The reaction MgO_{(s)} + C_{(s)} to Mg_{(s)} | vedclass

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Question

(C) For a reaction to be spontaneous,the Gibbs free energy change $\Delta G^o$ must be negative.The relationship is given by $\Delta G^o = \Delta H^o

Vedclass · Accepted Answer

$2480.3$

Vedclass · Answer

(C) For a reaction to be spontaneous,the Gibbs free energy change $\Delta G^o$ must be negative.The relationship is given by $\Delta G^o = \Delta H^o - T \Delta S^o$.At equilibrium,$\Delta G^o = 0$,so $T = \frac{\Delta H^o}{\Delta S^o}$.Given $\Delta H^o = 491.1 \ kJ \ mol^{-1} = 491100 \ J \ mol^{-1}$ and $\Delta S^o = 198.0 \ J \ K^{-1} \ mol^{-1}$.$T = \frac{491100 \ J \ mol^{-1}}{198.0 \ J \ K^{-1} \ mol^{-1}} = 2480.3 \ K$.Therefore,the reaction becomes spontaneous at temperatures above $2480.3 \ K$.

The reaction $MgO_{(s)} + C_{(s)} \to Mg_{(s)} + CO_{(g)}$,for which $\Delta_r H^o = +491.1 \ kJ \ mol^{-1}$ and $\Delta_r S^o = 198.0 \ J \ K^{-1} \ mol^{-1}$,is not feasible at $298 \ K$. The temperature above which the reaction will be feasible is ..... $K$.

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