For a reaction in a galvanic cell the value of `-/_\G^(@)` at certain temperature is not necessarily equal to:

Options

A. `nFE^(@)`
B. RT In K
C. `T/_\S^(@)-/_\H^(@)`
D. zero

Answer

To solve the question, we need to analyze the relationship between the standard Gibbs free energy change (ΔG°) and other thermodynamic quantities in a galvanic cell. The question asks for which of the given options ΔG° is not necessarily equal to at a certain temperature.

### Step-by-Step Solution:

1. **Understanding ΔG°**:
- The standard Gibbs free energy change (ΔG°) is a thermodynamic potential that can be used to predict the direction of a chemical reaction.
- The relationship between ΔG° and the cell potential (E°) is given by the equation:
\[ \Delta G° = -nFE° \]
- Here, n is the number of moles of electrons transferred, F is Faraday's constant, and E° is the standard cell potential.

2. **Analyzing the First Option**:
- The first option relates ΔG° to the cell potential E°. According to the equation mentioned, ΔG° is directly related to E°.
- Therefore, this option is **not correct** because ΔG° is indeed equal to -nFE°.

3. **Understanding the Relationship with Equilibrium Constant (K)**:
- The relationship between ΔG° and the equilibrium constant (K) is given by:
\[ \Delta G° = -RT \ln K \]
- This relationship holds true at equilibrium. However, it does not imply that ΔG° is equal to RT ln K under all conditions, only at equilibrium.
- Thus, this option is **correct** in the context of the question, as ΔG° is not necessarily equal to RT ln K at all times.

4. **Analyzing the Third Option (Enthalpy and Entropy)**:
- The Gibbs free energy can also be expressed in terms of enthalpy (ΔH°) and entropy (ΔS°):
\[ \Delta G° = \Delta H° - T\Delta S° \]
- This equation shows that ΔG° is related to both enthalpy and entropy. However, it does not imply that ΔG° is equal to zero.
- Therefore, this option is also **not correct** since ΔG° is not necessarily equal to zero.

5. **Conclusion**:
- The only option that ΔG° is not necessarily equal to at a certain temperature is the one relating to the equilibrium constant (K).
- Thus, the answer to the question is that ΔG° is not necessarily equal to RT ln K.

### Final Answer:
ΔG° is not necessarily equal to RT ln K at a certain temperature.