(Solved): 1. The balanced equation for the combustion of hexane, the main component of gasoline, is as follo ...

1. The balanced equation for the combustion of hexane, the main component of gasoline, is as follows: \( 2 \mathrm{C}_{6} \mathrm{H}_{14}(l)+19 \mathrm{O}_{2}(g) \rightarrow 12 \mathrm{CO}_{2}(g)+14 \mathrm{H}_{2} \mathrm{O}(l) \). From the table of thermodynamic data below, calculate \( \Delta_{\mathrm{r}} G^{\circ} \) for this reaction at \( 298 \mathrm{~K} \) in two ways: a. Calculate \( \Delta_{\mathrm{r}} H^{\circ} \) and \( \Delta_{\mathrm{r}} S^{\circ} \) from the \( \Delta_{\mathrm{f}} H^{\circ} \) and \( S^{\circ} \) values, and use \( \Delta_{\mathrm{r}} G^{\circ}=\Delta_{\mathrm{r}} H^{\circ}-T \Delta_{\mathrm{r}} S^{\circ} \). b. Calculate \( \Delta_{\mathrm{r}} G^{\circ} \) directly from the \( \Delta_{\mathrm{f}} G^{\circ} \) values.