`Delta G^(@)` of reversible reaction at its equilbrium is

Options

A. Positive
B. Negative
C. Always zero
D. May be(1) or (2)

Answer

To solve the question regarding the standard Gibbs free energy change (ΔG°) of a reversible reaction at equilibrium, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Gibbs Free Energy (ΔG)**:
- Gibbs free energy change (ΔG) indicates the spontaneity of a reaction. If ΔG is negative, the reaction is spontaneous; if ΔG is positive, the reaction is non-spontaneous.

2. **Relate ΔG° to the Equilibrium Constant (K)**:
- The relationship between standard Gibbs free energy change (ΔG°) and the equilibrium constant (K) is given by the equation:
\[ ΔG° = -RT \ln K \]
where:
- R = universal gas constant (8.314 J/(mol·K))
- T = temperature in Kelvin
- K = equilibrium constant of the reaction

3. **Consider the Reaction at Equilibrium**:
- At equilibrium, the forward and reverse reaction rates are equal, and thus the equilibrium constant (K) can be defined as:
\[ K_{eq} = \frac{k_{f}}{k_{b}} \]
where \(k_f\) is the rate constant for the forward reaction and \(k_b\) is the rate constant for the backward reaction.

4. **Evaluate K at Equilibrium**:
- At equilibrium, the concentrations of reactants and products do not change, and the value of K becomes 1 (since the rate of the forward reaction equals the rate of the backward reaction).

5. **Substitute K into the ΔG° Equation**:
- Substitute \(K = 1\) into the equation for ΔG°:
\[ ΔG° = -RT \ln(1) \]

6. **Calculate ΔG°**:
- Since the natural logarithm of 1 is 0:
\[ \ln(1) = 0 \]
- Therefore:
\[ ΔG° = -RT \cdot 0 = 0 \]

7. **Conclusion**:
- The standard Gibbs free energy change (ΔG°) of a reversible reaction at equilibrium is always 0.

### Final Answer:
\[ \Delta G^\circ = 0 \]