\(\mathrm{FeO}(\mathrm{s})+\mathrm{C}_{\text {(graphite) }} \rightarrow \mathrm{Fe}(\mathrm{s})+\mathrm{CO}(\mathrm{g}) \)
\(\Delta \mathrm{H}_{\text {reaction }}^{\circ}=\Delta \mathrm{H}_{\text {ffrpoduac) }}^{{ }^{\circ}}-\Delta \mathrm{H}_{\text {ffrectants) }}^s \)
\( =\left[\Delta \mathrm{H}_{\mathrm{f}(\mathrm{Fe})}+\Delta \mathrm{H}_{\mathrm{f}(\mathrm{CO})}\right]-\left[\Delta \mathrm{H}_{\mathrm{f}(\mathrm{Fe})}^{\circ}-\Delta \mathrm{H}_{\mathrm{f}(\mathrm{C})}\right] \)
\(=[0+(-110.5)]-[-266.3-0]\)
\(=156 \mathrm{~kJ}^{-1} \mathrm{~mol}^{-1} \)
\(\Delta \mathrm{S}_{\text {reaction }}^{\circ}=\Delta \mathrm{S}_{\text {product }}^{\circ}-\Delta \mathrm{S}_{\text {reactant }}^{\circ}\)
\(=\left[\Delta \mathrm{S}_{(\mathrm{Fe})}^{\circ}+\Delta \mathrm{S}_{(\mathrm{CO})}^{\circ}\right]-\left[\Delta \mathrm{S}_{(\mathrm{Fe} 0)}^{\circ}-\Delta \mathrm{S}^{\circ}{ }_{(0)}\right] \)
\(=[27.28+197.6]-[57.49+5.79]\)
\(=161 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\)
According to Gibb's equation,
\(\Delta \mathrm{G}^{\circ}=\Delta \mathrm{H}^{\circ}-\mathrm{T} \Delta \mathrm{S}^{\circ}\)
The reaction becomes spontaneous when \(\Delta \mathrm{G}^{\circ}\) is atleast zero or negative.
\(0=\Delta \mathrm{H}^{\circ}-\mathrm{T} \Delta \mathrm{S}^{\circ} \)
\(\mathrm{T} \Delta \mathrm{S}^{\circ}=\Delta \mathrm{H}^{\circ} \)
\(\Rightarrow \mathrm{T}=\frac{\Delta \mathrm{H}^{\circ}}{\Delta \mathrm{S}^{\circ}}=\frac{156 \mathrm{~kJ} \mathrm{~mol}^{-1}}{161 \mathrm{~J}^{-1} \mathrm{~mol}^{-1}} \)
\(=\frac{156000 \mathrm{~mol}^{-1}}{161 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}}=964 \mathrm{~K}\)
The temperature at which reaction becomes spontaneous is 964 K.