A reaction attains equilibrium, when the free energy change is

Options

A. (a) `1`
B. (b) `2`
C. (c) `3`
D. (d) `0`

Explanation

To solve the question regarding when a reaction attains equilibrium in terms of free energy change, we can follow these steps:

### Step-by-Step Solution:

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

2. **Identify the Relationship Between ΔG and Reaction Quotient (Q)**:
- The relationship between the change in free energy (ΔG) and the reaction quotient (Q) is given by the equation:
\[ ΔG = ΔG^0 + RT \ln(Q) \]
- Here, ΔG^0 is the standard free energy change, R is the universal gas constant, T is the temperature in Kelvin, and Q is the reaction quotient.

3. **Determine the Condition at Equilibrium**:
- At equilibrium, the reaction quotient (Q) equals the equilibrium constant (K). Therefore, we can rewrite the equation as:
\[ ΔG = ΔG^0 + RT \ln(K) \]

4. **Set ΔG to Zero at Equilibrium**:
- At equilibrium, the change in free energy (ΔG) is zero. Thus, we can set the equation to:
\[ 0 = ΔG^0 + RT \ln(K) \]

5. **Rearranging the Equation**:
- Rearranging gives us:
\[ ΔG^0 = -RT \ln(K) \]
- This indicates that while ΔG^0 (standard free energy change) may not be zero, ΔG (the free energy change at equilibrium) is indeed zero.

6. **Conclusion**:
- Therefore, when a reaction attains equilibrium, the free energy change (ΔG) is **zero**.

### Final Answer:
The free energy change (ΔG) when a reaction attains equilibrium is **0**.

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