One of the key reactions in the gasification of coal is the methanation reaction, in which methane is produced from synthesis gas—a mixture of CO and H₂.

(a) Is the equilibrium conversion of synthesis gas to methane favored at higher or lower temperatures? Higher or lower pressures?

(b) Assume you have 4.00 mol of synthesis gas with a 3 : 1 mole ratio of H₂(g) to CO(g) in a 15.0 L flask. What will be the mole fraction of CH₄(g) at equilibrium at 1000 K?

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CO(g) + 3 H₂(g) → CH4(g) + H₂O(g) A,H = -230 kJ mol-¹; Kc = 190 at 1000 K