Chemistry

Chemistry

Problem

For the combustion reaction CH4(g)+2 O2(g)→CO2(g)+2 H2O(ℓ)\mathrm{CH_4(g)+2\,O_2(g)\rightarrow CO_2(g)+2\,H_2O(\ell)}, ΔS298∘=−242.6  J mol−1 K−1\Delta S^{\circ}_{298}=-242.6\;\text{J\,mol}^{-1}\,\text{K}^{-1}. Determine ΔS298∘\Delta S^{\circ}_{298} for the reaction 12 CO2(g)+H2O(ℓ)→12 CH4(g)+O2(g)\mathrm{\dfrac12\,CO_2(g)+H_2O(\ell)\rightarrow \dfrac12\,CH_4(g)+O_2(g)}.
Intuitive explanation

The key insight is recognizing that the second reaction is the reverse of the first reaction scaled by one-half. When you reverse a reaction, entropy change flips sign; when you scale coefficients, you scale ΔS°\Delta S° proportionally. So you need to reverse the sign of the given ΔS°\Delta S° and then divide by 2 to account for the halved stoichiometry.

Intuitive explanation

The key insight is recognizing that the second reaction is the reverse of the first reaction scaled by one-half. When you reverse a reaction, entropy change flips sign; when you scale coefficients, you scale ΔS°\Delta S° proportionally. So you need to reverse the sign of the given ΔS°\Delta S° and then divide by 2 to account for the halved stoichiometry.

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