Free Energy of Water, Carbon Monoxide, Carbon Dioxide, and Methane Their
i Uetallurgical Significance
JOHN CHIPMAN,D e p a r t m e n t of Engineering Research, University of Michigan, Ann Arbor, hlich. For the purpose of studying the free energy at reaction, the direct determinations of Neumann and high temperatures of metallurgically important Kohler are shown to be in excellent agreement with substances, accurate equations f o r the free energy of recent indirect determinations. For the producer water, carbon monoxide, carbon dioxide, and gas reaction, four independent sets of datu are in methane are demanded. Equations in current fairly good agreement. Three independent equilibria involcing methane use are criticized on the basis of the choice of data are considered, and it is shown that each set of employed in their derivation. Simple expressions are given f o r the heat ca- data is in agreement (within its experimental error) pacities qf gases in the range 25-2000" G. These with the free energy value based upon the third law are based primarily upon Eastman's recent re- of thermodynamics. The equation adopted f o r the views. Recent thermochemical data of Roth and free energy of methane is based upon iWacDougall's of Rossini are employed in setting u p the free value f o r the entropy obtained f r o m spectroscopic energy equations. Equilibrium data are used in data. Free energy values are compared with those obevaluating the integration constants of these equatained f r o m other sets of equations at 298.1", 1200", tions. For the free energy of water, Eastman's and 1873" K. value at 298.1" K . is accepted. For the water gas
I
N T H E study of the chemical reactions which form the bases of metallurgical processes, it is a matter of great importance to know the conditions of equilibrium and the factors which affect the equilibrium state. This knowledge enables us to determine what reactions are possible under specified conditions and the limits t o which these reactions will continue. Many of the important metallurgical reactions have been subjected to exhaustive experimental study a t moderate temperatures, and the extrapolation of the equilibrium data to higher temperatures provides information which will be useful in the study of liquid metals and slags. Extrapolations of this sort have been attempted by LeChatelier (20),Styri (41),McCance (RS), and others; while the calculations were made with great care, the paucity of data upon which they were based and the nature of the assumptions which it was necessary to make were not conducive to their wide acceptance. Within recent years much progress has been made in the application of physical chemistry to the problems of steel making. Following the introduction of the high-frequency induction furnace as a tool for high-temperature research, great advances have been made in the study of' equilibria involving liquid metals, slags, and gases a t temperatures in the neighborhood of 1600" C. Many of these equilibria, concerning which a few years ago we had only a qualitative or a t best a roughly quantitative knowledge, can now be treated thermodynamically with a fair degree of precision. Since many of our most useful metallurgical processes are based upon oxidation, reduction, and carburization, the first substances selected for study are the basic oxidizing, reducing, and carburizing substances-namely, water, carbon monoxide, carbon dioxide, methane, and their elements, hydrogen, carbon, and oxygen. A knowledge of the properties of these substances is also esqential to the calculation of the free energy of many of the metallic oxides and carbides. It is therefore a matter of considerable importance that we have a set of accurate equations for the free energy of these gases.
The equations of Lewis and Randall (21) are, as a whole, the most reliable set of free energy equations available. It is unfortunate that in their treatment of the producer gas equilibrium they used only the earlier measurements of Rhead and Wheeler (84) rather than their later more accurate work (Si). Were it not for this oversight, the equations of Lewis and Randall, as well as those given in Randall's more recent compilation ( S I ) , might be accepted without changes. Eastman (8)has recently reviewed the data on three of the substances under consideration. His expressions for the free energy of the oxides of carbon are based upon certain indirect measurements of the water gas equilibrium which were not in agreement with the direct determinations. More recent indirect experiments have demonstrated the essential validity of the direct measurements. It is therefore no longer necessary to suppose that the direct determinations are in error, and Eastman's equations must be discarded in favor of a new set based upon the direct determinations and upon those indirect determinations which are in reasonable agreement with the results of the direct experiments.
HEATCAPACITIES I n order to express the heat of a reaction and the change in free energy as a function of temperature, it is necessary to know the molal heat capacities of the substances involved. A number of excellent reviews of the specific heats of gases have appeared within the past few years, and we may select from these the data which appear to be most, reliable. Eastman (7, 9) has based his equations primarily upon the results of researches utilizing the direct calorimetric and explosion methods. Nernst and Wohl (26) and Justi (2.9) have reviewed the spectroscopic data and have advanced the claim that these data are in agreement with the results of the best experimental determinations. Their claims are supported by the recent calorimetric researches of Chopin (3). Eucken and Liide ( I C ) point out certain possibilities of error in the interpretation of the spectroscopic data. iit the same time
1013
1014
IKDUSTRIAL AND
ENGINEERING
they present a new series of determinations of the heat capacities of the more important gases. Their results for oxygen and nitrogen are definitely lower than the spectroscopic values as represented by the Planck-Einstein equation, and are in somewhat better agreement with Eastman's empirical equations. There can be little doubt but that the spectroscopic method will ultimately furnish us much more accurate data than we possess a t the present time, not only in regard to specific heats, but on free energy as well. The correlation of the room temperature values for the free energy of water with the data on its dissociation a t high temperatures depends very largely upon the equations employed to express the heat capacities of the three gases-hydrogen, oxygen, and steam. Good agreement is obtained by the use of the equations of Lewis and Randall, or of Eastman, or those of the present paper. On the other hand, when the spectroscopic data are employed, the correlation is rather poor. Complete revision of the data on the heat capacity of gases is greatly to be desired, but anyone undertaking this important work should consider its bearing upon the free energy of water a t high and low temperatures. Until all uncertainties regarding the interpretation of the spectroscopic observations have been removed, it seems advisable to employ in the' calculations the results of direct experimental determinations, where these are available. The heat capacity equations given in Table I are based upon the data reviewed by Eastman, and differ only slightly from Eastman's equations. The differences are based upon the following considerations : Eastman gives two equations for each substance considered; the first is designed to represent the data with great precision over a limited range; the second is a rough approximation over a very wide temperature range. From the standpoint of ferrous metallurgy the useful range need not extend above 2000" C., and by restricting the range of applicability of the equation to this upper limit, it is possible to devise comparatively simple expressions which are in close agreement with the more complicated equations given by Eastman. The simple linear expression for water vapor deviates very little from Eastman's cubic equation (9). The expression for carbon dioxide follows the general course of Eastman's preferred equation a t moderate temperatures and does not attain the inordinately high values of his quadratic equation a t the higher temperatures. The equation for methane is based upon the observations of Eucken and Lude and their semi-empirical equation. OF SUBSTANCES AT 300' TABLE I. MOLALHEATCAPACITIES 2300' K.
SUBSTANC~ Hi Na, Oa, CO HzO
coz
CHI C (graphite)
TO
CP
6.70 6.50 7.20 7.40 3.60 1.20
+ 0.00072' + ++ 0.00102' 0.00277' 0.00667' - 1.50 X 10-sTz + 0,01802' - 4.20 X 10-67'2 + 0.00502' - 1.20 X 10-6TZ
Since the specific heat of graphite will also be required in formulating the free energy of the compounds of carbon, an equation for the heat capacity of this substance, based upon data of Schlapfer and DeBrunner (39) is included. This equation does not represent their data with great precision, but the agreement is as good as can be obtained by a simple algebraic expression. HEATSOF FORMATION
It will not be necessary to review the many determinations of the heats of formation of the substances in which we are interested. Rossini's values (37) for the heats of combustion of hydrogen, methane, and carbon monoxide and Roth's heat of combustion of graphite (38) provide the basis for the following heats of formation a t 25" C.:
Vol. 24, No. 9
CHEMISTRY
HzO(1): AH = -68,313 calories COP(g): AH = -94,272 calories CO(g): AH = -26,649 calories CHl(g): AH = -18,110 calories
I n his recent calculations on the water gas equilibrium, the results of which are in excellent agreement with the present work, Bryant (2) finds for the heat of vaporization of water a t 25" C. that AH = 10,441 calories. This value, combined with Rossini's heat of formation of liquid water, gives for water vapor a t 25" C.: HzO(g):
AH = -57,872 calories
By employing the heat capacity equations, the heats of formation are readily expressed as a function of temperature. The equations are:
+ '/zOz = HzO(g); AH = -57,120 - 2.75T + 0.00075T2 (1) C + '/zOz CO; AH = -27,070 + 2.05T - 0.00225T2 +" 0.40 x 1 0 - 6 ~ 3 (2) -94,210 - 0.30T + 0.0003TZ- 0.10 C+ COz; AH x-10 (3) C + 2H7 = CHI: AH = -15.320 - 11.00T + 0.0058T2 1.06 x 10-+3 Hz
=
0 2
=
=
-67'3
'
(4)
FREEENERGY OF WATER Eastman (8) has reviewed all of the available data on the free energy of water. He has found as a mean of three distinct sets of data the value -54,467 calories for the free energy of water vapor a t 298" K. This value, combined with the expression given above for the heat of formation, leads directly to the equation:' Hz
+0.00075T2 '/zOz HnO(g); AF' - 6.65T
=
-57,120
+ 2.75Tln T -
(5)
EQUILIBRIUM IN WATERGASREACTION The equation of the water gas reaction and the expression for the corresponding free energy change obtained directly from the thermal equations, are as follows: CO,
+
+
HP = CO H20; AF' = 10,020 0.0018T2 - 0.25 X 10-6 T3 IT
+
+ 0.40T In T +
(6)
The equation contains the integration constant, I, which must be evaluated from equilibrium data. The equilibrium constant of this reaction is K = pH'' and the equaPCOZ x pH2' tion expressing the value of this constant as a function of temperature is obtained by dividing the free energy equation by -4.575T, which gives: log R = -2190/T - 0.201 log T 10-8 T2
- I/4.575
- 0.0003937' + 5.46 X
(64
The value of 1 may now be obtained from measured values of K a t various temperatures. The quantity I is an exact constant over the entire range of temperature in which the heat capacity equations are valid. The experimental methods of determining the equilibrium constant of the water gas reaction fall into two classesdirect and indirect. I n the direct method a mixture of the gases is passed into a reaction chamber which is held a t constant temperature and usually contains a catalyst, and the composition of the effluent gases is determined by analysis. The indirect methods involve the determination of equilibria in two related reactions such as: 1 Since this paper was written, new determinations of the dissociation pressure of silver oxide have been published by Benton and Drake [ J . A m . Chem. Soc., 54, 2186 (1932)l. Their work leads t o a revised value for the free energy of water vapor. The mean of the three independent methods is now -54,500 calories at 298' K. The equations of this paper have been corrected, in proof, to conform to this standard.
I N D U S T R I A L A .ND E N G I N E E R I N G C H E M I S T R Y
September, 1932 FeO Fe3
Hz Fe + H2O; K = ++ CO = Fe + COZ;K =
pHZo/pHz
= ~ C O ~ / ~ C O
The ratio of these two constants is the constant for the water gas reaction. There have been marked discrepancies among 1,he indirect results and between the direct and indirect values. Eastman's equations (S),based upon the results of indirect determinations, gave values of K which were approximately 40 per cent higher than the direct values of Neumann and Kohler (28). From the standpoint of metallurgical calculations, the importance of deciding between these two sets of data, differing by 40 per cent, is enhanced by the fact that the indirect determinations involve the free energy of several metallic oxides which are of great metallurgical significance. It is only within the past two years that indirect data have been available which removed the uncertainty and confirmed the direct results. It is worthy of note that these new data also remove the doubt as to the free energy of ferrous oxide. For the details of the controversy regarding the water gas constant, and for comprehensive reviews of the experimental work on this reaction, the reader is referred to the publications of Eastman (6, 8, 10) and of Emmett and Schultz (11-19). For the present calculations we will consider only those determinations which appear to be free from tQe surface effects discussed by Emmett and Schultz. The investigation of Neumann and Kohler (88)has provided the most accurate of the directly determined values of the water gas constant. As a mean of twenty careful determinations a t 986" C. they found K = 1.611 * 0.006. Substitution of this value in Equation 6a gives, for the integration constant, I = -13.63 * 0.01. At temperatures below 986" and above 450" C., consistent results were obtained. The mean value of I calculated from their twenty experiments within this range is -13.70 * 0.10. Emmett and Schultz (11, 12) determined the equilibrium conditions in the reduction of cobalt oxide by hydrogen and by carbon monoxide. Combination of these data leads to the first three results in Table 11. They also (13) determined the equilibrium ratio of steam to hydrogen in the reduction of ferrous oxide and combined this with Eastman's "best values" for the corresponding equilibrium involving the oxides of carbon. The resulting values of the water gas constant, together with the corresponding integration constant, I , of Equation 6 are included in Table 11. TABLE
11.
WATER GAS CONSTANTS OF = pH20
TEMP. O
c.
450 615 570 600 700
800 900 1000
x
EMMETT AND
pa0
SYSTEH
P n z X PCOZ
co-coo co-coo co-coo
0.137 0.232 0.340 0.380 0.624 0.917 1.306 1.693 Average
Fe-FeO Fe-FeO Fe-FeO FeFeO Fe-FeO
SHULTZ
I qf
Equatlon 6 -13.70 -13.73 -13.77 -13.63 -13.61 -13.59 -13.66 -13.67 -18.67
1015
cision. It does, however, place definite narrow limits upon the possible values of the equilibrium constants. From these data we may obtain limiting values for the water gas constant. The maximum value is obtained by dividing the upper limit of the ratio H20/H2 by the lower limit of the ratio CO,/CO, while the corresponding minimum value is the lower limit of the ratio H20/H2divided by the upper limit for the ratio CO,/CO. These limiting values, along with the corresponding limiting values of the integration constant, are given in Table 111. TABLE111. LIMITIXG VALUESO F WATERGAS CONSTAXT FROM MURPHY'S DATA -I
P H ~ O ''0 Pcoz x P H ~
PH~O/PH~
PCO*/PCO
NonNonTEMP, Scaling scaling Scaling scaling
OF
Max.
Min.
EQUATION 6 Max. Min.
2.06 2.68 2.86 3.37 3.32 3.74
1.94 2.42 2.74 2.97 3.08 3.28
13.64 13.77 13.72 13.88 13.70 13.83
c. 1093 1204 1260 1316 1371 1427
0.358 0.309 0.289 0.272 0.244 0.178
0.339 0.297 0.282 0.260 0.236 0.171
0.69s 0.796 0.805 0.876 0.784 0.640
0.696 0.749 0.792 0.807 0.750 0.585
13.50 13.57 13.64 13.64 13.56 13.56
The extreme limiting values of I in Table I11 are -13.88 and -13.50, whereas the limits that might be designated as probable (the average of the maximum and minimum values, respectively) are -13.76 and -13.58. It is perhaps fortuitous that the lowest maximum value and the highest minimum value of I should be identical. This figure, - 13.64, may be considered the best value of I derived from these experiments. The uncertainty is estimated as about *0.06. The values of the integration constant of the water gas equation are summarized in Table IV. The agreement is better than could have been anticipated. The value derived from Neumann and Kohler's experiments a t 986" C.-namely, -13.63-will be adopted. The equation for the water gas reaction is therefore:
+
+
C 0 2 H2 = CO HzO(g); AF" = 10,020 0.0018T2 - 0.25 X 10-6 T3 - 13.63T TABLEIv.
+ 0.40Tln T +
(6)
INTEGR.4TION CONSTANT OF RANQE
I
986 450- 950 450-1000 1093-1427
-13.63 -13.70 -13.67 -13.64
MBTHOD
OBSERVER Neumann and Kohler Neumann and Kohler Emmett and Shultz Murphy, Wood, and Jominy
Direct Direct Indirect Indirect
EQUATIOK 6
c.
Av. DEVIATION fO.O1 rtO.10 rt0.05 f0.06
EQUILIBRIUM IN PRODUCER GAS REACTION The equation for the producer gas reaction and the expression for the change in free energy attending the reaction are:
+
C(graphite) COz = 2CO; A F o = 40,070 0.0048T2 - 0.45 X T3 IT
+
- 4.40Tln T
+ (7)
The corresponding expression for the equilibrium constant, K = P ~ C O / P C O , , is: f 0.05
The researches of Murphy, Wood, and Jominy (26) and of Jominy and Murphy (18) on the scaling of pure iron a t high temperatures in mixtures of carbon dioxide and carbon monoxide and of steam and hydrogen provide an additional check on the values of the water gas constant. hfurphy exposed samples of electrolytic iron to the action of carefully controlled gas mixtures and determined whether or not the sample was oxidized by the gas. The ratio of oxidizing to reducing substance in the gas was varied by small increments, and each mixture employed was characterized as scaling or nonscaling. The equilibrium ratio must lie between the highest nonscaling and the lowest scaling mixture. The investigation does not purport to establish the equilibrium ratio with extreme pre-
+
log K = -8758/T 2.213 log T 10-8 T2 - Ij4.575
- 0.00105T + 9.85
X
(7a)
The equilibrium has been investigated by Rhead and Wheeler @5), Jellinek and Diethelm ( I Y ) , and by Dent and Cobb ( 5 ) , and these three investigations show a very satisfactory degree of accord. Further confirmation of the validity of their measurements is found in the work of Becker ( 1 ) which is also of especial interest in establishing the free energy of iron carbide. Becker used an indirect method in which the carbon dioxide pressure in the reacbion chamber containing the graphite was fixed by the presence of strontium carbonate, and the equilibrium condition was determined by a simple measurement of the total pressure. His studies covered a range of temperature from 650" to 950"
1016
INDUSTRIAL AND ENGINEERING CHEMISTRY
C., but little accuracy can be ascribed to the results below 800" C. on account of the low pressures involved; therefore, only the results a t his four highest temperatures will be used. The results of the four investigations under consideration are summarized in Table V in which are given the observed values of the equilibrium constant and the corresponding values of the integration constant of Equation 7. When the average of all of these values of I is employed, Equation 7 becomes:
+
+
C(graphite) COZ= 2'20; AFo = 40,070 - 4.40Tln T 0.0048T2 - 0.45 X T 3 - 14.907' (7) TABLE V. EQUILIBRIUM AND INTEGRATION COXSTANTS OF EQUATION 7 OBSERVER
TEMP. 0
c.
800 800 800 810 850 850 900 900 915 950 950 1000
Becker Rhead and Wheeler Becker Jellinek and Diethelm Rhead and Wheeler Becker Rhead and Wheeler Jellinek and Diethelm Rhead and Wheeler Rhead and Wheeler
1000
1050 1100
K
E
P*CO/PCO~
6.11 5.30 5.38 6.32 13.3 15.1 28.0 34.2 51.0 58.8 63.5 112 122 220 389 Average
gated by Meyer and Henseling (24),Neumann and Jacob (27), Randall and Gerard (sa), and Pease and Chesebro (29). The free energy equation for this reaction is obtained by combining Equations 5, 9, and 10. COZ
-14.90 -14.63 -14.65 -14.62 -14.76 -15.03 -14.73 -15.12 -15.49 -14.80 -14.95 -14.80 -14.96 -14.96 -15.01 - 14.90
TEMP. O
1052 1080 1177 1224 1123 1273 1373 1473 1573 1673 1773
+ 2Hz CHa; AF" = -15,320 + 11.00Tln T + 0.50 X T 3 + I T (10) =
Equilibrium in this reaction has recently been investigated by Randall and Mohammad (3s) who also give a review of the earlier data. There is very little agreement among the various investigators of this equilibrium, and the results of Randall and Mohammad do not contribute to the removal of the uncertainty. It is well known that in the producer gas reaction the various forms of carbon give rise to slightly different equilibria, and Pring and Fairlie (30) found similar effects in the synthesis of methane. Randall and Mohammad deliberately deposited carbon upon their catalyzed graphite, and it seems probable that their equilibrium constants are those corresponding to deposited carbon rather than to graphite as the reactive solid phase. Their average results are included in Table VI but are given no weight in determining the integration constant. Of the many investigators who have studied the equilibrium in the direct synthesis of methane, only Pring and Fairlie (30) and Coward and Wilson (4)have obtained thoroughly consistent results. Their data are reproduced in part in Table VI with the corresponding integration constant of Equation 10. From the average of these two sets of data, Tve find as a tentative value for the integration constant, I l 0 = -50.7. Equilibrium conditions in the formation of methane and water from carbon dioxide and hydrogen have been investi-
Randall and Mohammad Randall and Mohammad Randall and Mohammad Randall and Mohammad Coward and Wilson Coward and Wilson Coward and Wilson Pring and Fairlie Pring and Fairlie Pring and Fairlie Pring and Fairlie
-
PCHJP~HZ
-I10
0.123 0.089 0.044 0.040 0.026 0.011 0.006
52.2 52.1 52.4 52.9 50.5 51.1 51.1 50.4 50.4 50.3 50.7 50.7
0.0024
0.0015 0 00094 0.00077 Average
TABLEVII. EQUILIBRIUM CONSTANT OF EQUATION 11 AND CORRESPONDINQ INTEGRATION COXSTANT OF EQUATION 10 K. 648 650 665.6 681 696 709 765 773 778
+
0.0058T2
K
OBSERVIDR
K.
T~MP.
FREEENERQY OF METHANE The equation for the direct synthesis of methane from its elements and the accompanying free energy change (Equation 4) is as ,follows: C(graphite)
+ 2H20(g); AF" = -35,350 + 16.20T + 0.45 X 10-6TT3f (110- 12.36)T (11)
TABLEVI. EQUILIBRIUM IN DIRECTSYNTHESIS OF METHASE
I
FREHEKERGY OF OXIDESOF CARBOS
+
+
4Hz = CHI In T - 0.0070T1
The logarithms of the equilibrium constants and the corresponding values of Ilo, the integration constant of Equation 10, are given in Table VII. The results of Randall and Gerard a t the lower temperatures are discarded. I n determining the average, each observer (rather than each value recorded) is given equal weight.
The equations obtained above (5, 6, and 7) may now be combined so as to yield expressions for the standard free energy of carbon monoxide and carbon dioxide. The resulting equations are: C + 1/z02 = CO; AF' = -27,070 - 2.05TIn T 0.00225T2 0.20 X 10-8 T 3 - 7.92T (8) C 02 = COz; AF' = -94,210 f 0.30T In T - 0.0003T2 0.05 X 1 0 - 6 T 3 - 0.942' (9)
+
VoI. 24, No. 9
LOOK
OBSERVER Randall and Gerard Randall and Gerard Randall and Gerard Meyer and Henseling Randall and Gerard Neumann and Jacob Meyer and Henseling Neumann and Jacob Pease and Chesebro
-110
3.606 3,590 3.278 3.131 2.670 2.644 1.695 1.580 1.432 Average
50.12 50.25 50.37 51.17 50.46 51.46 51.66 51.72 51.42 51.2
One other reaction remains to be considered-namely, the formation of methane and water from carbon monoxide and hydrogen. Equilibrium in this reaction was determined by Neumann and Jacob (27),whose results are shown in Table VIII. The free energy equation, obtained by combining Equations 5 , 8, and 10, is: GO
+ 3H2 = CH4+ H20; AF' = -45,370 + 15.8OTln T 0.0088T2 + 0.70 X 10-6T3+ + 1.27)T (12) (110
TABLEVIII. EQUILIBRIUM CONSTANT OF EQUATION 12 AND CORRESPONDINQ INTEGRATION CONSTANT OF EQUATION 10 TEMP.
Loo K
-110
K. 1133 1173 1213 1253 1307 1325
-2.369 -2.745 -3.091 -3.451 -4.061 -4.306
52.3 52.2 52.2 51.9 50.9 50.4 51.8
O
Average
There is a marked trend in the values of Ilo obtained from reactions 11 and 12. Such a trend in the integration constant may be due to the use of erroneous thermal data, to experimental inaccuracy, or to the effect of chemical reactions other than the one under investigation. Randall (32, 33) and his associates believed that the accepted value for the heat of formation of methane was a t fault and found that "complete agreement" between their two sets of data could be obtained by employing a calculated value for the heat of the reaction. Since the publication of Rossini's accurate determinations, this position is no longer tenable. Moreover, it seems highly improbable that any of the specific heat equations are sufficiently in error to account for the large variations observed within relatively narrow temperature ranges. It will
September, 1932
INDUSTRIAL AND ENGINEERING CHEMISTRY
be noted in Table VI1 that the trend is toward higher values of 110 a t the higher temperatures: whereas in Table VI11 the tendency is in the opposite direction. Neumann and Jacob found that their equilibrium measurements were complicated by secondary reactions. In the case of reaction 11 the side reactions were less disturbing a t the lower temperatures, whereas in reaction 12 they were less prominent at the higher temperatures. This should lead us to attach greater weight to the low temperature values of Table VI1 and to the high temperature results of Table VIII. Such weighing would in both cases reduce the average value of 110,bringing it more nearly into accord with the direct values of Table VI. Perhaps the most accurate method of obtaining the free energy of methane is that based upon the third law of thermodynamics. Recent calculations, based upon spectroscopic data, by Giauque, Blue, and Overstreet (16) and by Villars (42) have established the entropy of methane with greater accuracy than had previously been obtained by Storch (40) from thermal data. Their results have been recalculated by MacDougall (22) whose value (44.46 units for the thirdlaw entropy of methane a t 298.1' K.) will be used in the present calculations. The corresponding value for the entropy of hydrogen is that of Giauque (15)-31.23 units. The entropy of graphite, according to Rodebush (36) is 1.39 units. The entropy change attending the formation of methane from its elements a t 298.1' K. is, on the basis of the above figures, - 19.39 units. The heat of formation of methane from graphite and .~ calories. hydrogen has been found to be A H ~ Q=~ -18,110 The standard free energy of methane is therefore: AFo2ss.l = AH - TAS" = -12,330 calories
1017
The discrepancies among the free energy values given for water vapor are small and are due entirely to the different subsidiary data employed in the calculations, including heat of formation and heat capacity. On the other hand, the differences between the various values for the oxides of carbon are due to the use of fundamentally different equilibrium data in the treatment of the water gas and producer gas reactions. I n evaluating the difference between the free energy of carbon monoxide and that of carbon dioxide, the results of the new calculations are in much better agreement with the original equations of Lewis and Randall than with those of Eastman. I n the case of methane the present values are in complete disagreement with those of Randall and his eo-workers. The agreement with the original equation of Lewis and Randall is sufficient guarantee that the new values are in accord with best of the older data. LITERATURE CITED Becker, M. L., J. Iron Steel I n s t . (London), 121, 337 (1930). Bryant, IT. M. D., IND.ENQ.CHEM.,23, 1019 (1931). Chopin, M., Compt. rend.. 188. 1660 (1929). Coward, H. F., and Wilson, S. P., J. Chem. SOC.,1919, 1380. Dent, F. J., and Cobb, J. W., Ibid., 1929, 1903. Eastman, E. D., J. Am. Chem. SOC.,44, 975 (1922). Eastman, E. D., Bur. Mines, Tech. P a p e r 445 (1929). Eastman, E. D., Bur. Mines, I n f o r m a l i o n Circ. 6125 (1929). Eastman, E. D., Ibid., 6337 (1930). Eastman, E. D., and Evans, R. M., J. Am. Chem. Soc., 46, 888 (19241.
Emmett, P. H., and Shults J. F., Ibid., 51, 3249 (1929), Emmett, P. H., and Shultz, J . F., I h i d , 52, 1782 (1930). Emmett, P. H., and Shults, J. F., Ibid., 52, 4265 (1930). Eucken, 4.,and Liide, K. V., Z. physik. Chem., Abt. B, 5, 413 (1929).
Substitution of this figure in Equation 10 leads to the valueIlo = -50.94. This third-law value is in agreement with the mean of the two values of 110 found in Tables VI and VII, and is well within the experimental errors of the data represented in Table VIII. It appears that the uncertainty regarding the free energy of methane has been reduced from several entropy units to a few tenths of a unit. The third-law value, 110 = -50.94, is considered the best obtainable a t the present time, and Equation 10 is rewritten: C(grrtphite)
+ 2H2 = C H a ; AF" = -15,320 + 11.00Tln T + x 1 0 - 6 ~ 3- 5 0 . 9 4 ~ (10)
O . O O ~ ~ T0.50 *
SUMMARY OF FREEENERQY VALUES The net results of the present calculations are expressed in Equations 5, 8, 9, and 10. I n order to compare these equations with those previously in use, the standard free energies a t three standard temperatures are given in Table IX. The values ascribed to Eastman ( 8 ) are obtained from his approximate equations, whose range of applicability includes the three temperatures considered. VALUES TABLEIx. COMPARISON O F FREEENERGY
OBSERVER
FREEENERGY VALWEE. 298.1' K. 1200' K . 1873' K . W A T E R VAPOR
Lewis and Randall Eastman Chipman
-42970 -42800 -42780
-33440 -33448 -33390
-51985 -50370 -51120
-66080 -63370 -64270
-94260 -93647 -94010
-94240 -91490 -93130
-94200 -89720 -92450
METHANE
+ 2470
-54507 -54465 -54500 CARBON MONOXIDE
Lewis and Randall Eastman Chipman
-32510 -32265 -32720
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CARBON DIOXIDE
Lewis and Randall Eastman Chipman Lewis and Randall Randall and Mohammad Storch Chipman
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+IlG 9670
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RECEIVED April 15, 1932 This paper presents t h e first or a series of calculations on the free energy of substancea which are of importance in the manufacture of steel. These thermodynamic studiea constitute a part of a program of research on steel-making pra::ice w h i c h is being carried on b y University of Michifan in cnhperation uith t h e Timken Steel and Tube Company.
