Question

A reaction is spontaneous at low temperature, but non-spontaneous at high temperature. Which of the following conditions is true for the chemical reaction?

• A. \(\Delta H < 0, \Delta S < 0\)
• B. \(\Delta H > 0, \Delta S = 0\)
• C. \(\Delta H < 0, \Delta S > 0\)
• D. \(\Delta H > 0, \Delta S > 0\)

Hint:

If a reaction is spontaneous only at low temperatures, it is exothermic (\(\Delta H<0\)) and accompanied by a decrease in entropy (\(\Delta S<0\)).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The spontaneity of a reaction is determined by the Gibbs free energy equation: \(\Delta G = \Delta H - T\Delta S\). A reaction is spontaneous when \(\Delta G < 0\).

Step 2: Detailed Explanation:
Given: Spontaneous at low T, non-spontaneous at high T. • For \(\Delta G\) to be negative at low T and positive at high T, \(\Delta H\) must be negative (exothermic) and \(\Delta S\) must be negative (decrease in entropy). • At low T: \(\Delta G = (-) - T(-) = (-) + T|S|\). For low T, the T\(\Delta S\) term is small, so \(\Delta G\) is negative. • At high T: The T\(\Delta S\) term becomes large and positive, making \(\Delta G\) positive. This matches option (A).

Step 3: Final Answer:
The correct condition is \(\Delta H < 0, \Delta S < 0\), which corresponds to option (A).