Question

When will the change in Gibb’s free energy always be negative?

• A. \( \Delta H = \text{positive}, \Delta S = \text{negative at all temperatures.} \)
• B. \( \Delta H \) and \( \Delta S \) both positive at low temperature.
• C. \( \Delta H = \text{negative}, \Delta S = \text{positive, at all temperatures.} \)
• D. \( \Delta H \) and \( \Delta S \) both negative at high temperature.

Hint:

For a negative change in Gibb’s free energy, ensure that \( \Delta H \) is negative and \( \Delta S \) is positive, as this will guarantee a negative \( \Delta G \) at all temperatures.

Answer 1

The Correct Option is C

Step 1: Gibb’s Free Energy Equation.
The change in Gibb’s free energy \( \Delta G \) is given by the equation: \[ \Delta G = \Delta H - T \Delta S \] Where: \(\Delta H\) is the enthalpy change, \(\Delta S\) is the entropy change, T is the absolute temperature. Step 2: Conditions for negative \( \Delta G \).
For the change in Gibb’s free energy to always be negative, we need the condition: \[ \Delta H = \text{negative}, \quad \Delta S = \text{positive}. \] This ensures that the term \( -T \Delta S \) (which is always negative for positive \( \Delta S \)) dominates the equation, making \( \Delta G \) negative at all temperatures. Step 3: Analyzing the options.
(A) \( \Delta H = \text{positive}, \Delta S = \text{negative at all temperatures.} \): This would result in a positive \( \Delta G \), so this option is incorrect.
(B) \( \Delta H \) and \( \Delta S \) both positive at low temperature: This is not always true for negative \( \Delta G \).
(C) \( \Delta H = \text{negative}, \Delta S = \text{positive, at all temperatures.} \): This is the correct answer, as the condition leads to a negative \( \Delta G \) at all temperatures.
(D) \( \Delta H \) and \( \Delta S \) both negative at high temperature: This would not always lead to a negative \( \Delta G \).
Step 3: Conclusion.
The correct answer is (C).