For which of the following reactions `K_(p) = K_(c)`

Options

A. `2NOC1(g)hArr2NO(g) + C1_(2)(g)`
B. `N_(2)(g) + 3H_(2)(g)hArr2NH_(3)(g)`
C. `H_(2)(g) + C1_(2)(g)hArr2HC1(g)`
D. `N_(2)O_(4)(g)hArr2NO_(2)(g)`

Explanation

To determine for which of the given reactions \( K_p = K_c \), we can use the relationship between these two equilibrium constants:

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

Where:
- \( K_p \) is the equilibrium constant for partial pressures,
- \( K_c \) is the equilibrium constant for concentrations,
- \( R \) is the universal gas constant,
- \( T \) is the temperature in Kelvin,
- \( \Delta N \) is the change in the number of moles of gas (moles of products - moles of reactants).

For \( K_p \) to be equal to \( K_c \), the term \( (RT)^{\Delta N} \) must equal 1, which occurs when \( \Delta N = 0 \).

### Step-by-Step Solution:

1. **Identify the reactions**: We need to analyze the given reactions to find the change in the number of moles of gas (\( \Delta N \)) for each reaction.

2. **Calculate \( \Delta N \) for each reaction**:
- **Reaction 1**: Products = 3 moles, Reactants = 2 moles
\[ \Delta N = 3 - 2 = 1 \]
- **Reaction 2**: Products = 2 moles, Reactants = 4 moles
\[ \Delta N = 2 - 4 = -2 \]
- **Reaction 3**: Products = 2 moles, Reactants = 2 moles
\[ \Delta N = 2 - 2 = 0 \]
- **Reaction 4**: Products = 2 moles, Reactants = 1 mole
\[ \Delta N = 2 - 1 = 1 \]

3. **Determine where \( K_p = K_c \)**:
- From the calculations:
- Reaction 1: \( \Delta N = 1 \) → \( K_p \neq K_c \)
- Reaction 2: \( \Delta N = -2 \) → \( K_p \neq K_c \)
- Reaction 3: \( \Delta N = 0 \) → \( K_p = K_c \) (This is the correct option)
- Reaction 4: \( \Delta N = 1 \) → \( K_p \neq K_c \)

4. **Conclusion**: The reaction for which \( K_p = K_c \) is the third reaction, where the number of moles of products equals the number of moles of reactants.

### Final Answer:
The correct option is **Reaction 3**.