For an equilibrium reaction, if the value of standard Gibb's free energy, AG° is zero, then the value of equilibrium constant, K will be equal to

Options

A. Zero
B. 2
C. 1
D. 10

Answer

To solve the problem, we need to understand the relationship between the standard Gibbs free energy change (ΔG°) and the equilibrium constant (K) for a chemical reaction.

### Step-by-Step Solution:

1. **Understand the relationship between ΔG° and K**:
The relationship is given by the equation:
\[ \Delta G° = -RT \ln K \]
where:
- ΔG° is the standard Gibbs free energy change,
- R is the universal gas constant (8.314 J/(mol·K)),
- T is the temperature in Kelvin,
- K is the equilibrium constant.

2. **Substituting the given value**:
According to the problem, we have:
\[ \Delta G° = 0 \]
Substituting this into the equation gives:
\[ 0 = -RT \ln K \]

3. **Rearranging the equation**:
Since \( -RT \) is not zero (as R and T are positive constants), we can divide both sides by \( -RT \):
\[ \ln K = 0 \]

4. **Solving for K**:
To find K, we exponentiate both sides:
\[ K = e^{\ln K} = e^0 = 1 \]

5. **Conclusion**:
Therefore, the value of the equilibrium constant K is:
\[ K = 1 \]

### Final Answer:
The equilibrium constant K will be equal to **1**.

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