Question

The most important commercial process for generating hydrogen gas is the water-gas shift reaction: CH4(g) + H2O(g) → CO(g) + 3H2(g)

a) Use tabulated thermodynamic data to find ΔG° for this reaction at the standard temperature of 25°C.

b) Now calculate ΔG°₁₁₀₀ for this process when it occurs at 1100 K.

Answer 1

a) Enthalpy of Reaction

[1ΔH_f(CO (g)) + 3ΔH_f(H2 (g))] - [1ΔH_f(CH4 (g methane)) + 1ΔH_f(H2O (g))]
[1(-110.54) + 3(0)] - [1(-74.85) + 1(-241.82)] = 206.13 kJ
206.13 kJ     (endothermic)

Entropy Change

[1ΔS_f(CO (g)) + 3ΔS_f(H2 (g))] - [1ΔS_f(CH4 (g methane)) + 1ΔS_f(H2O (g))]
[1(197.9) + 3(130.59)] - [1(186.27) + 1(188.72)] = 214.68 J/K
214.68 J/K     (increase in entropy)

Free Energy of Reaction (at 298 K)

From ΔGf° values:
[1ΔG_f(CO (g)) + 3ΔG_f(H2 (g))] - [1ΔG_f(CH4 (g methane)) + 1ΔG_f(H2O (g))]
[1(-137.28) + 3(0)] - [1(-50.84) + 1(-228.59)] = 142.15 kJ
142.15 kJ     (nonspontaneous)

From ΔG = ΔH - TΔS:
142.12 kJ     (nonspontaneous)

b)Use the equation: delta-G = -RT ln K

thus, K = e^(-delta-G/(RT))

T = 1100 K, R = 8.314J/K.mol, and value of delta-G = 142.12 kJ  

K = e^(-142120J/8.314J/K.mol x 1100 K)

    = 1.78 x 10^-7