Tin is obtained from cassiterite by reduction with coke. Use the data given below to determine the m

Question

Tin is obtained from cassiterite by reduction with coke. Use the data given below to determine the minimum temperature (in K ) at which the reduction of cassiterite by coke would take place.\ At $298 \mathrm{~K}: \Delta_{f} H^{\circ}\left(\mathrm{SnO}_{2(s)}ight)=-581.0 \mathrm{~kJ} \mathrm{~mol}^{-1}$, $\Delta_{f} H^{\circ}\left(\mathrm{CO}_{2(\mathrm{~g})}ight)=-394.0 \mathrm{~kJ} \mathrm{~mol}^{-1}$, $S^{\circ}\left(\mathrm{SnO}_{2(\mathrm{~s})}ight)=56.0 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$, $S^{\circ}\left(\mathrm{Sn}_{(s)}ight)=52.0 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}, S^{\circ}\left(\mathrm{C}_{(s)}ight)=6.0 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$, $S^{\circ}\left(\mathrm{CO}_{2(\mathrm{~g})}ight)=210.0 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$.\ Assume that the enthalpies and the entropies are temperature independent.\

Professor PC Thomas Classes · Answer

(935): $\mathrm{SnO}_{2(s)}+\mathrm{C}_{(s)} ightarrow \mathrm{Sn}_{(s)}+\mathrm{CO}_{2(g)}$ From the given data,\ $\Delta_{r} H^{\circ}=\Delta H_{	ext {products }}^{\circ}-\Delta H^{\circ}$ reactants\ $\Delta_{r} H^{\circ}=-394.0+581.0=187 \mathrm{~kJ} / \mathrm{mol}$\ $\Delta_{r} S^{\circ}=52+210-56-6=200 \mathrm{~J} / \mathrm{K} \mathrm{mol}$\ Minimum temperature at which\ reaction will take place,\ $T=\frac{\Delta_{r} H^{\circ}}{\Delta_{r} S^{\circ}}=\frac{187 	imes 1000}{200}=935 \mathrm{~K}$