Question

What are the thermodynamic conditions for a reaction to be spontaneous at low temperature and non-spontaneous at high temperature?

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

Hint:

If both \( \Delta H \) and \( \Delta S \) are negative, reaction is spontaneous only at low temperature.

Answer 1

The Correct Option is D

Concept: Gibbs free energy: \[ \Delta G = \Delta H - T\Delta S \] For spontaneity: \[ \Delta G<0 \]

Step 1: Analyze condition.

• At low temperature $\rightarrow$ reaction is spontaneous
• At high temperature $\rightarrow$ reaction is non-spontaneous

Step 2: Apply equation.
If \( \Delta H<0 \) and \( \Delta S<0 \):
• At low \(T\): \( \Delta G<0 \) (spontaneous)
• At high \(T\): \( \Delta G>0 \) (non-spontaneous)