For a reaction $2 \mathrm{CO}(\mathrm{g})+\mathrm{O}_2(\mathrm{~g}) \rightleftharpoons 2…
For a reaction $2 \mathrm{CO}(\mathrm{g})+\mathrm{O}_2(\mathrm{~g}) \rightleftharpoons 2 \mathrm{CO}_2(\mathrm{~g})$, $\Delta_{\mathrm{r}} \mathrm{G}^0=-128 \mathrm{~kJ}$ at $300 \mathrm{~K}$. If $\Delta_{\mathrm{r}} \mathrm{S}^0$ of the reaction is $-40 \mathrm{~J} \mathrm{~K}^{-1}$, calculate $\Delta_{\mathrm{r}} \mathrm{U}$ of the reaction.
$-137.5 \mathrm{~kJ}$
$-128 \mathrm{~kJ}$
$-140 \mathrm{~kJ}$
$126.2 \mathrm{~kJ}$
Solution
$\Delta_{\mathrm{r}} \mathrm{G}^{\circ}=\Delta_{\mathrm{r}} \mathrm{H}^{\circ}-\mathrm{T} \Delta_{\mathrm{r}} \mathrm{S}^{\circ}$
or $-128=\Delta_{\mathrm{r}} \mathrm{H}^{\circ}+\left(300 \times 40 \times 10^{-3}\right)$
or $\Delta_{\mathrm{r}} \mathrm{H}^{\circ}=-140 \mathrm{~kJ}$
or $\Delta_{\mathrm{r}} \mathrm{U}^{\circ}+\Delta \mathrm{nRT}=-140$
or $\quad \Delta_{\mathrm{r}} \mathrm{U}^{\circ}=-140+\left(8.314 \times 10^{-3} \times 300\right) \quad[\because \Delta \mathrm{n}=-1]$
or $\Delta_{\mathrm{r}} \mathrm{U}^{\circ}=-140+2.5=-137.5 \mathrm{~kJ}$