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EEJ MAIN Chemistry QUESTION #7135
Question 1
A reaction $MgO(s) + C(s) \rightarrow Mg(s) + CO(g)$ has $\Delta_r H^{\circ} = +491.1\text{ kJ mol}^{-1}$ and $\Delta_r S^{\circ} = 198.0\text{ J K}^{-1}\text{ mol}^{-1}$. At what minimum temperature does this reaction become spontaneous?
  • $2040.5\text{ K}$
  • $1890.0\text{ K}$
  • $2480.3\text{ K}$✔️
  • $2380.5\text{ K}$
Correct Answer Explanation
A reaction becomes spontaneous when the Gibbs free energy $\Delta G < 0$. Since $\Delta G = \Delta H - T\Delta S$, the threshold temperature where $\Delta G = 0$ is $T = \frac{\Delta H}{\Delta S}$. Converting $\Delta H$ to Joules: $T = \frac{491100}{198} \approx 2480.3\text{ K}$. Above this temperature, the $T\Delta S$ term dominates, making $\Delta G$ negative.