Standard Gibb's energy of reaction ($∆{\mathrm{r}}_{ }$,G°) at a certain temperature car computed and as ${\mathrm{\Delta }}_{\mathrm{T}}{\mathrm{G}}^{\circ }={\mathrm{\Delta }}_{\mathrm{\Gamma }}{\mathrm{H}}^{\circ }-\mathrm{T}\cdot {\mathrm{\Delta }}_{\mathrm{r}}{\mathrm{S}}^{\circ }$and the change in the value of ${\mathrm{\Delta }}_{\mathrm{r}}{\mathrm{H}}^{\circ }$and ${\mathrm{\Delta }}_{\mathrm{r}}{\mathrm{S}}^{\circ }$ for a reaction with temperature can be computed as follows: 

$\begin{array}{l}{\mathrm{\Delta }}_{\mathrm{r}}{\mathrm{H}}_{{\mathrm{T}}_2}^{\circ }-{\mathrm{\Delta }}_{\mathrm{r}}{\mathrm{H}}_{{\mathrm{T}}_1}^{\circ }={\mathrm{\Delta }}_{\mathrm{r}}{\mathrm{C}}_{\mathrm{p}}^{\circ }\left({\mathrm{T}}_2-{\mathrm{T}}_1\right)\\ {\mathrm{\Delta }}_{\mathrm{r}}{\mathrm{S}}_{{\mathrm{T}}_2}^{\circ }-{\mathrm{\Delta }}_{\mathrm{T}}{\mathrm{S}}_{{\mathrm{T}}_1}^{\circ }={\mathrm{\Delta }}_{\mathrm{r}}{\mathrm{C}}_{\mathrm{p}}^{\circ }\ln \left(\frac{{\mathrm{T}}_2}{{\mathrm{T}}_1}\right)\\ {\mathrm{\Delta }}_{\mathrm{r}}{\mathrm{G}}^{\circ }={\mathrm{\Delta }}_{\mathrm{r}}{\mathrm{H}}^{\circ }-\mathrm{T}\cdot {\mathrm{\Delta }}_{\mathrm{r}}{\mathrm{S}}^{\circ }\\ \text{and by }{\mathrm{\Delta }}_{-}{\mathrm{G}}^{\circ }=-\mathrm{RTln}{\mathrm{K}}_{\mathrm{eq}}.\end{array}$

Consider the following reaction: $\mathrm{CO}\left(\mathrm{g}\right)+2{\mathrm{H}}_2\left(\mathrm{g}\right)\rightleftharpoons {\mathrm{CH}}_3\mathrm{OH}\left(\mathrm{g}\right)$ 

Given :

$\begin{array}{l}{\mathrm{\Delta }}_{\mathrm{f}}{\mathrm{H}}^{\circ }\left({\mathrm{CH}}_3\mathrm{OH},\mathrm{g}\right)=-201\mathrm{kJ}/{\mathrm{mol}}^{\mathrm{\prime }};{\mathrm{\Delta }}_{\mathrm{f}}{\mathrm{H}}^{\circ }(\mathrm{CO},\mathrm{g})=-114\mathrm{kJ}/\mathrm{mol}\\ {\mathrm{S}}^{\circ }\left({\mathrm{CH}}_3\mathrm{OH},\mathrm{g}\right)=240\mathrm{J}/\mathrm{K}-\mathrm{mol};{\mathrm{S}}^{\circ }\left({\mathrm{H}}_2,\mathrm{g}\right)=29{\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1}\\ {\mathrm{S}}^{\circ }(\mathrm{CO},\mathrm{g})=198\mathrm{J}/\mathrm{mol}-\mathrm{K};{\mathrm{C}}_{\mathrm{p}}^{\circ }\mathrm{m}\left({\mathrm{H}}_2\right)=28.8\mathrm{J}/\mathrm{mol}-\mathrm{K}\\ \left.{{\mathrm{C}}^{\circ }}_{\mathrm{n}-\mathrm{m}}\left(\mathrm{CO}\right)=29.4\mathrm{J}/\mathrm{mol}-\mathrm{K};{\mathrm{C}}_{0,\mathrm{m}}^{\circ }\left({\mathrm{CH}}_3\mathrm{OH}\right)=44\mathrm{J}/\mathrm{mol}\cdot \mathrm{K}\right)\end{array}$

$\text{ and }\ln \left(\frac{320}{300}\right)=0.06\text{, all data at }300\mathrm{K}$