Thermodynamics and Thermochemistry - Result Question 11
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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Answer:
Correct Answer: 11. (d)
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.
BETA
