For a dimerization reaction, $2 A_{(g)} \rightarrow A_{2(\mathrm{~g})}$, at $298 \mathrm{~K}, \Delta

Question

For a dimerization reaction, $2 A_{(g)} ightarrow A_{2(\mathrm{~g})}$, at $298 \mathrm{~K}, \Delta U^{\circ}=-20 \mathrm{~kJ} \mathrm{~mol}^{-1}, \Delta S^{\circ}=-30 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$, then the $\Delta G^{\circ}$ will be $\qquad$ J.(Rounded off to nearest integer)\

Professor PC Thomas Classes · Answer

$(-13538): \Delta H^{\mathrm{o}}=\Delta U^{\mathrm{o}}+\Delta n_{g} R T$ As $\Delta n_{g}=(1-2)=-1$\ $	herefore \quad \Delta H=-20 	imes 1000 \mathrm{~J} \mathrm{~mol}^{-1}+((-1) 	imes$\ $\left.8.314 \mathrm{JK}^{-1} \mathrm{~mol}^{-1} 	imes 298 \mathrm{~K}ight)$\ $=-22477.572 \mathrm{~J} \mathrm{~mol}^{-1}$\ $\Delta G^{\circ}=\Delta H^{\circ}-T \Delta S^{\circ}$\ $=-22477.572-(298 \mathrm{~K}) 	imes\left(-30 \mathrm{Jmol}^{-1} \mathrm{~K}^{-1}ight)$\ $=-13537.572 \mathrm{~J} \mathrm{~mol}^{-1} \simeq-13538 \mathrm{~J} \mathrm{~mol}^{-1}$\