Question

The signs of $\Delta H^\circ$ and $\Delta S^\circ$ for a reaction to be spontaneous at all temperatures respectively are

• A. positive, positive
• B. positive, negative
• C. negative, negative
• D. negative, positive

Hint:

A reaction is spontaneous at all temperatures if it is exothermic ($\Delta H^\circ<0$) and increases entropy ($\Delta S^\circ>0$), ensuring $\Delta G^\circ$ is always negative.

Answer 1

The Correct Option is D

Let’s break this down step by step to determine the signs of $\Delta H^\circ$ and $\Delta S^\circ$ for a reaction to be spontaneous at all temperatures and why option (4) is the correct answer.
Step 1: Understand the condition for spontaneity
The Gibbs free energy change determines spontaneity:
\[ \Delta G^\circ = \Delta H^\circ - T \Delta S^\circ \]
A reaction is spontaneous if $\Delta G^\circ<0$ at all temperatures.
Step 2: Analyze the signs of $\Delta H^\circ$ and $\Delta S^\circ$
If $\Delta H^\circ$ is negative (exothermic) and $\Delta S^\circ$ is positive (entropy increases):
\[ \Delta G^\circ = (\text{negative}) - T (\text{positive}) \]
$\Delta G^\circ$ is always negative. Other combinations don’t ensure spontaneity at all temperatures.
Step 3: Confirm the correct answer
For spontaneity at all temperatures, $\Delta H^\circ$ must be negative and $\Delta S^\circ$ must be positive, matching option (4).
Thus, the correct answer is (4) negative, positive.