# Explain why the reaction CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(g) is spontaneous at all temperatures, using both entropy and enthalpy considerations.

> IB DP Chemistry Higher Level (2023 syllabus) — R1.4 Entropy and spontaneity (HL only) · Explain · 4 marks

## Mark scheme (4 marks)

1. The reaction is highly exothermic (ΔH° is large and negative / releases energy to surroundings), so the enthalpy term favours spontaneity.
2. The entropy change of the system is positive (ΔS > 0) because the number of moles of gas increases from 3 to 3 — wait — correcting: moles of gas go from 3 mol gas reactants to 3 mol gas products, so ΔS_sys ≈ 0; however, the large negative ΔH means the entropy of the surroundings (ΔS_surr = −ΔH/T) is large and positive, favouring spontaneity.
3. ΔG = ΔH − TΔS; because ΔH is strongly negative and ΔS_total (system + surroundings) is positive, ΔG is negative at all temperatures.
4. Because ΔH is negative and ΔS_system is approximately zero (or slightly positive), the −TΔS term does not become large enough to make ΔG positive even at very high temperatures, so spontaneity is maintained across all temperatures.

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