Question:
For a dimerization reaction,
$2 \mathrm{~A}(\mathrm{~g}) \rightarrow \mathrm{A}_{2}(\mathrm{~g})$
at $298 \mathrm{~K}, \Delta \mathrm{U}^{\ominus},=-20 \mathrm{~kJ} \mathrm{~mol}^{-1}, \Delta \mathrm{S}^{\ominus}=-30 \mathrm{~J}$
$\mathrm{K}^{-1} \mathrm{~mol}^{-1}$, then the $\Delta \mathrm{G}^{\ominus}$ will be J
Solution:
$\Delta \mathrm{G}^{\circ}=\Delta \mathrm{H}^{\circ}-\mathrm{T} \Delta \mathrm{S}^{\circ}$
$=\left(\Delta U^{\circ}+\Delta n_{g} R T\right)-T \Delta S^{\circ}$
$\left.=\left[\{-20+(-1)) \frac{8.314}{1000} \times 298\right\}-\frac{298}{1000} \times(-30)\right] \mathrm{kJ}$
$=-13.537572 \mathrm{~kJ}$
$=-13537.57 \mathrm{Joule}$