In which of the following reaction `K_(p) gt K_(c)`

Options

A. `N_(2)(g)+3H_(2)(g)hArr2NH_(3)(g)`
B. `H_(2)(g)+I_(2)(g)hArr2HI(g)`
C. `PCl_(3)(g)+Cl_(2)(g)hArrPCl_(2)(g)`
D. `2SO_(3)(g)hArr2 SO_(2) (g) + O_(2) (g) `

Answer

To determine in which of the given reactions \( K_p \) is greater than \( K_c \), we need to analyze the change in the number of moles of gas (\( \Delta N_g \)) for each reaction. The relationship between \( K_p \) and \( K_c \) is given by the equation:

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

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

### Step-by-Step Solution:

1. **Identify the reactions and calculate \( \Delta N_g \)**:
- **Reaction A**: \( N_2 + 3H_2 \rightleftharpoons 2NH_3 \)
- Moles of products = 2 (from \( 2NH_3 \))
- Moles of reactants = 1 (from \( N_2 \)) + 3 (from \( 3H_2 \)) = 4
- \( \Delta N_g = 2 - 4 = -2 \)

- **Reaction B**: \( H_2 + I_2 \rightleftharpoons 2HI \)
- Moles of products = 2 (from \( 2HI \))
- Moles of reactants = 1 (from \( H_2 \)) + 1 (from \( I_2 \)) = 2
- \( \Delta N_g = 2 - 2 = 0 \)

- **Reaction C**: \( PCl_3 + Cl_2 \rightleftharpoons PCl_5 \)
- Moles of products = 1 (from \( PCl_5 \))
- Moles of reactants = 1 (from \( PCl_3 \)) + 1 (from \( Cl_2 \)) = 2
- \( \Delta N_g = 1 - 2 = -1 \)

- **Reaction D**: \( 2SO_3 \rightleftharpoons 2SO_2 + O_2 \)
- Moles of products = 2 (from \( 2SO_2 \)) + 1 (from \( O_2 \)) = 3
- Moles of reactants = 2 (from \( 2SO_3 \))
- \( \Delta N_g = 3 - 2 = 1 \)

2. **Determine the relationship between \( K_p \) and \( K_c \)**:
- For **Reaction A**: \( \Delta N_g = -2 \) → \( K_p < K_c \)
- For **Reaction B**: \( \Delta N_g = 0 \) → \( K_p = K_c \)
- For **Reaction C**: \( \Delta N_g = -1 \) → \( K_p < K_c \)
- For **Reaction D**: \( \Delta N_g = 1 \) → \( K_p > K_c \)

3. **Conclusion**:
- The only reaction where \( K_p \) is greater than \( K_c \) is **Reaction D**.

### Final Answer:
**The correct answer is Reaction D: \( 2SO_3 \rightleftharpoons 2SO_2 + O_2 \)**, where \( K_p > K_c \).