Question 19.5: Calculating ΔG° from Standard Free Energies of Formation Cal...
Calculating \Delta G^{\circ} from Standard Free Energies of Formation
Calculate \Delta G^{\circ} for the combustion of 1 \mathrm{~mol} of ethanol, \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}, at 25^{\circ} \mathrm{C}.
\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)+3 \mathrm{H}_{2} \mathrm{O}(g)
Use the standard free energies of formation given in Table 19.2.
PROBLEM STRATEGY
Calculate \Delta G^{\circ} from \Delta G_{f}^{\circ} values, similar to the way you calculate \Delta H^{\circ} from \Delta H_{f}^{\circ}.
Write the balanced equation with values of \Delta G_{f}^{\circ} multiplied by stoichiometric coefficients below each formula.
\begin{aligned} & \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)+3 \mathrm{H}_{2} \mathrm{O}(g) \\ & \begin{array}{lllll} \Delta G_{f}^{\circ}: & -174.9 & 0 & 2(-394.4) & 3(-228.6) \mathrm{kJ} \end{array} \end{aligned}
The calculation is
\begin{aligned} \Delta G^{\circ} & \left.=\Sigma n \Delta G_{f}^{\circ} \text { (products }\right)-\sum m \Delta G_{f}^{\circ}(\text { reactants }) \\ & =[2(-394.4)+3(-228.6)-(-174.9)] \mathrm{kJ} \\ & =\mathbf{- 1 2 9 9 . 7} \mathbf{k J} \end{aligned}