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

💡 Solution & Explanation

I notice the question references "B" as the correct answer, but the options aren't provided in your message. Let me explain the general principle for determining spontaneity at all temperatures: ## Key Concept: Gibbs Free Energy A reaction is spontaneous at all temperatures when: $$\Delta G = \Delta H - T\Delta S < 0 \text{ at all } T$$ This requires: - $\Delta H < 0$ (exothermic) - $\Delta S > 0$ (entropy increases) **Why both conditions are essential:** $$\Delta G = \Delta H - T\Delta S$$ - If $\Delta H < 0$ and $\Delta S > 0$: Both terms favor spontaneity ($-T\Delta S$ is always negative), so $\Delta G < 0$ **at all T** ✓ - If $\Delta H > 0$ and $\Delta S < 0$: Both terms oppose spontaneity, so $\Delta G > 0$ at all T (never spontaneous) - If $\Delta H < 0$ and $\Delta S < 0$: Spontaneous only at low T - If $\Delta H > 0$ and $\Delta S > 0$: Spontaneous only at high T ## Answer **Option B** is correct if it describes a reaction that is **exothermic ($\Delta H < 0$) with an increase in entropy ($\Delta S > 0$)** — such as combustion reactions or dissolution of gases in water. To verify, confirm that the chosen reaction shows both negative $\Delta H$ and positive $\Delta S$.