In which of the following equilibrium `K_c` and `K_p` are not equal ?

Options

A. `2NO(g)hArrN_2(g)+O_2(g)`
B. `SO_2(g)+NO_2(g)hArrSO_3(g)+NO(g)`
C. `H_2(g) +I_2(g)hArr2HI(g)`
D. `2C(s)+O_2(g)hArr2CO_2(g)`

Explanation

To determine in which of the following equilibria \( K_c \) and \( K_p \) are not equal, we need to understand the relationship between these two equilibrium constants.

### Step 1: Understand the relationship between \( K_c \) and \( K_p \)

The relationship between \( K_c \) and \( K_p \) is given by the formula:

\[ K_p = K_c \cdot R^T \Delta n \]

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

### Step 2: Calculate \( \Delta n \)

To find out when \( K_c \) and \( K_p \) are not equal, we need to evaluate \( \Delta n \) for the given equilibria.

- If \( \Delta n = 0 \), then \( K_p = K_c \) (since anything raised to the power of 0 is 1).
- If \( \Delta n \) is not equal to 0, then \( K_p \) will not equal \( K_c \).

### Step 3: Analyze the given equilibria

1. **Equilibrium 1**:
- Products: 2 moles of gas
- Reactants: 2 moles of gas
- \( \Delta n = 2 - 2 = 0 \) → \( K_p = K_c \)

2. **Equilibrium 2**:
- Products: 2 moles of gas
- Reactants: 2 moles of gas
- \( \Delta n = 2 - 2 = 0 \) → \( K_p = K_c \)

3. **Equilibrium 3**:
- Products: 2 moles of gas
- Reactants: 1 mole of gas (solid is not counted)
- \( \Delta n = 2 - 1 = 1 \) → \( K_p = K_c \cdot R^T \) (which means \( K_p > K_c \))

### Conclusion

In the third equilibrium, \( K_p \) and \( K_c \) are not equal because \( \Delta n \) is not zero. Therefore, the correct option is the one corresponding to the third equilibrium.