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

💡 Solution & Explanation

I need to see the options to provide a complete answer. However, I can explain the general principle for spontaneity at all temperatures. **Key Concept:** For a reaction to be spontaneous at **all temperatures**, we use the Gibbs free energy equation: $$\Delta G = \Delta H - T\Delta S$$ For spontaneity: $\Delta G < 0$ at all temperatures. **Analysis of different cases:** | Case | $\Delta H$ | $\Delta S$ | Spontaneous at all T? | |------|-----------|-----------|----------------------| | **Exothermic + Increase in entropy** | $-$ | $+$ | **YES** ✓ | | Exothermic + Decrease in entropy | $-$ | $-$ | Only at low T | | Endothermic + Increase in entropy | $+$ | $+$ | Only at high T | | Endothermic + Decrease in entropy | $+$ | $-$ | NO (never) | **For option B to be correct:** - $\Delta H < 0$ (exothermic) - $\Delta S > 0$ (entropy increases) This makes $\Delta G = (-)-(T)(+) = $ **always negative**, ensuring spontaneity at all temperatures. **Why other cases fail:** - Negative $\Delta H$, negative $\Delta S$: Spontaneous only at low T - Positive $\Delta H$, positive $\Delta S$: Spontaneous only at high T - Positive $\Delta H$, negative $\Delta S$: Never spontaneous **Answer: Option B describes a reaction that is exothermic with an increase in entropy—the only condition ensuring spontaneity at all temperatures.**