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 determine in which of the following equilibria a change in pressure will not affect the equilibrium, we can follow these steps:

### Step 1: Understand the Principle
According to Le Chatelier's Principle, if a system at equilibrium is subjected to a change in pressure, temperature, or concentration, the system will adjust itself to counteract that change. Specifically, for changes in pressure, the equilibrium will shift towards the side with fewer moles of gas.

### Step 2: Analyze the Reactions
Let's consider a general reaction:
\[ aA(g) + bB(g) \rightleftharpoons cC(g) + dD(g) \]

- Count the number of moles of gaseous reactants and products on both sides.
- If the total number of moles of gas is the same on both sides, a change in pressure will not affect the equilibrium position.

### Step 3: Evaluate Each Option
1. **Option 1:** \( 3A(g) + 4B(g) \rightleftharpoons 2C(g) \)
- Reactants: 3 + 4 = 7 moles of gas
- Products: 2 moles of gas
- **Effect:** Yes, changing pressure will affect the equilibrium.

2. **Option 2:** \( 2A(g) + 2B(g) \rightleftharpoons 2C(g) + 2D(g) \)
- Reactants: 2 + 2 = 4 moles of gas
- Products: 2 + 2 = 4 moles of gas
- **Effect:** No, changing pressure will not affect the equilibrium.

3. **Option 3:** \( 2A(g) \rightleftharpoons 1B(g) + 1C(g) \)
- Reactants: 2 moles of gas
- Products: 1 + 1 = 2 moles of gas
- **Effect:** Yes, changing pressure will affect the equilibrium.

4. **Option 4:** \( 1A(g) + 1B(g) \rightleftharpoons 2C(g) \)
- Reactants: 1 + 1 = 2 moles of gas
- Products: 2 moles of gas
- **Effect:** Yes, changing pressure will affect the equilibrium.

### Conclusion
The only equilibrium that will not be affected by a change in pressure is **Option 2**, where the number of moles of gaseous reactants equals the number of moles of gaseous products.

---