Question

The enthalpy change for a given reaction at 298 K is \( -x \, \text{J mol}^{-1} \). For the reaction to be spontaneous at 298 K, the entropy change at that temperature

• A. can be negative, but numerically greater than \( x/298 \)
• B. can be negative, but numerically smaller than \( x/298 \)
• C. cannot be negative
• D. can be positive

Hint:

For spontaneity, the Gibbs free energy must be negative. Entropy change must balance the enthalpy change for this condition to be met.

Answer 1

The Correct Option is A

Step 1: Gibbs Free Energy.
For the reaction to be spontaneous, \( \Delta G = \Delta H - T \Delta S \) must be negative. If \( \Delta H \) is negative, then \( \Delta S \) must be positive or sufficiently large negative to ensure spontaneity. Thus, the entropy change can be negative but must be numerically greater than \( x/298 \).
Step 2: Conclusion.
The correct answer is (A), can be negative, but numerically greater than \( x/298 \).