One of the following equilibrium is not affected by change in volume of the falsk :

Options

A. ` PCl_5( g) hArr PCl_3(g) +Cl_2(g)`
B. ` N_2(g) +3H_2(g) hArr 2NH_3(g)`
C. ` N_2 (g) +O_2(g) hArr 2NO(g)`
D. ` SO_2Cl_2(g) hArr SO_2(g) +Cl_2(g)`

Explanation

To solve the question regarding which equilibrium is not affected by a change in the volume of the flask, we need to analyze the relationship between the number of moles of reactants and products in each equilibrium reaction. Here’s a step-by-step solution:

### Step 1: Understand the concept of equilibrium and volume change
Equilibrium in a chemical reaction can be affected by changes in concentration, temperature, and volume. According to Le Chatelier's principle, if a change is applied to a system at equilibrium, the system will adjust to counteract that change.

### Step 2: Define delta n
Delta n (Δn) is defined as the difference in the number of moles of products and reactants:
\[ \Delta n = n_p - n_r \]
Where:
- \( n_p \) = number of moles of products
- \( n_r \) = number of moles of reactants

### Step 3: Analyze the effect of volume changes
1. **If Δn > 0**: There are more moles of products than reactants. Increasing the volume will shift the equilibrium to the right (towards products) to counteract the change.
2. **If Δn < 0**: There are more moles of reactants than products. Increasing the volume will shift the equilibrium to the left (towards reactants).
3. **If Δn = 0**: The number of moles of products equals the number of moles of reactants. Changes in volume will not affect the position of the equilibrium.

### Step 4: Identify the equilibria
We need to evaluate the given equilibria (which are not provided in the question but are typically given in such questions) to find their Δn values.

1. **Reaction 1**: \( A \rightleftharpoons B + C \)
- Δn = (1 + 1) - 1 = 1 (Δn > 0)

2. **Reaction 2**: \( D + E \rightleftharpoons F \)
- Δn = 1 - (1 + 1) = -1 (Δn < 0)

3. **Reaction 3**: \( G + H \rightleftharpoons I + J \)
- Δn = (1 + 1) - 2 = 0 (Δn = 0)

4. **Reaction 4**: \( K \rightleftharpoons L + M \)
- Δn = (1 + 1) - 1 = 1 (Δn > 0)

### Step 5: Conclusion
From the analysis, the equilibrium that is not affected by a change in volume is the one where Δn = 0. Therefore, the correct answer is the equilibrium represented by Reaction 3 (or whichever reaction corresponds to Δn = 0).