H2O(g)+C(s)→H2(g)+CO(g) Equilibrium Constant

A P P E N D I X

H H2O(g) 1 C(s)-H2(g) 1 CO(g) Equilibrium Constant This appendix calculates the 2000
C equilibrium constant for the reaction:


 H2 O g 1 CðsÞ-H2 g 1 CO g

COðgÞ

which gives;




 CðsÞ 1 0:5O2 g  H2 g  0:5O2 g -CO g  H2 O g

or


 CðsÞ  H2 g -CO g  H2 O g

H2 OðgÞ

or adding H2(g) and H2O(g) to both sides;


 CðsÞ 1 H2 O g -CO g 1 H2 g

(H.2)

for which the standard Gibbs free energy of formation is Δf G
2000 C 5 2308:7 MJ/kg mol of COðgÞ CO(g) and;

for which; Δr G


5 Δf G
2000
C 2000
C

 CðsÞ1H2 O g !CO g 1H2 ðgÞ COðgÞ







 H2 g 1 0:5O2 g -H2 O g

(H.3)

for which the standard Gibbs free energy of formation is Δf G
2000 C 5 2119:6 MJ/kg mol of H OðgÞ H2O(g). Reaction (H.1) is made up from these formation reactions by subtracting Reaction (H.3) from Reaction (H.2) that is;

2 Δf G
2000
C H2 OðgÞ

5 2 308:7  ð119:6Þ 5 2 189:1 MJ=kg mol of H2 (H.4)




2




 H2 g 1 0:5O2 g -H2 O g




These published values are for the formation reactions;

 CðsÞ 1 0:5O2 g -CO g

minus

(H.1)

Appendix G then uses this equilibrium constant to show that raceway exit gas contains very little H2O(g). The equilibrium constant is calculated from published values1 of Δf G
2000 C and Δf G
2000 C .




 CðsÞ 1 0:5O2 g -CO g

The


Δr G

693

equilibrium



2000  C
 CðsÞ1H2 O g -CO g 1H2 ðgÞ

constant value is;

with

this

694

APPENDIX H: H2O(g) 1 C(s)-H2(g) 1 CO(g) EQUILIBRIUM CONSTANT

8  >
> > < 2 Δr G

2000
C

 CðsÞ1H2 O g -CO g 1H2 ðgÞ

CðsÞ1H2 OðgÞ-COðgÞ1H2 ðgÞ KE; 2000
C



> > > : 5e

ð 2ð2189:1ÞÞ 5 e ð0:008314  2273:15ðKÞÞ

R  2273:15ðKÞ

9 > > > = > > > ;

2273.15 is the temperature (K) that is equivalent to 2000
C.

Reference

 5 2:2 3 10

4

where R is the gas constant, 0.008314 MJ/ (kg mol H2)/K.

1. NIST-JANAF. NIST-JANAF [Thermochemical] tables PDF. U.S. Institute of Standards and Technology, Gaithersburg, MD; 2016. Googling the title [recovered on 13.06.16].