INDUSTRIAL AND ENGINEERING CHEMISTRY
78
Vol. 18, No. 1
A Thermodynamic Consideration of the Synthetic Methanol Process' By K e n n e t h K. Kelley STANFORD UNIVERSITY, CALIF.
I
N VIEWiof the industrial importance of the synthetic production of methanol, it has appeared worth while to make a study of the reaction CO
+ 2H2
= CHaOH
from the standpoint of thermodynamics. For any reaction the free-energy change involved is of predominant importance, for it determines whether or not the reaction is thermodynamically possible and in the case of a reversible reaction enables us to locate the position of the equilibrium. I n this paper the free-energy equation for the reaction under consideration is deduced. The data on which some of the calculations are based are quite meager and so the h a 1 result is offered as a n approximation only. The symbols used throughout conform to the system of Lewis and RandalL2 The free energy of formation and the heat of formation are known for both methanol and carbon monoxide a t 298" A. CHIOH (l):AF,:, = -44,500 ca1.I AH,:, = -59,900 caL4 CO (g):AF,;, = -32,500 caL6 AH,:, = -26,150 caL6 (g)
-
gas, (I)
= liquid
Therefore, for the reaction
+
CO ( g ) 2Hz ( g ) = CHIOH (1) AF,:, = -12,000 cal. and AH& = -33,750 cal.
Since the process under consideration deals with the methanol in the gaseous state, we must now obtain the AH and AF for the vaporization process. The former is known t o be 9000 caL6 [CH30H (1) = CH30H (g): AH = 9000 cal.] .and the latter can be calculated from the equation 1J~9
as does that of methane, the value C, = 12.56 caLg at T = 350" being used to get the constant term. It is not possible to say just how much this equation may be in error. From these equations, C p for 1 mol of carbon monoxide 0.00178T1and subplus 2 mols of hydrogen equals 20.14 tracting this from the equation for the methanol,
+
AH
-
'
AH,:, = -24,750 cal.
From data given by Partington and Shilling8 the following empirical equations may be obtained for the specific heats of the substances involved in calories per mol per degree: C, = 6.65 0.00070T Hz
L F = -2c300 A F = -21,300
where I is the constant of integration. Substituting the value AF = -10,950 at T = 298" A., I is found to be -42.5, and so the free-energy equation in the final form becomes, A F = -21,800
Received November 12, 1925. "Thermodynamics," 1923. McGraw-HI11 Book Co., New York 8 Parks, J . A m . Chem. SOC.,47, 338 (1925). 4 Based on Richards' and Davis' value for heat of combustion, Ibzd., 4 2 , 1614 (1920). 8 Footnote 2, p. 576. 6 Landolt-Bornstein, Tabellen, 1923, p. 1482. 7 I b i d . . p. 1361. "Specific Heats of Gases," 1924. Ernest Benn, Ltd., London. 1
*
+ 32.2T log
T-0.00825T2-42.5T
Using this equation the free-energy change for the reaction may be calculated for any temperature and consequently the equilibrium constant K = ( P(HP 2C)H' 3 0( Hp C) O ) ,since AF = -RTln K . I n Table I several values of AF and K are tabulated. Table I
300 400 500 600 700 800 900
(PCHIOH)
AF Cals. -10,800 6,100
(PH2)' ( P C O )
- 1,150 +- 3,900
670 206 316 386 154 138 206
-I- 9,050
4-14,200
+ 19,400
X 106 X 101 X 10-2 X 10-4
X 10-6 X 10-0
x 10-7 To ascertain the extent of the methanol formation let us assume as a first approximation that the substances behave like perfect gases and that when equilibrium is reached the pressure of the hydrogen is 50 atmospheres and that of the carbon monoxide 25 atmospheres. From the mass action equation the corresponding pressure of the methanol may then be calculated. The results are tabulated in Table 11. Table I1 Tem erature
g A.
+ + + 0.000.78T 0.0183T
The equation for hydrogen reproduces the experimental values perfectly to three significant figures, and that for carbon monoxide gives a maximum deviation of 0.6 per cent. The equation for the methanol was calculated assuming that its specific heat increased with the temperature at the same rate 2
+I +f 32.2T 14.OTln T-0.00825T2 + I T log T-O.O0825T* + I T f 1 4 . 0 In T-0.00825T
A.
To obtain the free-energy change involved at other temperatures we must use the equations
-
-2yoo
- = T
where PI is 125 mm.,' the vapor pressure of the methanol .at 298" A., and PZis 760 mm. This gives CH30H (1) = CH30H (g) : AF = 1050 cal. Combining these results,
CO C, = 6.84 CH30H C, = 6.16
+
6T
AF
Temperature
AF,;, = -10,950 cal.
+
A H = -21,300-14.OT f 0.00825T2 AF -= 7 _ _ 21,300 14.0 T2 -jT 0.00825
P2
+ 2H2 ( g ) = CHsOH (g).
+
AC, = -14.0 0.0165T = AHo -14.0T 0.00825T2
f AC, dT
where AH, is the constant of integration. Substituting the value AH = -24,750 a t T = 298", AH0 is found to be -21,300 cal. and therefore a t any temperature T ,
AF=RTlnp1
CO ( 8 )
=
300 400 500 600 700 800 900
Pressure CHsOH Atmos. 4.19 X 10'2 1.29 x 108 1.98 x 106 2.41 X 10s 9G.2 8.62 1.29
This table shows that under these conditions the process would be readily workable up to a temperature of 700" A., so far as the thermodynamic considerations pertaining to this reaction are concerned. However, analogous to the Ilaber reaction, the lowest temperature at which a practically feasible reaction rate can be obtained is desirable. A recent publicationlo gives some experimental results of Patart which indicate the best conditions to be 150 atmospheres total pressure and 600" to 900' A. temperature. 9
10
Stevens, A n n . p h y s . , 7, 286 (1902).
Lormand, THISJOURNAL, 17, 430 (1925).
