21.9: Standard Entropies Can Be Used to Calculate Entropy Changes of Chemical Reactions

Entropy is a state function, so we can calculate values for a process using any path. This allows us to calculate the entropy change of a chemical reaction using standard entropies. Specifically, we sum the entropies of the products and subtract the entropies of the reactions:

\[\Delta_{rxn}S^\circ = \sum_{\text{Products}}{v_i S^\circ_i} - \sum_{\text{Reactants}}{v_i S^\circ_i} \nonumber \]

Where \(v_i\) is the stoichiometric coefficient. Let's look at the combustion of methane:

\[\ce{CH_4} \left( g \right) + 2 \ce{O_2} \left( g \right) \rightarrow 2 \ce{H_2O} + \ce{CO_2}\left(g\right) \nonumber \]

The standard entropies are:

Molecule	Entropy \(\left(\frac{\text{J}}{\text{mol}\cdot\text{K}}\right)\)
\(\ce{CH_4}\)	\(186.25^1\)
\(\ce{O_2}\)	\(205.15^1\)
\(\ce{H_2O}\)	\(188.84^1\)
\(\ce{CO_2}\)	\(213.79^1\)

The entropy for the combustion of methane is:

\[\Delta S^\circ = \left[ 2 \left( 188.84 \right) + 1 \left( 213.70 \right) \right] - \left[ 1 \left( 186.25 \right) + 2 \left( 205.15 \right) \right] = -5.17 \: \frac{\text{J}}{\text{mol} \cdot \text{K}} \nonumber \]

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