Example 16.6: Determination of \(ΔS°\)
Calculate the standard entropy change for the combustion of methanol, CH3OH:
\(\ce{2CH3OH(l)}\)\(\ce{ + }\)\(\ce{3O2(g)}\)\(\ce{->}\)\(\ce{2CO2(g)}\)\(\ce{ + }\)\(\ce{4H2O(l)}\)\(\ce{ }\)
Solution
The value of the standard entropy change is equal to the difference between the standard entropies of the products and the entropies of the reactants scaled by their stoichiometric coefficients.
\(ΔS°_{\mathrm{298}} = \sum (ν \cdot S°_{\mathrm{\ce{products},298}}) - \sum (ν \cdot S°_{\mathrm{\ce{reactants},298}})\)
\(S°_{\mathrm{\ce{H2O(l)},298}}\) \(= 70.0\ \frac{\mathrm{J}}{\mathrm{mol}\ \mathrm{K}}\)
\(S°_{\mathrm{\ce{CH3OH(l)},298}}\) \(= 126.8\ \frac{\mathrm{J}}{\mathrm{mol}\ \mathrm{K}}\)
\(S°_{\mathrm{\ce{O2(g)},298}}\) \(= 205.03\ \frac{\mathrm{J}}{\mathrm{mol}\ \mathrm{K}}\)
\(ΔS°_{\mathrm{298}}\) \(= \sum (2 \cdot S°_{\mathrm{\ce{CO2(g)},298}}, 4 \cdot S°_{\mathrm{\ce{H2O(l)},298}}) - \sum (2 \cdot S°_{\mathrm{\ce{CH3OH(l)},298}}, 3 \cdot S°_{\mathrm{\ce{O2(g)},298}})\)
\(\ \ \ =\sum (2 \cdot 213.8\ \frac{\mathrm{J}}{\mathrm{mol}\ \mathrm{K}}, 4 \cdot 70.0\ \frac{\mathrm{J}}{\mathrm{mol}\ \mathrm{K}}) - \sum (2 \cdot 126.8\ \frac{\mathrm{J}}{\mathrm{mol}\ \mathrm{K}}, 3 \cdot 205.03\ \frac{\mathrm{J}}{\mathrm{mol}\ \mathrm{K}})\)
\(\ \ \ =\sum (427.60\ \frac{\mathrm{J}}{\mathrm{mol}\ \mathrm{K}}, 280.00\ \frac{\mathrm{J}}{\mathrm{mol}\ \mathrm{K}}) - \sum (253.60\ \frac{\mathrm{J}}{\mathrm{mol}\ \mathrm{K}}, 615.090\ \frac{\mathrm{J}}{\mathrm{mol}\ \mathrm{K}})\)
\(\ \ \ =707.60\ \frac{\mathrm{J}}{\mathrm{mol}\ \mathrm{K}} - 868.69\ \frac{\mathrm{J}}{\mathrm{mol}\ \mathrm{K}}\)
\(\ \ \ =-161.1\ \frac{\mathrm{J}}{\mathrm{mol}\ \mathrm{K}}\)
\(\ce{ΔS°= -161.1J/mol·K}\)
Think about it: The entropy in this reaction decreases (less freedom). What would you expect for the same reaction if water as a product would form as a gas
\((S°_{\mathrm{\ce{H2O(g)},298}}\) is
188.8 J/(mol K))?
a) The entropy would increase because the number of gas particles increases
b) The entropy would increase because the number of gas particles increases
c) The entropy would increase because the number of gas particles increases
d) The entropy would increase because the number of gas particles increases