Question

In conversion of limestone to lime,
$CaC{O}_{3(s)}\to Ca{O}_{(s)}+C{O}_{2(g)}$
the values of $\Delta H^{\circ }$ and $\Delta S^{\circ }$ are $+179.1kJmo{l}^{-1}$ and $160.2J/K$ respectively at $298K$ 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. $1118K$
• B. $1008K$
• C. $1200K$
• D. $845K$

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 $T>1117.9K\approx 1118K$