In which of the following equilibrium ,change in volume of the system does not alter the number of moles:

Options

A. `N_(2)(g)+O_(2)(g)hArr2NO(g)`
B. `PCl_(5)(g)hArrPCl_(3)(g)+Cl_(2)(g)`
C. `N_(2)(g)+3H_(2)(g)hArr2NH_(3)(g)`
D. `SO_(2)Cl_(2)(g)hArrSO_(2)hArrSO_(2)(g)+Cl_(2)(g)`

Answer

To determine in which of the given equilibria a change in volume does not alter the number of moles, we need to analyze each reaction by calculating the change in the number of moles of gas (ΔNg) involved in the reaction.

### Step-by-Step Solution:

1. **Identify the Reactions**: We have four reactions to analyze:
- Reaction 1: N2(g) + O2(g) ⇌ 2NO(g)
- Reaction 2: PCl5(g) ⇌ PCl3(g) + Cl2(g)
- Reaction 3: N2(g) + 3H2(g) ⇌ 2NH3(g)
- Reaction 4: SO2Cl2(g) ⇌ SO2(g) + Cl2(g)

2. **Calculate ΔNg for Each Reaction**:
- **Reaction 1**:
- Products: 2 moles of NO
- Reactants: 1 mole of N2 + 1 mole of O2 = 2 moles
- ΔNg = moles of products - moles of reactants = 2 - 2 = 0
- **Conclusion**: Change in volume does not alter the number of moles.

- **Reaction 2**:
- Products: 1 mole of PCl3 + 1 mole of Cl2 = 2 moles
- Reactants: 1 mole of PCl5
- ΔNg = 2 - 1 = 1
- **Conclusion**: Change in volume alters the number of moles.

- **Reaction 3**:
- Products: 2 moles of NH3
- Reactants: 1 mole of N2 + 3 moles of H2 = 4 moles
- ΔNg = 2 - 4 = -2
- **Conclusion**: Change in volume alters the number of moles.

- **Reaction 4**:
- Products: 1 mole of SO2 + 1 mole of Cl2 = 2 moles
- Reactants: 1 mole of SO2Cl2
- ΔNg = 2 - 1 = 1
- **Conclusion**: Change in volume alters the number of moles.

3. **Final Conclusion**: The only reaction where a change in volume does not alter the number of moles is Reaction 1: N2(g) + O2(g) ⇌ 2NO(g).

### Answer:
The correct option is **Reaction 1: N2(g) + O2(g) ⇌ 2NO(g)**, as changing the volume does not alter the number of moles in this equilibrium.