Iil'DUSTRIAL A X D ENGINEERING CHE.VISTRY
September, 1931
the industrial preparation of a stable emulsion. There are many other factors that must also be taken into consideration such as the protection from destruction by fermentation, putrefaction or mold growth, suitable viscosity, low interfacial tension, p.H control, and degree of dispersion and means of attaining it. Quantitative measurements on the strength of the films are in progress. Summary A simple method of studying the formation and properties of films of emulsifiers at liquid-liquid interfaces has been developed and the properties and behavior of such films with eight different emulsifying agents and four different oils described. These observations have been helpful in the determination of suitable conditions for preparation of stable emulsions. Literature Cited (1) Ascherson, M e m 4cad S a , 7 , 837 (1838). ( 2 ) Ascherson, Muller's A r c h , 1840, 44 (3) Bancroft, J Phys. Chem , 16, 177, 345, 475, 739 (1912) 17, 501 (1913). 19, 275, 513 (1915)
1019
Briggs, J . Phys. Chem., 19, 210 (1915). Briggs and Schmidt, Ibid., 19, 479 (1915). Briggs and Schmidt, Ibid., 19, 496-7 (1915). Clark and Mann. J . Bioi. Chem.. 62, 179-SO (1922). Finkle, Draper, and Hildebrand, J . A m . Chem. SOC.,46, 2780 (1923). Griffin, Ibid., 45, 1648 (1923). Harkins and Beeman, Ibid., 51, 1692-3 (1929). Hdrkins. Davies, and Clark, Ibid., 39, 592 (1917). Hattori, J . Pharm. SOC.Japan, N o . 616, 123 (1925) Hattori and Ogimura, Ibid., 49, 1147-9 (1929). Hauser, IND.ENG.CHEM.,18, 1146 (1926). Holmes and Cameron, J . A m . Chem. Soc., 44, 66 (1922). Holmes and Williams, Ibid., 47, 1323 (1925). Langmuir, Met. Chem. Eng.,16, 468 (1915); J . A m . Chem. Sot., 39, 1848 (1917). Lewis, Phil. M a g . , [6] 16, 499 (1908). Limburg, Rec. fraw. chim.,46, 885 (1926). Meulen, van der, and Riemann, J . A m . Chem. SOC.,46, 876 (1924). Nugent, Trans. Faraday Soc., 17, 703-7 (1922). Prieger, Biochem. Z . , 217, 331-6 (1930). Ramsden, Proc. Roy. Soc. (London),.1,72, 160 (1903). Robertson, "Pbysikalische Chemie der Proteine," p. 308 (1912). Sheppard, J. Phys. Chem., 23, 634 (1919). Storch, .4nalysl, 22, 197 (1897). Wiegner, Kolloid-Z., 16, 118 (1914). Wilson and Ries, Colloid Symposium, Monograph, 1, 145 (1923).
Calculations on Water-Gas Equilibrium Choice of Suitable Molecular-Heat Equations Heat of Reaction and Free Energy as a Function of the Temperature' W. M. D. Bryant CHEMICAL DEPARTMENT, Du PONTAMMONIA CORPORATION, U'ILMINGTOX, DEL.
The thermal and equilibrium data for the water-gas reaction are assembled and discussed. AHzgs.l for the reaction COn(g) H2(g) = CO(g) HZO(g) is calculated to be 9751 calories. This value is combined with molecular heat equations from several sources to yield expressions for A H a s a function of the temperature. These equations, in turn, are used to show the order of agreement existing between molecular-heat equations of different sources. For this reaction specific heat equations of Lewis a n d Randall, of Eucken, and of Eastman give similar results. Partington and Shilling's equations do not agree with these results. Expressions for the free-energy change, A F " , and its temperature coefficient are derived, as well a s for the
corresponding reaction isochores. The equilibrium value of Neumann and Kohler a t 1259.1" K. is used to determine the integration constants. I t is shown that the molecular-heat equations of Lewis and Randall, of Eucken, and of Eastman, satisfactorily reproduce the experimental equilibrium constants in the water-gas reaction. I t is also shown t h a t Partington and Shilling's molecular-heat equations fail to reproduce these values. AFo198.1 for the water-gas reaction is calculated. Numerical results ranging from 6828 to 6750 calories are obtained depending on the specific heats used. These values constitute the first step in a recalculation of the free energy of formation of carbon monoxide and dioxide.
H E recent appearance of valuable new thermal and equilibrium data for the water-gas reaction makes it desirable to construct new expressions for the corresponding heat of reaction and free-energy change. These new data are of such a character that they fix within narrower limits the older directly determined equilibrium values, and permit of a more reliable extrapolation of the free energy to lower temperatures. Aside from its technical value, the water-gas equilibrium affords access to the free energy of formation of the oxides of carbon. The early thermal data for the water-gas reaction are fully summarized by Haber (16). Apparently no direct experimental work has been done on this equilibrium above 1000° C. since that of Haber and Richardt (19) and that of Allner ( 1 ) . The lower range, which a t present is of greater industrial importance, has been rather extensively studied. The obscure
Karlsruhe thesis of Engels (10) has been cited by Keuniann and Kohler (SO) with whose work Engels' values are in good agreement. Reinders (38) mentions an equally obscure paper of van Groningen (1;) and while it has not been possible thus far to obtain van Groningen's actual figures, Reinders declares them to be in harmony with the work of Hahn (20),and of Haber (16). In 1924 Eastman and Evans ( 7 ) suggested that the equilibrium measurements of the carbon nionoxidecarbon dioxide and water-hydrogen ratios over ferrous oxide and ferric oxide might be combined to yield true values for the water-gas equilibrium. The values so obtained were consistently about 40 per cent higher than previous direct determination would indicate. To clear up this matter, Neumann and Kohler (30) redetermined the values of the constant,
+
T
1
Received May 12, 1931.
+
INDUSTRIAL A N D ENGINEERIXG CHEMISTRY
1020
They were able to check the previous direct determinations. Neumann and Kohler’s equilibrium determinations are more consistent than those of the earlier workers, and the large number of individual observations made serves to further improve present knowledge of this reaction. Eastman (5) has recently published more data to support the high values obtained by the indirect method, particularly those from the oxidation-reduction equilibria in the presence of a tin-stannic oxide solid phase (8). Very convincing evidence in favor of the correctness of the direct equilibrium values is presented by Emmett and Shultz (9) who have obtained equilibrium constants by the indirect method, which are in good agreement with the work of Neumann and Kohler. They used a flow method and have shown that the anomalous results in the iron oxide systems obtained by Eastman and others (7,41, 42, 43) are traceable to the reactions
++
+ +
FeO Hz = Fe H1O F e ~ 0 4 HZ = 3Fe0 HzO
of the more recent work. The discrepancy between Haber’s and Hahn’s high-temperature results is plainly apparent in Figure 2 and is fully discussed elsewhere (17). Eastman’s points are given for purposes of comparison. Selection of Thermal Data
It is well known that the calculation of equilibrium in gaseous systems over wide ranges of temperature requires a knowledge of four factors: the molecular heats of the reactants and products, the heat of reaction, a t least one known value of the equilibrium or equivalent free-energy data, and the deviations of the substances from the perfect gas. I n the case of a reaction taking place at one atmosphere and elevated temperatures, it is generally agreed that the assumption of perfect gases introduces only errors that are negligibly small. This can safely be assumed t o hold in the reaction COz ( g )
and that they are associated with the static method of attaining equilibrium first used by Deville (3). Results by this method, in fair agreement with those of Emmett and Shultz (9),have, however, been obtained by several experimenters ( 1 1 3,37) * Survey of Available Equilibrium Data
Figures 1 and 2 show graphically how the various determinations of the equilibrium constant of the water-gas reaction agree among themselves. The work of all the experimenters mentioned, except van Groningen, is shown in these diagrams. It will be noticed that Neumann and Kohler’s, and Emmett and Shultz’s points check very well, while Engels’ values show fair agreement but are less consistent; also that Hnhn’s low-temperature points are all a trifle lower than those
Vol. 23, No. 9
+ Hz
( g ) = CO (g)
+ HzO (g)
Hence only the first three factors need be considered here. I n the water-gas reaction, the equilibrium and heat of reaction are known with considerable accuracy, and will be of service in selecting the most likely expressions for the molecular heats. Such a procedure has already been tried by Partington and Shilling (36, 36) whose work, however, is marred by errors as will be shown further on. A number of authors (4, 6, 11, 13, 14, 11,94, 33, 40) have summarized the present experimental knowledge of the specific heats of gases in the form of analytical expressions for the most part empirical in nature. After careful comparison of a large number of these equations with the experimental specific heats, equations from four such compilations were selected for the present work. These molecular-heat equations are as follows:
0.c
4:
3
-1.0
s
3-l
-1.5
-2l
FIGUWi - W A T e r r - G h b
EQUILIBRIUM
Curve I , fquation 38; curve 2, t q u d i o n s 36 and 39; c u r v e 3 , t q u o t i o n 37. Erperimentol Determinntims: b? Neumann and K3hIer,t928. direct and rever5e reactions; 0 Emmett and Sholtz,1929, Cc-COO equilibria, $Emmett and S h H r , 1330, Pe-FeO equilibria; .EngeIs, 1911; mHahn, i903; 0 Ea5tman and Evone, t924, Fe- h O equilibria; 0 Castman and equilibria. Evons, 1914, FcO-Fesq squilibrio, V eastman and Robinson, 1928, 5n-5n0,
INDUSTRIAL A N D ENGINEERING CHEMISTRY
September, 1931
Lewis and Randall ( 2 4 ) : CO: C, = 6.50 0.OOlOT HzO: C, = 8.81 0.0019T 0.00000222T2 COS: C i = 7.0 0.0071T - 0.00000186TZ H1: C, = 6.50 0.0009T Partington and Shilling ( 3 4 ) : CO: C, = 4.924 0.00017T f 0.00000031T2 Hz0: Cu = 6.901 - 0.0019T 0.00000234T2 COz: Cw = 5,547 0.0045T - 0.00000102T2 Hz:- C, = 4.659 0.0007T
++ + + + +
(1) (21 (3\
+
(4) (5) (6) 17)
+
The heat of reaction a t 298.1' K., just computed, may then be substituted into the integrated forms of expressions, Equations 17 and 18, which, for convenience in treating the diverse types of specific heat equations, may be formulated as follows:
@j
+ 215. (990 7) +
* (F)+ * (7)
\
J
/
(13)
Eastman: CO: C, = 6.76 HzO: C, = 8.32 COz:
H~:
+ +
+ +
. ~ -960 (21) Con ( g ) HI ( g ) Hz0 (1) CO (g); A H z s B= Hz0 (1) = Hz0 (g); AHzg8.1 = 10,441 (22) COZ(g) HZ(g) = HzO(g) CO (g); / ~ H Z O=B .9751' I (23)
AH
Cot: C, = 6.96
+- 0,000653T 0.000606T + 0.00000013T~( 4 ) + 0.00000270T2 0.0000000006145T3(6:) C, = 5.07 + 0.01630T - 0.00001290Tz + 0.00000000391T314) c, = 6.85 + 0 . 0 0 0 2 8 ~+ 0.00000022~~ (4j
(11)
(13) (14) (15)
(isj
'
Combining the molecular-heat equations for carbon monoxide and water, and subtracting those for carbon dioxide and hydrogen, the difference may be integrated with respect t o the temperature according to the Kirchoff formula (25)?
1021
= A H 0
+ ACpo T 4-
0
ST
where Cm and Gorepresent the constant part of the speciiic heats, and C', and C'", the temperature coefficient. Equations 24 and 25 are then solved for AHoand AEo. The completed expressions for the temperature variation of the heat of reaction are given below and the source of the molecular heats indicated: Lewis and Randall: AH = 9570 1.81T - 0.00445T2
+ 0.00000136T' Partington and Shilling: AE = 9512 + 1.619T - 0.00311P + 0.00000122T' +
Eucken:
AH 2$
= 9612
+ 0.99T + 0
AH and AE are the heats of reaction a t constant pressure and constant volume, respectively, and are practically identical in the present case where the reaction takes place without change in the number of molecules. In computing the heat absorbed in the water-gas reaction, the heats of combustion of hydrogen and carbon monoxide recently determined by Rossini ($9) were used. These values are given directly for 25' C. and 1 atmosphere, and undoubt. ~ the edly surpass all earlier work in precision. A H B ~ for water-gas reaction is calculated as follows:
Adding Equations 19 and 20 yields: Con ( g )
+ HZ
(9)
HzO (1)
+ CO (g); PJ-lzzss.~ = -960
(21)
The heat of vaporization of water a t 298.1 O K. and 1 atmosphere was calculated from the heat of vaporization a t 373.1 OK. (22) by means of the molecular heats of liquid (23) and gaseous water (6) (see Equation 14), and found to be 10,441 calories. The value is combined with that of Equation 21 to give Equation 23, the quantity sought:
*
Eucken uses the Planck-Einstein function designated as $ t o express the temperature coefficients of the molecular heats of gases. Since the integration of this function is difficult, the tabulated integral!;
f
-
ST
TO
C'TdT a n d f T d_T C'TdT for different values of -.Bo have been 0 Ts 0 T given on pages 406-407. They are designated as Q. and t,respectively. I Lewis and Randall's system of notation will be used throughout except in the treatment of the Planck-Einstein function in which case Eucken, Jette, and LaMer (12) will be followed.
(26) (27)
s'[$ + * (F)+ (39)
(F) (F) 2*
- 15. or
(24)
A C',d T
Eastman: AH = 9420
(y)] dT
(28)
+ 3.16T - 0.008314T20.000000001131T4 + 0.00000517T3- (29)
Equations 26,27,28, and 29 have been solved for a number of temperatures to show the order of agreement that exists between the work of these authorities. The results are given in Table I and are plotted in Figure 3. Table I-Heat of Reaction at Various Temperatures Using Molecular Heats from Several Sources AH AE ( AC, LSWIS ( ACVPAF.TINQAH AH
T
t
OK.
*C. 25.0 126.9 226.9 326.9 426.9 526.9 626.9 726.9 926.9 1126.9 1326.9 1526.9
298.1 400 500 600 700 800 900 1000 1200 1400 1600 1800
AND
TON AND SEIL.LINQ)
9751 9669 9532 9348 9122 8866 8585 8290 7654 7114 6645 6342
9751 9740 9697 9627 9539 9442 9339 9241 9085 9031 9137 9465
RANDALL)
(ACp
(AC+
9751 9618 9415 9174 8911 8648 8376 8112 7602 7126 6620 6251
9751 9656 9496 9293 9059 8811 8557 8305 7829 7391 6956 6449
EUCKBN)EASTMAN)
4 Before the appearance of Rossini's work, the value AHrt1.1 = 9730 was calculated from the older thermochemical data. T h e chief uncertainty lay in t h e heat of combustion of carbon monoxide determined by Thomsen [Thcrmochem. Untersuchungen. 2, 285 (1886)1,and Berthelot [Ann. chim. phys., 20, 255 (15SO)I. These values, 67,960 and 68,300, respectively, were corrected for systematic errors as directed by Swietoslawski ("OstwaldDruckers Handbuch der Allgemeinen Chemie," Vol. VII, p. 95, Akademische Verlagsgesellschaft, Leipzig, 1925) and converted t o 15' calories by means of the factor 4.1519/4.185. T h e resulting values 67,638 and 67,567 were calculated to 298.1' K. by means of specific heats and the average, 67,610,combined with the heat of combustion of hydrogen [Roth, 2.Elcklrochem., 26, 288 (1920)] and Lewis and Randall's value for the heat of vaporization of water at 298.1" K. ["Thermodynamics," p. 477, McGraw-Hill, 19231 to obtain the above heat of reaction. This value is inferior t o the one used in the present paper, although probably better than those previously derived from uncorrected thermochemical data.
1022
INDUSTRIAL A X D ENGINEERISG CHEMISTRY
Vol. 23, KO.9
0.4
0.0
-0.4
d-Ql
Y
el
4.2
4.6
-2.c
-2 4
FIGUQE2 - WATER-GAS€QUILW~UM INCLUDING WORK AT F L A H ~TEMPERATURES. 38; curve 2 , Equoticns 36 and 39; c u r v e 3 , E q o o f i o r , 37.
C u r v e 1, L q u o t i o n
Exper!rnan-tal Dckrninafiona: 0 Lmmcitond Sholfr, 1929-30; o Neumann and K;ihlecl928; 0 Hober and Qchordt, i904, 0 Allnu; 1905; - 0 - E a s f m o n , 1914-28.
SHahn, 1903;
Inspection will show that the values of AH calculated from the molecular heats of Lewis and Randall, Eucken, and Eastman are fairly concordant, the greatest differences scarcely exceeding 300 calories. On the other hand, A E from Partington and Shilling’s equations (in this case comparable with A H ) shows temperature variation of entirely different character. The values differ from those of the first group by more than 1000 calories a t temperatures below 1200” K. This fact in itself is in no way prejudicial to the work of Partington and Shilling, but merely serves to expose a complete lack of agreement between these two groups of authorities, However, other evidence is available to show that Partington’s specific heats are not in harmony with the known equilibrium in the water-gas reaction, while those of Lewis and Randall, Eucken, and Eastman will be shown to he in good agreement. A few years ago Partington and Shilling (36) published an article on the water-gas equilibrium with which their specific heats seemed to agree. Shortly afterward a small arithmetical error in this work was found by Travers and duly corrected by the authors (36) leaving the apparent agreement better than before. An unfortunate error in the conversion of their AC, from the Centigrade to the Kelvin scale
4 tngelo, i9Ctj
has been detected.6 When the proper correction is made, the order of agreement between experiment and calculation is greatly impaired. The substitution of more recent AH and equilibrium values is not sufficient to remove the discrepancy, as an inspection of Table I1 and Figures 1 and 2 will show. Thus the only conclusion that can be drawn is that Partington and Shilling’s specific heats are not able to correlate the other experimental data for the water-gas equilibrium. Although the failure of specific heats to check with reliable thermal and equilibrium data leaves those specific heats open to question, complete agreement is no assurance that the C, and C, equations for the individual gases are correct, since compensating errors in the individual equations may cancel, leaving the summation sensibly correct. It is believed that this is the case with Lewis and Randall’s C, kquations for carbon dioxide and water, which probably are not representntive of the most recent experimental work, yet serve satisfactorily in calculating the present equilibrium. Eucken’s molecular-heat formulas are more difficult to use than East-
+ +
:The equation given in (36) reads: Log K = --2126/T 1.077 log T - 0.0~898T 0 08133 T2 0.5425. When the error noted here is corrected, the expression should read: Log K -2140/T 0.815 log T - 0.0~680T 0.0~133T2 C 0.0147.
+ +
-
-
ISDC'STRIAL Ah'D ENGINEERING CHEIVISTRY
September, 1931
man's, although both seem t o follow experiment closely. Eucken's equations are probably unique in th%tthey possess some theoretical significance, since their temperature coefficients can be deduced from spectral measurements, although a t present such interpretation of spectra presents many difficulties. Temperature Coefficient of Free-Energy Change and Its Expression in Form of Reaction Isochore
1023
Eastman:
x fH10 x fHt
+
-2059.0 1.5904 logio T T 0.001817T +b.0000005650T2-0.00000000008240T3 log10
fCO
fCOi
+i
(39)
The integration constants, I and i, in the two previous sets of equations may be computed with considerable precision from the carefully determined equilibrium value of Neumann and Kohler (31) a t 986' C., which is the mean of twenty individual observations. This result is as follows:
When the heat of reaction has been expressed as a function of the temperature, it is a simple matter to derive an equation for the free-energy change a t any temperature and to express this in terms of the fugacities (corrected partial pressures) of the molecular species present a t equilibrium. Ifinis and Randall (26) have outlined fully how this may be accomplished by means of the following relations:
AF' = -RT In K 6
and
(31)
Applying these principles to Equations 26, 27, 28, and 29 the following free-energy equations are obtained : Lewis and Randall: AF" = 9570 - 1.81T In T
+ 0.00445T2 - 0.00000068TJ +IT
Partington and Shilling: AA" = 9512 - 1.619T ln T
(32)
+ 0.00311T2 - 0.00000061T3
+ IT
(33)
T*K
Eucken: AF' = 9612 - 0.99 T In T
-
T
The I values for each of the free-energy equations and the constant i for the corresponding van't Hoff equations are tabulated below, each opposite the number of its respective formula:
5800
2300
IL Eastman: AF' = 9420
(3F) - (69)] + $
IT
dT
(34) EQUATION
- 3.16 T In T + 0.008314T2 - 0.000002585T3
+ 0.0000000003770T4+ I T
(35)
These in turn are converted to the form of the integrated van't Hoff isochore by means of Equation 31, where
RT In K
=
4.5750T logloK
+z
(36)
Partington and Shilling:
xfa20 f C 0 2 x fHz
+ 0.814810gio T 0.0006798T + 0.0000001333Tz+ i -2079.1
(37)
Eucken: f C 0
log,,
fCOz
x fHz0 XfHz
EQUATION
36 37 38 39
- --2101.0 f 0.4983 loglo T
+ 0.2186
~
K may be assumed identical with K , and K c in the present case since, at 1 atmosphere and high temperatures, deviation from the perfect 8
gas must be less than the experimental errors in determining the equilibrium. However, for extrapolation to lower temperatures, the calculated value K will be equal to the quotient of the fugacities rather than of the partial pressures.
0,0331 -0.0229 0.8985 - 1.5313
Equations 36, 37, 38, and 39 were solved for a number of temperatures. For purposes of comparison the resulting equilibrium constants are given in Table 11.
T K. 298.1 400 450 500 550 600 650 700 750 800 850 900 950 1000 1050 1100 1200 1400 1600 1800
1
(36)
-
Isotherms for Water-Gas Reaction
___-__fCO
0.000973T f 0.000000149T2 f C 0
I -0.1514 0,1048 -4.1106 7,0057
Table 11-Equilibrium
Lewis and Randall:
log10
32 33 34 35
XfHzCdfcoz
(37)
x fH,----(38)
(39)
OC.
1.12 x 7.29 X 2.78 X 8.00x 1.89 X 3.81 X 6.85 X 1.12 x 1.73 X 2.49 X 3.45 x 4.50 X 5.72 X 7.14 X 8.60 X 1.03 1.39 2.17 2.93 3.63
10-6
10-4 10-3
10-8 10-9
10-2 10-P 10-1 10-1 10-1 10-1 10-1 10-1 10-1 10-1
It will be recalled that the equilibrium constants given in Table I1 have been calculated using the heat of reaction from Rossini's heats of combustion of CO and Ht; the equilibrium data of Neumann and Kohler a t 1259.1 K.; and the respective molecular heat equations of Lewis and Randall, Partington and Shilling, Eucken, and Eastman.
INDUSTRIAL AND ENGINEEEING CHEMISTRY
1024
VoI. 23, No. 9
of Constants, f c o X f H 2 0 / f C O t X f,, from Several Sources __-_-____EQ”A~I~N LEWISAND RANDALL NEUMANN A K D KOHLBR 36 38
Table 111-Comparison
T
1
If. 500 600 700
0
0
c.
226.9 326.9 426.9 526.9 626.9 726.9 1126.9 1526.9
800
900 1000 1400 1800
HABER
5.75 x 10-8 2.91 X 10-3 8.96 X 10-1 2.02 x 10-1 3 . 6 8 X 10-1
6.76 X 10-1 2.12 3.69
5.20 X 2.77 X 8.91 x 2.10 x 4.01 X 6 62 X 2.18 3.88
10-8 10-2 10-2
10-1 10-1
10-1
It is readily apparent from Table I1 that the constants calculated from the equations of Lewis and Randall, Eucken, and Eastman are in good agreement. The values from Partington’s specific heats, it will be noticed, differ from these. The curves corresponding to the calculated values in Table I1 are given in Figures 1 and 2, together with the experimental points. Noteworthy correlation of Neumann and Kohler’s values with the indirect determinations of Emmett and Shultz approached through the cobalt-cobaltous oxide and iron-ferrous oxide systems will be observed in the case of Equations 36, 38, and 39. This correlation is probably closest in the case of Equation 38, derived from Eucken’s C, formulas. It is believed that the agreement of these equations with experiment is real, and not a result of accumulated errors. In addition to the experimental data just mentioned, Engels’ results, although less homogeneous agree reasonably well. Haber and Richardt’s, and Allner’s determinations above 1000° C. are shown in Figure 2. The calculated curves agree satisfactorily with these values although the experimental data are not as consistent as those already mentioned. Eastman’s determinations are shown in both of the diagrams and although thoroughly self-consistent, they differ from all the other data given. I n the author’s opinion the analytical expressions for AH, AF, and the equilibrium constant K , based upon the speciiic-heat equations of Eucken and of Eastman, are the most reliable, since they reproduce experiment satisfactorily and a t the same time are representative of present knowledge of specific heats. It is not possible to say with certainty which of these two series of formulas is the more reliable. Survey of Earlier Equations for Water-Gas Equilibrium
There are a few earlier equations for the water-gas equilibrium which will be briefly discussed. Such expressions have been derived by Haber (I@, Lewis and,Randall (27), Neumann and Kohler (Jb), and Eastman (5). The first two have been derived from older data and hence cannot be expected to agree completely with the present calculations. Neumann and Kohler’s equation is similar to Equation 38 and the agreement with experiment is good. For purposes of extrapolation to lower temperatures, this equation is probably less reliable, since some specific heats used differ from Eucken’s latest values, and since the heat of reaction is not an independently determined quantity but has apparently been derived from their own equilibrium determinations. Eastman’s equation has been derived from the abnormally high indirectequilibrium experiments and for that reason is not in harmony with the present calculation. This equation will not be further considered. The equilibrium constants from the remaining three expressions are compared with those from Equations 36,38, and 39 a t several temperatures in Table 111. Standard Free-Energy Change in Water-Gas Reaction
There is frequent; need for values of the free-energy change at 298.1 K., the standard reference temperature most used by Lewis and Randall (29), for the calculation of other reactions. O
Both these authorities (28) and Eastman (5) have calculated
7.91 x 3.77 X 1.12 x 2.49 x 4.50 x 7.26 x 2.23 3.65
10-3 10-2
10-1 10-1 10-1
10-1
7.23 X 3.53 x 1.07 X 2.40 X 4 42 x 7.09 X 2.16 3.70
10-3 10-2
lo-: 10-
10-1 10-1
8.00
_______39
7
x lo-:
3.81 x 1.12 x 2.49 X 4.50 X 7.14 X 2.17 3.63
7.34 x 3.66 X 1.07 X 2,39X 4.38 x 7.02 X 2.18 3.81
10-1
10-1 10-1 10-1
10-1
10-1 10-1
10-1 10-1 10-1 10-1
the free energy of the water-gas reaction as a means of approaching the corresponding free energy of formation of carbon monoxide and dioxide. These latter quantities are obtained by combining the free-energy data for the water-gas reaction with those for the reactions, C (&graphite) COP(g) = 2CO (g), the well-known producer-gas reaction, and H P (g) ‘/2 0 2 (g) = HPO (g), the synthesis of water vapor, both of which may be computed with considerable accuracy. The free-energy change accompanying the water-gas reaction a t 298.1 O K. and 1 atmosphere, as calculated from each of the Equations 32,34, and 35 is as follows:
+
EQUATION
AF
+
‘itu
32 34 35
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