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Standard Gibbs energy of reaction \( \left(\Delta_{\mathrm{r}} \mathrm{G}\right) \) at a certain temperature can be computed as \( \Delta_{\mathrm{r}} \mathrm{G}=\Delta_{\mathrm{r}} \mathrm{H}-\mathrm{T} . \Delta_{\mathrm{r}} \mathrm{S} \) and the change in the value of \( \Delta_{\mathrm{r}} \mathrm{H} \) and \( \Delta_{\mathrm{r}} \mathrm{S} \) for a reaction with temperature can be computed as follows:
\[
\begin{array}{r}
\Delta_{\mathrm{r}} \mathrm{H}_{\mathrm{T}_{2}}^{\circ}-\Delta_{\mathrm{r}} \mathrm{H}_{\mathrm{T}_{1}}^{\circ}=\Delta_{\mathrm{r}} \mathrm{C}_{\mathrm{p}}^{\circ}\left(\mathrm{T}_{2}-\mathrm{T}_{1}\right) \\
\Delta_{\mathrm{r}} \mathrm{S}_{\mathrm{T}_{2}}^{\circ}-\Delta_{\mathrm{r}} \mathrm{S}_{\mathrm{T}_{1}}^{\circ}=\Delta_{\mathrm{r}} \mathrm{C}_{\mathrm{p}}^{\circ} \ln \left(\frac{\mathrm{T}_{2}}{\mathrm{~T}_{1}}\right) \\
\Delta_{\mathrm{r}} \mathrm{G}=\Delta_{\mathrm{r}} \mathrm{H}-\mathrm{T} \cdot \Delta_{\mathrm{r}} \mathrm{S} \\
\text { by } \Delta_{\mathrm{r}} \mathrm{G}=-\mathrm{RT} \ln \mathrm{K}_{\text {eq. }}
\end{array}
\]
- and
- Consider the following reaction :
\( \quad \mathrm{CO}(\mathrm{g})+2 \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{CH}_{3} \mathrm{OH}(\mathrm{g}) \)
Given : \( \Delta_{\mathrm{i}} \mathrm{H} \quad\left(\mathrm{CH}_{3} \mathrm{OH}, \mathrm{g}\right)=-201 \mathrm{~kJ} / \mathrm{mol} ; \quad \Delta_{\mathrm{f}} \mathrm{H} \quad(\mathrm{CO}, \mathrm{g})=-114 \mathrm{~kJ} / \mathrm{mol} \)
\[
\begin{array}{ll}
\mathrm{S}\left(\mathrm{CH}_{3} \mathrm{OH}, \mathrm{g}\right)=240 \mathrm{~J} / \mathrm{K}-\mathrm{mol} ; & \mathrm{S}\left(\mathrm{H}_{2}, \mathrm{~g}\right)=29 \mathrm{JK}^{-1} \mathrm{~mol}^{-1} \\
\mathrm{~S}(\mathrm{CO}, \mathrm{g})=198 \mathrm{~J} / \mathrm{mol}-\mathrm{K} ; & \mathrm{C}_{\mathrm{p}, \mathrm{m}}\left(\mathrm{H}_{2}\right)=28.8 \mathrm{~J} / \mathrm{mol}-\mathrm{K} \\
\mathrm{C}_{\mathrm{p}, \mathrm{m}}(\mathrm{CO})=29.4 \mathrm{~J} / \mathrm{mol}-\mathrm{K} ; & \mathrm{C}_{\mathrm{p}, \mathrm{m}}\left(\mathrm{CH}_{3} \mathrm{OH}\right)=44 \mathrm{~J} / \mathrm{mol}-\mathrm{K}
\end{array}
\]
and
\( \ln \left(\frac{320}{300}\right)=0.06 \), all data at \( 300 \mathrm{~K} \)
\( \Delta_{\mathrm{r}} \mathrm{S} \) at \( 300 \mathrm{~K} \) for the reaction is :
- (A) \( 152.6 \) *J/K-mol
(B) \( 181.6 \mathrm{~J} / \mathrm{K}-\mathrm{mol} \)
(C) \( -16 \mathrm{~J} / \mathrm{K}-\mathrm{mol} \)
(D) none of these
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