In which of the following cases, the reaction is spontaneous at all temperatures ? — Thermodynamics and Thermochemistry Chemistry Question

💡 Solution & Explanation

# Spontaneity Analysis Using Gibbs Free Energy For a reaction to be spontaneous at **all temperatures**, we use: $$\Delta G = \Delta H - T\Delta S$$ **Condition for spontaneity at all temperatures:** $$\Delta G < 0 \text{ for all } T$$ This requires: - $\Delta H < 0$ (exothermic) - $\Delta S > 0$ (entropy increases) **Why this works:** - Both terms contribute negatively to $\Delta G$ - The $-T\Delta S$ term is always negative (regardless of temperature magnitude) - Since $\Delta H$ is also negative, $\Delta G$ remains negative at all $T$ values **Other cases (not spontaneous at all T):** - $\Delta H > 0, \Delta S > 0$: Spontaneous only at high $T$ - $\Delta H < 0, \Delta S < 0$: Spontaneous only at low $T$ - $\Delta H > 0, \Delta S < 0$: Never spontaneous (non-spontaneous at all $T$) **Option B must show:** An exothermic reaction ($\Delta H < 0$) with an increase in entropy ($\Delta S > 0$), making it spontaneous across all temperature ranges.