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(A) For a reaction to be spontaneous,the Gibbs free energy change $\Delta G^{\circ}$ must be less than $0$.Given the equation: $\Delta G^{\circ} = \De

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$1118$

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(A) For a reaction to be spontaneous,the Gibbs free energy change $\Delta G^{\circ}$ must be less than $0$.Given the equation: $\Delta G^{\circ} = \Delta H^{\circ} - T \Delta S^{\circ}$.At equilibrium,$\Delta G^{\circ} = 0$,so $T = \frac{\Delta H^{\circ}}{\Delta S^{\circ}}$.Given values: $\Delta H^{\circ} = 179.1 \ kJ \ mol^{-1} = 179100 \ J \ mol^{-1}$ and $\Delta S^{\circ} = 160.2 \ J \ K^{-1} \ mol^{-1}$.Substituting these values into the equation:$T = \frac{179100 \ J \ mol^{-1}}{160.2 \ J \ K^{-1} \ mol^{-1}} \approx 1117.97 \ K$.Since the reaction is endothermic and entropy increases,the reaction becomes spontaneous at temperatures above $1118 \ K$.

$\Delta_{\text{r}}H^0$	$\Delta_{\text{r}}S^0$	$\Delta_{\text{r}}G^0$	Description
$(a) (+)$	$(-)$	$(+)$	$(i) \text{ Non-spontaneous at all temperatures}$
$(b) (-)$	$(-)$	$(-)$	$(ii) \text{ Spontaneous at low temperatures}$
$(c) (-)$	$(+)$	$(-)$	$(iii) \text{ Spontaneous at all temperatures}$

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