Chemistry: Equilibrium Math Question 8

Question

The water-gas shift reaction is crucial to many industrial processes:

H₂O(g) + CO(g) ↔ H₂(g) + CO₂(g)

The equilibrium constant for this reaction is K = 3.087012 at 802.0 K. If a vessel is initially charged with 2 bar each of H₂O(g) and CO(g), what is the final equilibrium pressure of H₂(g)?

Answer 1

H₂O(g) + CO(g) ===> H₂(g) + CO₂(g)

2..............2....................0...............0.........Initial

-x...........-x..................+x............+x..........Change

2-x........2-x.................x................x..........Equilibrium

K = 3.087 = (H₂)(CO₂)/(H₂O)(CO)

3.087 = (x)(x)/(2-x)(2-x)

3.087 = x²/(4 - 4x + x²)

x² = 3.087x² -12.35x + 12.35

2.087x² -12.35x + 12.35 = 0

x = 1.27

P(H₂) = 1.27 bar