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# The following equation shows the conversion of limes stone to lime $CaCO_3(s)\longrightarrow CaO(s) + CO_2(g)$. The values of $\Delta H^\circ$ and $\Delta S^\circ$ are $+179.1\; kJ$ and $160.2\; J/K$ respectively at $298\; K$ and $1\; bar$. Assuming that $\Delta H^\circ$ and $\Delta S^\circ$ do not change with temperature, minimum temperature above which conversion of lime stone to lime will be spontaneous is

(a) 1118 K
(b) 1008 K
(c) 1200 K
(d) 845 K

$\Delta G^\circ = \Delta H^\circ - T \Delta S^\circ$
Since, $\Delta H^\circ$ is +ve and $T\Delta S$ is also +ve, for $\Delta G^\circ$ to be -ve.
$T\Delta S^\circ > \Delta H^\circ i.e., T > \frac{\Delta H^\circ}{\Delta S^\circ}$
i.e., $\frac{179100 J}{160.2J/K} > 1118$ K