Question

Calculate ΔG⁰ for the reaction

\[\ce{CH_{4(g)} + H_{2(g)}-> C2H_{6(g)}}\]

State whether the reaction is spontaneous or not. (Given: K_P = 3.358 × 10¹⁷, T = 25° C, R = 8.314 × 10⁻³ kJK⁻¹ moI⁻¹)

Answer 1

\[\ce{CH_{4(g)} + H_{2(g)}-> C2H_{6(g)}}\]

Given: K_P = 3.358 × 10¹⁷, T = 25° C = 298 K

= R = 8.314 × 10⁻³ kJK⁻¹ moI⁻¹

∵ ΔG⁰ = − 2.303 RTlog₁₀ K_P

∴ ΔG⁰ = − 2.303 × 8.314 × 10⁻³ × 298 × log₁₀ (3.358 × 10¹⁷)

= − 2.303 × 8.314 × 10⁻³ × 298 × 17.526

ΔG⁰ = − 100 kJ mol⁻¹

The value of ΔG⁰ is negative, i.e. decreasing.

Hence the reaction is spontaneous.