Assume $\Delta H$ and $\Delta S$ are independent of temperature. For $\mathrm{MgCO}{}_3(\mathrm{s})\to \mathrm{MgO}(\mathrm{s})+\mathrm{CO}{}_2(\mathrm{g})$: $\Delta H=117\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$ and $\Delta S=175\mathrm{J}{\mathrm{K}}^{-1}\mathrm{mo}{\mathrm{l}}^{-1}$. For $\mathrm{CaCO}{}_3(\mathrm{s})\to \mathrm{CaO}(\mathrm{s})+\mathrm{CO}{}_2(\mathrm{g})$: $\Delta H=178\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$ and $\Delta S=165\mathrm{J}{\mathrm{K}}^{-1}\mathrm{mo}{\mathrm{l}}^{-1}$. The decomposition temperature is taken as the temperature at which $\Delta G^{\circ }=0$. How much higher is the decomposition temperature of $\mathrm{CaCO}{}_3$ than that of $\mathrm{MgCO}{}_3$?

1. Aabout $370\mathrm{K}$
2. Babout $669\mathrm{K}$
3. Cabout $1079\mathrm{K}$
4. Dabout $410\mathrm{K}$