Calculate equilibria constant

Question

The following equilibria were attained at 823K:

CoO(s) + H2(g) ↔ Co(s) + H2O(g)

CoO(s) + CO(g) ↔ Co(s) + CO2(g)

Based on these equilibria, calculate the equilibrium constant for H2(g) + CO2(g) ↔ CO(g) + H2O(g) at 823K.

Answer 1

GIVEN:

(1) CoO(s) + H₂(g) <==> Co(s) + H₂O(g) K1 = [H₂O] / [H₂]

(2) CoO(s) + CO(g) <==> Co(s) + CO₂(g) K2 = [CO₂] / [CO]

TARGET EQ:

H₂(g) + CO₂(g) <==> CO(g) + H₂O(g)

PROCESS:

copy eq.1: CoO(s) + H₂(g) <==> Co(s) + H₂O(g) .. K = K1 = [H₂O] / [H₂]

reverse eq.2: Co(s) + CO₂(g) <==> CoO(s) + CO(g) .. K = 1/K2 = [CO] / [CO₂]

Add both & combine/cancel like terms:

H₂(g) + CO₂(g) <==> H₂O(g) + CO(g) = TARGET EQUATION

Keq = [H₂O] / [H₂] x [CO] / [CO₂]

Keq = [H₂O][CO] / [H₂][CO₂]

NOTE: we cannot calculate a value since we weren't given values for the original reactions.