In an equilibrium reaction for which `Delta G^(@) = 0` , the equilibrium constant K =

Options

A. 0
B. 1
C. 2
D. 10

Explanation

To determine the value of the equilibrium constant \( K \) when \( \Delta G^\circ = 0 \), we can follow these steps:

### Step-by-Step Solution:

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

2. **Set \( \Delta G^\circ \) to zero:**
Given that \( \Delta G^\circ = 0 \), we can substitute this value into the equation:
\[ 0 = -RT \ln K \]

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

4. **Solve for \( K \):**
To find \( K \), we need to exponentiate both sides:
\[ K = e^0 \]
Since \( e^0 = 1 \):
\[ K = 1 \]

### Final Answer:
Thus, when \( \Delta G^\circ = 0 \), the equilibrium constant \( K \) is equal to 1.

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