In which of the following equilibrium , change in pressure will not affect the equilibrium ?

Options

A. `N_2(g) +3H_2(g) hArr 2NH_3(g)`
B. `H_2(g) +I_2(g) hArr 2HI(g)`
C. `PCI_5(g) hArr PCI_3(g) +CI_2(g)`
D. `N_2O_4(g) hArr 2NO_2(g)`

Answer

To solve the problem of determining which equilibrium will not be affected by a change in pressure, we need to apply Le Chatelier's principle. According to this principle, if a change is made to a system at equilibrium, the system will adjust to counteract that change. Specifically, when it comes to pressure changes, the equilibrium will only be affected if there is a difference in the number of moles of gaseous reactants and products.

### Step-by-Step Solution:

1. **Understand Delta NG**:
- Delta NG (ΔNG) is defined as the difference in the number of moles of gaseous products and gaseous reactants.
- Mathematically, it is expressed as:
\[ \Delta NG = \text{(Number of moles of gaseous products)} - \text{(Number of moles of gaseous reactants)} \]

2. **Analyze Each Option**:
- We will calculate ΔNG for each option provided in the question.

**Option A**:
- Reaction: 2 gaseous products and 4 gaseous reactants.
- Calculation:
\[ \Delta NG = 2 - 4 = -2 \]

**Option B**:
- Reaction: 2 gaseous products and 2 gaseous reactants.
- Calculation:
\[ \Delta NG = 2 - 2 = 0 \]

**Option C**:
- Reaction: 1 gaseous product and 1 gaseous reactant.
- Calculation:
\[ \Delta NG = 1 - 1 = 0 \]

**Option D**:
- Reaction: 2 gaseous products and 1 gaseous reactant.
- Calculation:
\[ \Delta NG = 2 - 1 = 1 \]

3. **Determine Which Option is Correct**:
- From our calculations:
- Option A: ΔNG = -2
- Option B: ΔNG = 0
- Option C: ΔNG = 0
- Option D: ΔNG = 1
- According to Le Chatelier's principle, a change in pressure will not affect the equilibrium if ΔNG = 0. Therefore, both Option B and Option C will not be affected by a change in pressure.

4. **Final Answer**:
- The options where a change in pressure will not affect the equilibrium are **Option B** and **Option C**.