1961. ACCEPTED J a n u a r y 28, 1962. the equation agree, however, within 0.6%. Presented before t h e Southmide Chemical Conference, Wilson D a m , .41a., The average values of the equilibrium constants determined by October 18-20, 1951.
TABLE 111. THERMODYNAMIC FUXCTIONS~ 7
7
-;,;;
243010
-'!:!:
O,
.
CORRESPONDENCE Algebraic Representation of Vapor-Liquid Equilibria SIR: I n connection Kith the paper entitled "An Algebraic Representation of Vapor-Liquid Equilibria" by Prahl @),it should be mentioned t h a t although the author of t h e article presents an excellent correlation for vapor-liquid equilibrium data, he has neglected t o point out its important thermod3mamic significance and the limitations of the method which are brought out thereby. Starting out with Equation 3 of the Prahl article and applying the method outlined in another paper ( I ) , this thermodynamic significance may be shown as follow^:
From Equation 3 of Prahl ( 2 ) a21
=
- 22 c BA+ 22
(1)
Taking logarithms and differentiating d 1%
0121
[-
-1 1 = 2.303 __ A -
~2
1 + By dx2 ] - 2
From Equation 9 of Gilmont et nl. ( 1 )
(2)
INDUSTRIAL A N D ENGINEERING CHEMISTRY
June 1952 log y1
=
-
S”‘
XZ
52
=0
d log
SIR: I am indebted t o 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;% =
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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 t o 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 t o two parameters. That does not imply, however, a limitation t o the physical systems to which it can be applied. For the acetic acidbenzene system, for instance, Rosanoff @)had to go t o 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 t o 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 t o follow in order to avoid unnecessary calculation is t o calculate the 01 values for the experimeatal x - y points. Plot LY us. x. If the 01 us. x plot is a horizontal straight line, 01 = c, use y = 1-
cx
x 3. cx
If the CY 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 t o 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 t o 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 t o infinity; thus, in order t o 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.,4 2 , 1 2 0 (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. NORTH TONAWANDA, N. Y.
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
