Which one of the equation is currect ?

Options

A. `Delta G = DeltaG^0+ nRT log Q`
B. `Delta G^0=Delta G+ nRT log Q`
C. `Delta G = Delta G^0+ nRT ln Q`
D. `Delta G^0 =Delta G + nRT ln Q`

Answer

To solve the question regarding which equation is correct, we will analyze each option based on the known relationship between Gibbs free energy change (ΔG) and standard Gibbs free energy change (ΔG°).

### Step-by-Step Solution:

1. **Understand the Definitions**:
- ΔG: Gibbs free energy change for a reaction under non-standard conditions.
- ΔG°: Gibbs free energy change for a reaction under standard conditions (1 atm, 25°C).
- n: Number of moles of reactants/products.
- R: Universal gas constant (8.314 J/(mol·K)).
- T: Temperature in Kelvin.
- Q: Reaction quotient.

2. **Recall the Relationship**:
The relationship between ΔG and ΔG° is given by the equation:
\[ \Delta G = \Delta G° + nRT \ln Q \]
This equation indicates how the Gibbs free energy change (ΔG) is affected by the reaction quotient (Q) and the standard Gibbs free energy change (ΔG°).

3. **Analyze Each Option**:
- **Option A**: ΔG = ΔG° + nRT log Q
- Incorrect because it uses "log" instead of "ln".
- **Option B**: ΔG° = ΔG + nRT log Q
- Incorrect for the same reason as Option A and also because it incorrectly places ΔG on the left.
- **Option C**: ΔG = ΔG° + nRT ln Q
- Correct, as it matches the known equation.
- **Option D**: ΔG° = ΔG + nRT ln Q
- Incorrect because it incorrectly places ΔG on the left side.

4. **Conclusion**:
Based on the analysis, the correct equation is:
\[ \Delta G = \Delta G° + nRT \ln Q \]
Therefore, **Option C** is the correct answer.