In which one of the following equilibria, `K_p ne K_c` ?

Options

A. `NO_2(g) +SO_2(g) hArr NO(g) +SO_3(g)`
B. `2HI(g) hArr H_2(g) + I_2(g)`
C. `2NO(g) hArr N_2(g) + O_2(g)`
D. `2C(s) + O_2(g) hArr 2CO(g)`

Explanation

To determine in which equilibrium \( K_p \neq K_c \), we need to understand the relationship between \( K_p \) and \( K_c \). The relationship is given by the equation:

\[ K_p = K_c (RT)^{\Delta N_g} \]

where:
- \( R \) is the universal gas constant,
- \( T \) is the temperature in Kelvin,
- \( \Delta N_g \) is the change in the number of moles of gas, calculated as the moles of gaseous products minus the moles of gaseous reactants.

### Step-by-Step Solution:

1. **Identify \( \Delta N_g \)**:
- For each equilibrium reaction provided in the options, calculate \( \Delta N_g \) by subtracting the total number of moles of gaseous reactants from the total number of moles of gaseous products.

2. **Evaluate Each Option**:
- For each equilibrium, determine if \( \Delta N_g \) is zero, positive, or negative.
- If \( \Delta N_g = 0 \), then \( K_p = K_c \).
- If \( \Delta N_g \neq 0 \), then \( K_p \neq K_c \).

3. **Analyze the Options**:
- **Option A**: Calculate \( \Delta N_g \).
- **Option B**: Calculate \( \Delta N_g \).
- **Option C**: Calculate \( \Delta N_g \).
- **Option D**: Calculate \( \Delta N_g \).

4. **Select the Correct Option**:
- The option where \( \Delta N_g \neq 0 \) is the one where \( K_p \neq K_c \).

### Example Calculation for Each Option:
- **Option A**:
- Reactants: 2 moles of gas, Products: 2 moles of gas.
- \( \Delta N_g = 2 - 2 = 0 \) (So, \( K_p = K_c \))

- **Option B**:
- Reactants: 2 moles of gas, Products: 2 moles of gas.
- \( \Delta N_g = 2 - 2 = 0 \) (So, \( K_p = K_c \))

- **Option C**:
- Reactants: 2 moles of gas, Products: 2 moles of gas.
- \( \Delta N_g = 2 - 2 = 0 \) (So, \( K_p = K_c \))

- **Option D**:
- Reactants: 1 mole of gas (O2), Products: 1 mole of gas (CO2), and solid carbon does not count.
- \( \Delta N_g = 2 - 1 = 1 \) (So, \( K_p \neq K_c \))

### Conclusion:
The correct answer is **Option D**, where \( K_p \neq K_c \).