For which of the following reaction does the equilibrium constant depend on the units of concentration?

Options

A. `NO(g) hArr 1/2 N_(2)(g)+1/2 O_(2)(g)`
B. `C_(2)H_(5)OH(l)+CH_(3)COOH(l) hArr CH_(3)COOC_(2)H_(5)(l)+H_(2)O(l)`
C. `2HI(g) hArr H_(2)(g)+I_(2)(g)`
D. `COCl_(2)(g) hArr CO(g)+Cl_(2)(g)`

Answer

To determine for which reaction the equilibrium constant depends on the units of concentration, we will analyze each reaction step by step.

### Step-by-Step Solution:

1. **Identify the Reactions**: We have four reactions to analyze:
- Case A: \( \text{NO (g)} \rightleftharpoons \frac{1}{2} \text{N}_2 (g) + \frac{1}{2} \text{O}_2 (g) \)
- Case B: \( \text{C}_2\text{H}_5\text{OH (aq)} + \text{H}_2\text{O (l)} \rightleftharpoons \text{CH}_3\text{COOC}_2\text{H}_5 (l) + \text{H}_2\text{O (l)} \)
- Case C: \( \text{2HI (g)} \rightleftharpoons \text{H}_2 (g) + \text{I}_2 (g) \)
- Case D: \( \text{COCl}_2 (g) \rightleftharpoons \text{CO (g)} + \text{Cl}_2 (g) \)

2. **Write the Equilibrium Constant Expression**:
- **Case A**:
\[ K_c = \frac{[\text{N}_2]^{1/2}[\text{O}_2]^{1/2}}{[\text{NO}]} \]
- **Case B**:
\[ K_c = \frac{[\text{CH}_3\text{COOC}_2\text{H}_5][\text{H}_2\text{O}]}{[\text{C}_2\text{H}_5\text{OH}][\text{CH}_3\text{COOH}]} \]
- **Case C**:
\[ K_c = \frac{[\text{H}_2][\text{I}_2]}{[\text{HI}]^2} \]
- **Case D**:
\[ K_c = \frac{[\text{CO}][\text{Cl}_2]}{[\text{COCl}_2]} \]

3. **Determine the Units for Each Case**:
- **Case A**:
- Units:
\[ K_c = \frac{(mol/L)^{1/2} \cdot (mol/L)^{1/2}}{(mol/L)} = \frac{(mol/L)}{(mol/L)} = \text{unitless} \]
- **Case B**:
- Units:
\[ K_c = \frac{(mol/L) \cdot (mol/L)}{(mol/L) \cdot (mol/L)} = \text{unitless} \]
- **Case C**:
- Units:
\[ K_c = \frac{(mol/L) \cdot (mol/L)}{(mol/L)^2} = \text{unitless} \]
- **Case D**:
- Units:
\[ K_c = \frac{(mol/L) \cdot (mol/L)}{(mol/L)} = (mol/L) \]

4. **Conclusion**:
- The equilibrium constant \( K_c \) for Case D has units of concentration (molar), while the others are unitless. Therefore, the equilibrium constant depends on the units of concentration only for Case D.

### Final Answer:
The equilibrium constant depends on the units of concentration for **Case D**.