JULY, 1937
INDUSTRIAL AND ENGINEERING CHEMISTRY
845
CORRESPONDENCE Thermodynamic Calculation of Vapor-Phase Hydration of Ethylene SIR:Bliss and Dodge (2)recently published the results of a direct, experimental determination of the equilibrium constants a t several temperatures for the reaction:
From their results and the earlier experimental data of Stanley, Youell, and Dymock ( 1 4 ) , they thus derived the general freeenergy equation, AF"
-9600
+ 28.2 T
(1)
for this gas-phase reaction and then calculated the corresponding equilibrium constants a t intervals of 100" between 400" and 700"K. This experimental investigation is a valuable contribution, and it is to be hoped that Dodge and his collaborators will continue to make such equilibria studies for other organic reactions. The present writer, however, cannot agree with the statements of Bliss and Dodge regarding the thermodynamic calculation of the equilibrium constant from thermal data. Among other things they say: "Sanders and Dodge (15) reviewed the situation on the thermodynamic calculation of the equilibrium con. stant and came to the conclusion that this method was of little value because of the widely divergent results obtained. The present authors have made further calculations using other combinations of thermal data, some of which became available after the earlier paper was published. The results confirm the conclusions already reached." This writer feels that such statements were justifiable four years ago when the paper by Sanders and Dodge was written, because the thermal data then available for ethylene were distinctly unreliable. However, the situation has greatly improved during the past two years, principally because of the excellent combustion studies of Rossini a t the National Bureau of Standards, and today it is possible to calculate quite reliable equilibrium constants for this reaction from the thermal data alone. The object of the present communication is to demonstrate this point. From the combustion value of Rossini (11) for ethyl alcohol vapor (336,780 * 100 calories), that of Rossini (12) for ethylene (337,280 .i; 70 calories), and the heat of vaporization of water (10,499 * 3 calories) a t 298.1" K. given by Giauque and Stout ( 5 ) ,we obtain AH298 = -11,000 * 130 calories for the reaction in question. The entropy of liquid ethyl alcohol a t 298.1 ' K. is 38.40 p 0.30 entropy units (E. U.) according to Kelley ( 7 ) . The heat of vaporization of ethyl alcohol is taken as 10,120 calories per mole by Rossini ( 1 1 ) ; the corresponding entropy of vaporization thus becomes 33.95 * 0.07 E. U. Fiock, Ginnings, and Holton (4) give 0.0771 atmosphere for the vapor pressure of ethyl alcohol a t 298.1 O K.; hence the entropy change for compressing the saturated vapor to the standard pressure of 1 atmosphere is -5.09 * 0.005 E. U. Combination of these data then yieldsSo?98= 07.3 * 0.31 E. U. for alcoholvapor a t the hypothetical pressure of 1 atmosphere. Taking the estimate of Parks (8) for the entropy of ethylene (S 02g5 = 52.3 * 0.3 E. U.) and Gor-
don's value ( 6 ) for gaseous water ( S o 2 p 8 = 45.10 * 0.005E. U.), we obtain ASo288 = -30.1 * 0.5 E. U. for this reaction. Accordingly, the free-energy change at 298.1 K. becomes: AF'zss = -11,000
+ (298.1) (30.1)-2030 =
* 200 calories (2)
The corresponding equilibrium constant for the vapor-phase hydration of ethylene a t 298.1 " K. is H, = 3080 with a probable maximum uncertainty of about 40 per cent. What is really desirable is a general free-energy equation (similar to Equation 1) which will be valid over a range of temperatures. If AC, for the reaction is assumed to be zero, Equation 2 yields the simple general form: AF" = -11,000
+ 30.1T
(3)
This assumption of zero value for AC, represents only a rough first approximation, but the resulting equation cannot involve us in serious error if we do not try to apply it too far above 298' K. A more reliable AC, value is obtainable with the equation, ACp = -6.43
+ 0.0133 T
(4)
which the writer derived from the following heat-capacity relations: 0.0224 T CzH4 (g); C p = 3.68 HzO (g); C p = 7.25 0.0023 T CsH60H (g); C p = 4.50 0.038 T I n this case the linear equation for ethylene conforms within 1.1 per cent t o the experimental values of Eucken and Partz (3) and of Beeck (1) between 290" and 573" K., and that for steam agrees within 0.8 per cent up to 750 O K. with the highly accurate statistical C , values published by Gordon. The equation for ethyl alcohol vapor is the one derived previously by Parks and Huffman (IO),mainly from Regnault's specific heat value a t 437' and Thibaut's value a t 623" K. It is undoubtedly the weakest point in the present calculations, since the C, values thereby obtainable may, perhaps, be in error by 5 per cent. With the data in Equations 2 and 4 the general free-energy equation
+ +
AF"
= -9674
+
+ 6.43 T h T - 0.00665 T a - 9.01 T
(5)
was derived by the usual thermodynamic procedures (9). This should be appreciably more accurate than Equation 3 between 300" and 700" K.
TABLE I. COMPARISON OF A F" AND K, VALUES T &quation 1 K. 298.1 400 600 600 700
-1,200 1,680 4.600 7,320 10,140
AF."
Equation 3
-2,030 1,040 4,050 7,060 10,070
-Derived
K X 108-
Equation' Equation Equatron Equation 5 1 3 5 -2,030 1069 4:139 7,206 10,249
769 3,080 3,080 120 270 260 16.5 10.7 16.9 2.36 2.14 2.68 0.63 0.68 0.71
-~~~~
In Table I the writer compares the free-energy values calculated by Equations 3 and 5 with those obtainable from the equation of Bliss and Dodge (Equation l ) . Undoubtedly the values given by Equation 1 are the more reliable a t 500°, 600", and 700' K., since a t these temperatures they are closely related to the experimentally measured equilibrium constants; those given by Equations 3 and 5 are safer at 298" and 400" K. However, it is clear from these data that the new equations, especially 5 , are
VOL. 29, NO. 7
INDUSTRIAL AND ENGINEERING CHEMISTRY
846
in fair agreement with the results of the equilibrium studies. This fact is also brought out by the comparison of the equilibrium constants derived from the three free-energy equations, as tabulated in columns 5, 6, and 7. -4direct comparison of the results obtainable from Equations 3 and 5 with the experimentally measured equilibrium constants of Bliss and Dodge provides still another way of testing the exactness of the thermodynamic calculation of the equilibrium. At 623 O K. Bliss and Dodge found K p = 0.00149, whereas Equation 3 gives 0,00190 and Equation 5, 0.00167. At 651 K. their experimental value was 0.00126 as against 0.00129 by Equation 3 and 0.00114 by Equation 5 . I n the writer’s opinion this agreement, especially with Equation 5, is very satisfactory and serves to indicate quite fairly the potentialities of the thermodynamic calculation of equilibria.
Literature Cited Beeck, O., S. Chem. Phys., 4, 680 (1936). Bliss, R. H., and Dodge, B. F., IND.ENQ.CHEM.,29, 19 (1937). Eucken, A., and Partz, A., 2. physik. Chem., ZOB, 184 (1933). Fiock, E. F., Ginnings, D. C., and Holton, W. B., Bur. Standards S.Research, 6, 881 (1931). Giauque, W. F., and Stout, J. W., S.Am. Chem. SOC., 58, 1144 (1936).
Gordon, A. R., J . Chem. Phys., 2, 65 (1934). Kelley, K. K., S.Am. Chem. Soc., 51, 779 (1929). Parks, G. S., Chem. Rev., 18, 325 (1936). Parks, G. S., and Huffman, H. M. “Free Energies of Some Organic Compounds,” A. C. S. Monograph No. 60, pp. 23-5, New York, Chemical Catalog Go., 1932. lbid., p. 125. Rossini, F. D., Bur. Standards J. Research, 13, 189 (1934). Tbid., 17, 636 (1936). Sanders, F. J., and Dodge, B. F., IND.ENG.CHEM.,26, 208 (19x41. \ - - - - I .
(14) Stanley, H. M., Youell, J. E., and Dymock, J. B., J . SOC.Chem. Znd., 53, 205T (1934).
I would be one of the last to belittle the value of thermodynamics in the prediction of chemical equilibrium, and I am glad t o have Parks correct any false impression that our paper may have created. We may conclude that the equilibrium conditions for the ethylene hydration reaction, a t least a t low pressures, are well established as a result both of the recent work on heats of reaction and absolute entropy and of the direct experimental measurements of the equilibrium constants. It would appear desirable to continue the attack on organic reaction equilibria along both of these lines. I hope that Parks and his co-workers and Rossini, to mention only a few of the investigators on the thermodynamic side, will continue to supply accurate thermal data. I should also like to point out that, even if we can calculate from thermal data the equilibrium constant for a given reaction, i t will still be desirable to carry out direct experimental studies of the same reaction. This is not only because of the desirability of having check results by independent methods, but also because we learn a great deal about the reaction from the direct experimental study that cannot be obtained from the thermodynamic calculations. For example, the important practical questions of pressure, temperature, and catalyst to realize a rate of reaction that permits an approach to equilibrium, and of the extent of side reactions, are answered only by an experimental investigation. Literature Cited (1) Kistiakowsky, G. B., Romeyn, H., Jr., Ruhoff, J. R., Smith, H. A., and Vaughan, W. E., S.Am. Chem. SOC.,57, 65-75 (1936). (2) Parka, G. S., Chem. Rev., 18, 325-34 (1936). (3) Rossini, F. D., Bur. Standards S. Research, 13, 21 (1934).
BARNETTF. DODGE Y A L UNIVERBITY, ~ NEWHAVEN,CONN. May 17,1937
GEORGES. PARKS STANFORD UNIVERBITY, CALIF. -4pril 2, 1937
Correction
,....
Attention is called to an article by C. D. West [ J . Am. Chem. SIR: Parks points out that the free-energy change for the ethylSoc., 59,742 (1937) ] on “Optical Properties and Polymorphism of ene hydration reaction can now be calculated from thermal data Paraffins” where the author points out an error in the article by withconsiderable confidence. This has been made possible largely ENG.CHEM.,28, 856 (1936)j on “Commercial ParafPage [IND. by the new value of the heat of combustion of ethylene obtained fin Waxes.” by Rossini a t the Bureau of Standards. Our work on the experiI n Table I1 of Page’s article the ordinary and extraordinary mental study of this reaction was completed more than a year berefractive indices are reversed, so that the column no - ne is fore this value was published, and our paper was submitted nearly actually ns - no,and the mean refractive index n is incorrect. 6 months prior to its publication. Consequently a t the time that Table VI is therefore incorrect also. Table VII, corrected, is our calculations for the paper were made, our pessimistic stategiven here. ment about the value of the thermodynamic calculation may have been justified. It is true, however, that prior to the submission TABLE VII. TRUEDENSITYOF, AND VOLUME PERCENTAIR IN, SOLID COMMERCIAL PARAFFIN WAXES of our paper the data on heat of combusion of
ethane Obtained by Rossini )(’ and On heat Of hy41.P. of Wax drogenation of ethylene by KistiakoTTsky ( 1 ) perF. o e. mitted a more accurate calculation of the free 121 49.4 energy of hydration than had been possible a t the tirne our work was started. These data were used 126 52.2 by Parks (2) to compute a value for the free energy of ethylene formation-namely, 15,820 in the usual 131 55.0 units’ If this is combined with the best 136 57.8 data on ethyl alcohol and water (the same data used by Parks in his communication), the value of 141 60.6 -1790 is obtained for the standard free energy of the hydration reaction in the vapor phase. This is to be compared with Parks’s value of -2030 a s given above, The equilibrium constant, K p , a t 700” K., based on the former A F ” value, is 1.62 x 10-3 compared to 2.36 X 10-8 given by Parks. Considering the circumstances, this is good agreement and on this basis the statement of Bliss and myself was certainly too pessimistic.
r D at
200 C.
Temp. OF.
0
di
d2 (Calod.)
(Obsnvd.) (Obsvd.)
dz
- dl
Vol. % Air
O C .
0.3343
50 10.0 60 16.6
1.5153 1.5136
0.900 0.897
0.902 0.899
0.002 0.002
$0.23 $0.23
0.3342
50 10.0 60 15.6
1.5179 1.5155
0.911 0.909
0,906 0.902
-0.005 -0.007
-0.55 -0.77
0.3339
50 16.6 60 50 10.0 15.6 60 15.6 70 21.1
0.912 0.909 0,917 0.914 0.914 0.911
0.907 0.904 0:911 0.909 0.913 0.909
-0.006 -0.005
0.3341
1.5182 1.6160 1,5213 1.5197 1.6214 1.5192
-0,005 -0.001
-0.56 -0.65 -0.55 -0.41 -0.10
-0.002
-0.22
10 .o
60
0.3337
-0,006
The difference between the calculated and observed densities now becomes so small as to be attributable to experimental error.
oILcoMPANY ( I ~ CASPER,WYO.,May 13, 1937
J. M. PAGE, JR. ~
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