Under which combination of enthalpy change (ΔH) and entropy change (ΔS) is a chemical reaction guaranteed to be spontaneous at all temperatures?

Answer and explanation

Correct answer: C. Delta H < 0 and Delta S > 0

  1. Step 1: The criterion for spontaneity at constant temperature and pressure is given by the Gibbs-Helmholtz equation: .
  2. Step 2: For a process to be spontaneous, must be negative ().
  3. Step 3: If (negative) and (positive), then is strictly negative at any absolute temperature ().
  4. Step 4: Adding two negative terms yields a that is negative at all temperatures, ensuring unconditional spontaneity.
Answer
ΔH < 0 (exothermic) and ΔS > 0 (increase in entropy)
Why not the others: 'ΔH > 0 and ΔS < 0' yields a positive at all temperatures, meaning the reaction is non-spontaneous under all conditions; 'ΔH > 0 and ΔS > 0' is spontaneous only at high temperatures (); 'ΔH < 0 and ΔS < 0' is spontaneous only at low temperatures ().

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