Find K for the reaction: CH4 (g) + O2 (g) ⇌ CH2O (g) + H2O (g)

Question

Given the following equilibrium equations and their corresponding equilibrium constants:

CO2 (g) + H2O(g) ⇌ O2 (g) + CH2O (g) K1 = 6.1 x 108

CH4 (g) + 2O2 (g) ⇌ CO2 (g) + 2H2O (g) K2 = 1.2 x 1014

Find K for the reaction: CH4 (g) + O2 (g) ⇌ CH2O (g) + H2O (g)

Answer 1

Given:

i) CO₂ (g) + H₂O(g) ⇌ O₂ (g) + CH₂O (g) ... K1 = 6.1 x 10⁸

ii) CH₄ (g) + 2O₂ (g) ⇌ CO₂ (g) + 2H₂O (g) ... K2 = 1.2 x 10¹⁴

Find K for

iii) CH₄ (g) + O₂ (g) ⇌ CH₂O (g) + H₂O (g)

Procedure:

Add i and ii and combine/cancel like terms:

CO₂ (g) + H₂O(g) ⇌ O₂ (g) + CH₂O(g)

CH₄ (g) + 2O₂ (g) ⇌ CO₂ (g) + 2H₂O (g)

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CO₂(g) + H₂O(g) + CH₄(g) + 2O₂(g) <==> O₂(g) + CH₂O(g) + CO₂(g) + 2H₂O(g)

CH₄(g) + O₂(g) <==> CH₂O(g) + H₂O(g) .. this is the desired equation.

To find the K value, we must multiply the original K values as follows:

6.1x10⁸ x 1.2x10¹⁴

K = 7.3x10²²