Question

Which of the following conditions are not suitable for a spontaneous reaction?

• A. \(\Delta H\lt 0\) and \(\Delta S\gt 0\) at low temperature
• B. \(\Delta H\lt 0\) and \(\Delta S\lt 0\) at high temperature
• C. \(\Delta H\lt 0\) and \(\Delta S\lt 0\) at low temperature
• D. \(\Delta H\gt 0\) and \(\Delta S\gt 0\) at high temperature

Hint:

Remember the spontaneity criterion: \[ \Delta G=\Delta H-T\Delta S. \] \[ \Delta H\lt 0,\ \Delta S\gt 0 \] is spontaneous at all temperatures. \[ \Delta H\gt 0,\ \Delta S\lt 0 \] is never spontaneous. \[ \Delta H\lt 0,\ \Delta S\lt 0 \] is spontaneous only at low temperature. \[ \Delta H\gt 0,\ \Delta S\gt 0 \] is spontaneous only at high temperature.

Answer 1

The Correct Option is B

Step 1: Recall the criterion for spontaneity.
A reaction is spontaneous when the Gibbs free energy change is negative. \[ \Delta G=\Delta H-T\Delta S \] For spontaneity, \[ \Delta G\lt 0 \]

Step 2: Analyze Option (1).
Given, \[ \Delta H\lt 0,\qquad \Delta S\gt 0 \] Therefore, \[ \Delta G=\Delta H-T\Delta S \] Both terms contribute negatively. Hence, \[ \Delta G\lt 0 \] at all temperatures.
So, this condition is suitable for spontaneity.

Step 3: Analyze Option (2).
Given, \[ \Delta H\lt 0,\qquad \Delta S\lt 0 \] Then, \[ \Delta G=\Delta H+T|\Delta S| \] At high temperature, the positive term \[ T|\Delta S| \] becomes very large and can exceed \(|\Delta H|\). Hence, \[ \Delta G\gt 0 \] at high temperature.
Therefore, the reaction is not spontaneous under this condition.

Step 4: Analyze Option (3).
Given, \[ \Delta H\lt 0,\qquad \Delta S\lt 0 \] At low temperature, \[ T|\Delta S| \] is small. Thus, the negative \(\Delta H\) term dominates and \[ \Delta G\lt 0 \] Hence, the reaction can be spontaneous at low temperature.

Step 5: Analyze Option (4).
Given, \[ \Delta H\gt 0,\qquad \Delta S\gt 0 \] Then, \[ \Delta G=\Delta H-T\Delta S \] At high temperature, the term \[ T\Delta S \] becomes large and may exceed \(\Delta H\). Thus, \[ \Delta G\lt 0 \] and the reaction becomes spontaneous.

Step 6: Final conclusion.
The condition that is not suitable for a spontaneous reaction is \[ \boxed{\Delta H\lt 0 \text{ and } \Delta S\lt 0 \text{ at high temperature}} \] Hence, the correct option is \[ \boxed{(2)} \]