In conversion of lime-stone to lime, CaCO3(s)⟶CaO(s)+CO2(g) he values of ΔH∘ and ΔS∘ are 179.1kJmol-1 and 160.2JK−1mol−1 respectively at 298 K and 1 bar. Assuming that ΔH∘and ΔS∘do not change with temperature, temperature above which conversion of limestone to lime will be spontaneous is

In conversion of lime-stone to lime, ${CaCO}_{3} (s) ⟶ CaO (s) + {CO}_{2} (g)$ he values of $Δ H^{\circ}$ and $Δ S^{\circ}$ are $179.1 {kJmol}^{- 1}$ and $160.2 {JK}^{- 1} {mol}^{- 1}$ respectively at 298 K and 1 bar. Assuming that $Δ H^{\circ}$ and $Δ S^{\circ}$ do not change with temperature, temperature above which conversion of limestone to lime will be spontaneous is

A
$1008 K$
B
$1200 K$
C
$845 K$
D
$1118 K$

Solution:

The temperature at which given reaction exists as equilibrium is

$T_{eq} = \frac{Δ H^{\circ}}{Δ S^{\circ}} = \frac{179.1 \times 10^{3} {mol}^{- 1}}{160.2 {JK}^{- 1} {mol}^{- 1}} = 1118 K$

At $T > T_{eq}, Δ G^{\circ}$ of the reaction will be negative and hence the given reaction will be spontaneous.

Solution:

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