At equilibrium, the value of equilibrium constant K is

Options

A. `1`
B. `2`
C. `3`
D. `0`

Explanation

To solve the question about the value of the equilibrium constant \( K \) at equilibrium, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Equilibrium**:
At equilibrium, the system has reached a state where the concentrations of reactants and products remain constant over time. This is when the forward and reverse reactions occur at the same rate.

2. **Recall the Relationship Between Gibbs Free Energy and Equilibrium Constant**:
The relationship between Gibbs free energy (\( \Delta G \)) and the equilibrium constant (\( K \)) is given by the equation:
\[ \Delta G = -nRT \ln K \]
where:
- \( n \) = number of moles of the reaction,
- \( R \) = universal gas constant,
- \( T \) = temperature in Kelvin,
- \( K \) = equilibrium constant.

3. **Set \( \Delta G \) to Zero at Equilibrium**:
At equilibrium, the change in Gibbs free energy (\( \Delta G \)) is zero. Therefore, we can set up the equation:
\[ 0 = -nRT \ln K \]

4. **Solve for \( K \)**:
Since \( nRT \) is not zero (as long as the temperature is above absolute zero), we can divide both sides of the equation by \( -nRT \):
\[ 0 = \ln K \]
This implies:
\[ K = e^0 \]
Since \( e^0 = 1 \), we find that:
\[ K = 1 \]

5. **Conclusion**:
Thus, at equilibrium, the value of the equilibrium constant \( K \) is equal to 1.

### Final Answer:
The value of the equilibrium constant \( K \) at equilibrium is **1**.

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