Question

For a reaction to be spontaneous at all temperatures, the values of enthalpy change and entropy change should be

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

Hint:

We need delta G negative at every T, so enthalpy must fall and entropy must rise.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
The Gibbs equation is \(\Delta G = \Delta H - T\Delta S\). A reaction is spontaneous when \(\Delta G\) is negative.

Step 2: Detailed Explanation
Check each sign combination:
(A) \(\Delta H > 0\), \(\Delta S > 0\): \(\Delta G\) is negative only at high T. Not at all temperatures.
(B) \(\Delta H < 0\), \(\Delta S > 0\): both terms push \(\Delta G\) negative, since \(-T\Delta S\) is negative. This holds at every T.
(C) \(\Delta H < 0\), \(\Delta S < 0\): spontaneous only at low T.
(D) \(\Delta H > 0\), \(\Delta S < 0\): \(\Delta G\) is always positive, so never spontaneous.

Final Answer:
Only option (B) gives a negative \(\Delta G\) at all temperatures. \[ \boxed{\Delta H < 0, \Delta S > 0} \]