Chemistry

Problem

Consider the combustion of methane carried out in two different ways. Reaction A:

\text{CH}_4\,(g) + 2\,\text{O}_2\,(g) \rightarrow \text{CO}_2\,(g) + 2\,\text{H}_2\text{O}\,(l)

Reaction B:

\text{CH}_4\,(g) + 2\,\text{O}_2\,(g) \rightarrow \text{CO}_2\,(g) + 2\,\text{H}_2\text{O}\,(g)

Absolute molar entropies at 298 K are provided.

Substance	$S^\circ$ (J mol $^{-1}$ K $^{-1}$ )
$\text{CH}_4\,(g)$	186
$\text{O}_2\,(g)$	205
$\text{CO}_2\,(g)$	214
$\text{H}_2\text{O}\,(l)$	70
$\text{H}_2\text{O}\,(g)$	189

(a) Calculate

\Delta S^\circ_{298}

for Reaction A. (b) Calculate

\Delta S^\circ_{298}

for Reaction B. (c) Quantitatively determine by how much (in J mol

^{-1}

^{-1}

) the entropy change differs between the two reactions and account for the difference in terms of the physical states of the products. (d) Discuss how the sign and magnitude of

\Delta S^\circ

for Reaction A could influence the minimum temperature required for the combustion to be thermodynamically favorable.

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