Question

When will the reaction become spontaneous at all temperatures?

• A. \( \Delta H = -\text{ve}, \Delta S = +\text{ve}, \Delta G = -\text{ve} \)
• B. \( \Delta H = +\text{ve or -ve}, \Delta S = 0, \Delta G = 0 \)
• C. \( \Delta H = -\text{ve}, \Delta S = -\text{ve}, \Delta G = -\text{ve or +ve} \)
• D. \( \Delta H = +\text{ve}, \Delta S = -\text{ve}, \Delta G = +\text{ve} \)

Hint:

For spontaneity at all temperatures, \( \Delta H \) should be negative and \( \Delta S \) should be positive, leading to \( \Delta G \) always being negative.

Answer 1

The Correct Option is A

Step 1: Understanding spontaneity.
For a reaction to be spontaneous at all temperatures, the Gibbs free energy change (\( \Delta G \)) must be negative. According to the equation: \[ \Delta G = \Delta H - T\Delta S \] The reaction is spontaneous when \( \Delta H \) is negative (exothermic reaction) and \( \Delta S \) is positive (increase in disorder).
Step 2: Analyzing the options.
(A) \( \Delta H = -\text{ve}, \Delta S = +\text{ve}, \Delta G = -\text{ve} \): Correct. This combination ensures spontaneity at all temperatures.
(B) \( \Delta H = +\text{ve or -ve}, \Delta S = 0, \Delta G = 0 \): Incorrect. This condition does not guarantee spontaneity.
(C) \( \Delta H = -\text{ve}, \Delta S = -\text{ve}, \Delta G = -\text{ve or +ve} \): Incorrect. A negative \( \Delta S \) would not make the reaction spontaneous at higher temperatures.
(D) \( \Delta H = +\text{ve}, \Delta S = -\text{ve}, \Delta G = +\text{ve} \): Incorrect. This would not lead to spontaneity under any condition.
Step 3: Conclusion.
The correct answer is (A), where both \( \Delta H \) is negative and \( \Delta S \) is positive, making the reaction spontaneous at all temperatures.