Increase in volume of container does not affect the equilibria

Options

A. `N_(2) + O_(2) hArr 2NO` (gaseous )
B. `CaCO_(3)(s) hArr CaO(s) + CO_(2)(g)`
C. `C_(2)H_(5) OH (l) + CH_(3) "COOH"(l) hArr CH_(3) "COOC"_(2) H_(5) (l) + H_(2) `O(l)
D. `PCl_(5) hArr PCl_(3) + Cl_(2)` (gaseous )

Answer

To determine whether an increase in the volume of a container affects the equilibrium of a reaction, we need to analyze the reactions provided and consider the principles of chemical equilibrium, particularly focusing on gaseous reactions.

### Step-by-Step Solution:

1. **Identify the Reactions**:
We have four reactions to analyze:
- Reaction 1: \( N_2O_2 \rightleftharpoons 2NO \)
- Reaction 2: \( CaCO_3 (s) \rightleftharpoons CaO (s) + CO_2 (g) \)
- Reaction 3: \( C_2H_5OH (l) + CH_3COOH (l) \rightleftharpoons C_2H_5OCOCH_3 (l) + H_2O (l) \)
- Reaction 4: \( PCl_5 (g) \rightleftharpoons PCl_3 (g) + Cl_2 (g) \)

2. **Determine the Phase of Each Component**:
- In Reaction 1, both \( N_2O_2 \) and \( NO \) are gases.
- In Reaction 2, \( CaCO_3 \) is solid, \( CaO \) is solid, and \( CO_2 \) is gas.
- In Reaction 3, all components are liquids.
- In Reaction 4, all components are gases.

3. **Analyze the Effect of Volume Change**:
- **Gaseous Reactions**: For reactions involving gases, an increase in volume leads to a decrease in pressure. According to Le Chatelier's principle, if the number of moles of gas changes, the equilibrium will shift to counteract the change.
- **Solid and Liquid Reactions**: The equilibrium of reactions involving solids and liquids is not affected by volume changes since their concentrations do not change with volume.

4. **Count Moles of Gases**:
- **Reaction 1**: \( N_2O_2 \) (1 mole) to \( 2NO \) (2 moles). The increase in volume will affect this equilibrium since the number of moles of gas increases.
- **Reaction 2**: \( CaCO_3 (s) \) to \( CaO (s) + CO_2 (g) \). Here, there is 1 mole of gas produced. The increase in volume will affect this equilibrium.
- **Reaction 3**: All components are liquids, so the increase in volume will not affect the equilibrium.
- **Reaction 4**: \( PCl_5 (g) \) (1 mole) to \( PCl_3 (g) + Cl_2 (g) \) (2 moles). The increase in volume will affect this equilibrium.

5. **Conclusion**:
The equilibria that are not affected by an increase in volume are:
- Reaction 3: \( C_2H_5OH (l) + CH_3COOH (l) \rightleftharpoons C_2H_5OCOCH_3 (l) + H_2O (l) \)

### Final Answer:
The increase in volume of the container does not affect the equilibria for the reaction involving only liquids (Reaction 3).