Question

In conversion of limestone to lime,
$CaCO _{3(s)} \rightarrow CaO _{(s)}+ CO _{2(g)}$
the values of $\Delta H^{\circ}$ and $\Delta S^{\circ}$ are $+179.1\, kJ\, mol ^{-1}$ 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, temperature above which conversion of limestone to lime will be spontaneous is

• A. $1118 \,K$
• B. $1008 \,K$
• C. $1200 \,K$
• D. $845 \,K$

Answer 1

Answer: (A)

$\Delta G^{\circ}=\Delta H^{\circ}-T \Delta S^{\circ}$

For a spontaneous process, $\Delta G^{\circ} < 0$

i.e. $ \Delta H^{\circ}-T \Delta S^{\circ} < 0$

or $ \Delta H^{\circ} < T \Delta S^{\circ}$ or, $T \Delta S^{\circ} > \Delta H^{\circ}$

or $T > \frac{\Delta H^{\circ}}{\Delta S^{\circ}}$ i.e. $T > \frac{179.1 \times 1000}{160.2}$

or $T > 1117.9 K \approx 1118 K$