Which of the following options will be correct for the stage of half completion of the reaction : `AhArrB` ?

Options

A. `DeltaG^(@)=0`
B. `DeltaG^(@)gt0`
C. `DeltaG^(@)lt0`
D. `DeltaG^(@)=-RTln2`

Explanation

To solve the question regarding the stage of half completion of the reaction \( A \rightleftharpoons B \), we need to analyze the concepts of Gibbs free energy (\( \Delta G \)) and the equilibrium constant (\( K \)).

### Step-by-Step Solution:

1. **Understanding the Reaction**:
The reaction given is \( A \rightleftharpoons B \). This means that A can convert to B and vice versa.

2. **Half Completion of the Reaction**:
When the reaction is said to be half completed, it implies that the concentrations of A and B are equal. This is an important point because at this stage, the system is at equilibrium.

3. **Equilibrium Condition**:
At equilibrium, the Gibbs free energy change (\( \Delta G \)) for the reaction is zero. This is because the system is balanced, and there is no net change in the concentrations of reactants and products.

4. **Gibbs Free Energy and Equilibrium Constant**:
The relationship between Gibbs free energy change and the equilibrium constant is given by the equation:
\[ \Delta G = \Delta G^\circ + RT \ln Q \]
where \( Q \) is the reaction quotient. At equilibrium, \( Q = K \) (the equilibrium constant), and \( \Delta G = 0 \).

5. **Conclusion**:
Since the reaction is at half completion (equilibrium), we conclude that:
- \( \Delta G^\circ = 0 \)
- The equilibrium constant \( K \) will be approximately equal to 1, indicating that the concentrations of A and B are equal.

Thus, the correct answer for the stage of half completion of the reaction \( A \rightleftharpoons B \) is that \( \Delta G^\circ = 0 \) and \( K \approx 1 \).