Under which circumstances would the free energy change for a reaction be relatively temperature independent?

Options

A. `DeltaH^(@)` is negative.
B. `DeltaH^(@)` is positive
C. `DeltaS^(@)` has a large positive value
D. `DeltaS^(@)` has a small magnitude.

Answer

To determine the circumstances under which the free energy change (\( \Delta G \)) for a reaction is relatively temperature independent, we can analyze the equation that relates free energy change to enthalpy change (\( \Delta H \)) and entropy change (\( \Delta S \)):

### Step-by-Step Solution:

1. **Understand the Gibbs Free Energy Equation**:
The Gibbs free energy change is given by the equation:
\[ \Delta G = \Delta H - T \Delta S \]
Here, \( \Delta G \) is the change in free energy, \( \Delta H \) is the change in enthalpy, \( T \) is the temperature in Kelvin, and \( \Delta S \) is the change in entropy.

2. **Identify the Factors Affecting \( \Delta G \)**:
From the equation, we see that \( \Delta G \) is influenced by both \( \Delta H \) and \( T \Delta S \). The term \( T \Delta S \) indicates that the temperature plays a significant role in determining \( \Delta G \).

3. **Consider the Cases for \( \Delta S \)**:
To find when \( \Delta G \) is relatively temperature independent, we need to analyze the behavior of \( \Delta S \):
- **Case 1**: If \( \Delta S \) is very small, then \( T \Delta S \) will also be small, but \( \Delta G \) will still depend on \( T \) since it will be influenced by the temperature.
- **Case 2**: If \( \Delta S \) is very large, then \( T \Delta S \) will dominate the equation. In this case, even if the temperature changes, the large value of \( \Delta S \) will ensure that \( \Delta G \) remains negative, making it less sensitive to temperature variations.

4. **Conclusion**:
Therefore, the free energy change (\( \Delta G \)) for a reaction will be relatively temperature independent when the entropy change (\( \Delta S \)) is very large. This is because a large \( \Delta S \) will ensure that the term \( T \Delta S \) significantly influences \( \Delta G \) regardless of temperature fluctuations.

### Final Answer:
The free energy change (\( \Delta G \)) for a reaction is relatively temperature independent when the entropy change (\( \Delta S \)) is very large.