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Standard Gibbs energy of reaction \( \left(\Delta_{r} G\right) \) at a certain temperature can be computed as \( \Delta_{r} G=\Delta_{r} H-T \). \( \Delta_{r} S \) and the change in the value of \( \Delta_{r} H \) and \( \Delta_{r} S \) for a reaction with temperature can be computed as follows :
\[
\begin{array}{r}
\Delta_{r} H_{T_{2}}^{\circ}-\Delta_{r} H_{T_{1}}^{\circ}=\Delta_{r} C_{p}^{0}\left(T_{2}-T_{1}\right) \\
\Delta_{r} S_{T_{2}}^{0}-\Delta_{r} S_{T_{1}}^{\circ}=\Delta_{r} C_{p}^{\circ} \ln \left(\frac{T_{2}}{T_{1}}\right) \\
\Delta_{r} G=\Delta_{r} H-T \cdot \Delta_{r} S \\
\Delta_{r} G=-R T \ln K_{\text {eq. }}
\end{array}
\]
- and
- Consider the following reaction :
\[
\mathrm{CO}(\mathrm{g})+2 \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{CH}_{3} \mathrm{OH}(\mathrm{g})
\]
Given : \( \Delta_{\mathrm{f}} \mathrm{H} \quad\left(\mathrm{CH}_{3} \mathrm{OH}, \mathrm{g}\right)=-201 \mathrm{~kJ} / \mathrm{mol} ; \quad \Delta_{\mathrm{f}} \mathrm{H} \quad(\mathrm{CO}, \mathrm{g})=-114 \mathrm{~kJ} / \mathrm{mol} \)
\[
\begin{array}{ll}
\mathrm{S}\left(\mathrm{CH}_{3} \mathrm{OH}, \mathrm{g}\right)=240 \mathrm{~J} / \mathrm{K}-\mathrm{mol} ; & \mathrm{S}\left(\mathrm{H}_{2}, \mathrm{~g}\right)=29 \mathrm{JK}^{-1} \mathrm{~mol}^{-1} \\
\mathrm{~S}(\mathrm{CO}, \mathrm{g})=198 \mathrm{~J} / \mathrm{mol}-\mathrm{K} ; & \mathrm{C}_{\mathrm{p}, \mathrm{m}}\left(\mathrm{H}_{2}\right)=28.8 \mathrm{~J} / \mathrm{mol}-\mathrm{K} \\
\mathrm{C}_{\mathrm{p}, \mathrm{m}}(\mathrm{CO})=29.4 \mathrm{~J} / \mathrm{mol}-\mathrm{K} ; & \mathrm{C}_{\mathrm{p}, \mathrm{m}}\left(\mathrm{CH}_{3} \mathrm{OH}\right)=44 \mathrm{~J} / \mathrm{mol}-\mathrm{K}
\end{array}
\]
and
\( \ln \left(\frac{320}{300}\right)=0.06 \), all data at \( 300 \mathrm{~K} \)
- \( \Delta_{\mathrm{r}} \mathrm{S} \) at \( 320 \mathrm{~K} \) is :
(A) \( 155.18 \mathrm{~J} / \mathrm{mol}-\mathrm{K} \)
(B) \( 150.02 \mathrm{~J} / \mathrm{mol}-\mathrm{K} \)
(C) \( 172 \mathrm{~J} / \mathrm{mol}-\mathrm{K} \)
(D) none of these
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