Thermodynamics and Thermochemistry - Result Question 86
####11. The reaction, $\operatorname{MgO}(s)+C(s) \rightarrow \operatorname{Mg}(s)+CO(g)$,
for which $\Delta _r H^{\circ}=+491.1 kJ mol^{-1}$ and $\Delta _r S^{\circ}=198.0 JK^{-1} mol^{-1}$, is not feasible at $298 K$.
Temperature above which reaction will be feasible is
(a) $2040.5 K$
(b) $1890.0 K$
(c) $2380.5 K$
(d) $2480.3 K$
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Solution:
- According to Gibbs-Helmholtz equation,
$$ \Delta _r G^{\circ}=\Delta _r H^{\circ}-T \Delta _r S^{\circ} $$
For a reaction to be feasible (spontaneous)
$$ \begin{aligned} & \Delta _r G^{\circ}<0 \ & \Delta _r H^{\circ}-T \Delta _r S^{\circ}<0 \end{aligned} $$
Given, $\Delta _r H^{\circ}=+491.1 kJ mol^{-1}$,
$$ \Delta _r S^{\circ}=198 JK^{-1} mol^{-1} $$
$\therefore 491.1 \times 10^{3}-T \times 198<0$
$$ T>\frac{491.1 \times 10^{3}}{198}=2480.3 K $$
$\therefore$ Above $2480.3 K$ reaction will become spontaneous.
