For which of the following reaction `K_(p)` and `K_(c)` are not same?

Options

A. `H_(2)(g)+Cl_(2)(g)hArr2HCl(g)`
B. `2SO_(3)(g)hArr2SO_(2)(g)+O_(2)(g)`
C. `N_(2)(g)+O_(2)(g)hArr2NO_(g)`
D. none of these

Answer

To determine for which of the given reactions \( K_p \) and \( K_c \) are not the same, we can use the relationship between \( K_p \) and \( K_c \):

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

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 number of moles of gaseous products minus the number of moles of gaseous reactants.

### Step-by-Step Solution:

1. **Identify the reactions**: We need to analyze each reaction provided in the options to find \( \Delta n \).

2. **Calculate \( \Delta n \) for each reaction**:
- **Reaction 1**:
- Products: 2 moles (let's assume \( A + B \rightleftharpoons 2C \))
- Reactants: 2 moles
- \( \Delta n = \text{moles of products} - \text{moles of reactants} = 2 - 2 = 0 \)
- Therefore, \( K_p = K_c \).

- **Reaction 2**:
- Products: 3 moles (let's assume \( 2A \rightleftharpoons B + C \))
- Reactants: 2 moles
- \( \Delta n = 3 - 2 = 1 \)
- Therefore, \( K_p \neq K_c \).

- **Reaction 3**:
- Products: 2 moles (let's assume \( 2C \rightleftharpoons A + B \))
- Reactants: 2 moles
- \( \Delta n = 2 - 2 = 0 \)
- Therefore, \( K_p = K_c \).

3. **Conclusion**: From the calculations, only in Reaction 2 do we have \( \Delta n \neq 0 \). Thus, \( K_p \) and \( K_c \) are not the same for this reaction.

### Final Answer:
The correct option is Reaction 2.