Match list -I with list-II and choose the correct answer from the codes given below.
`{:("List-I","List-II"),(N_2O_3hArrNO+NO_2,K_p=K_c(RT)),(NH_3hArr1/2N_2+3/2H_2,K_c=K_p(RT)),(2SO_2+O_2hArr2SO_3,K_c=K_p),(N_2+O_2hArr2NO,K_p=K_c(RT)^2),("",Deltan = 0):}`

Answer

To solve the problem of matching List-I with List-II, we need to analyze each reaction in List-I and determine the relationship between \( K_p \) and \( K_c \) based on the change in the number of moles of gas (\( \Delta n \)).

### Step 1: Analyze the first reaction
**Reaction:** \( N_2O_3 \rightleftharpoons NO + NO_2 \)

- **Products:** 1 mole of NO + 1 mole of NO2 = 2 moles
- **Reactants:** 1 mole of \( N_2O_3 \) = 1 mole
- **Change in moles (\( \Delta n \)):** \( \Delta n = n_p - n_r = 2 - 1 = 1 \)

**Relationship:** \( K_p = K_c (RT)^{\Delta n} = K_c (RT)^1 \)

### Step 2: Analyze the second reaction
**Reaction:** \( NH_3 \rightleftharpoons \frac{1}{2} N_2 + \frac{3}{2} H_2 \)

- **Products:** \( \frac{1}{2} N_2 + \frac{3}{2} H_2 = 2 \) moles
- **Reactants:** 1 mole of \( NH_3 \) = 1 mole
- **Change in moles (\( \Delta n \)):** \( \Delta n = 2 - 1 = 1 \)

**Relationship:** \( K_c = K_p (RT)^{-1} \)

### Step 3: Analyze the third reaction
**Reaction:** \( 2SO_2 + O_2 \rightleftharpoons 2SO_3 \)

- **Products:** 2 moles of \( SO_3 \) = 2 moles
- **Reactants:** 2 moles of \( SO_2 + 1 \) mole of \( O_2 = 3 \) moles
- **Change in moles (\( \Delta n \)):** \( \Delta n = 2 - 3 = -1 \)

**Relationship:** \( K_p = K_c (RT)^{-1} \)

### Step 4: Analyze the fourth reaction
**Reaction:** \( N_2 + O_2 \rightleftharpoons 2NO \)

- **Products:** 2 moles of \( NO \) = 2 moles
- **Reactants:** 1 mole of \( N_2 + 1 \) mole of \( O_2 = 2 \) moles
- **Change in moles (\( \Delta n \)):** \( \Delta n = 2 - 2 = 0 \)

**Relationship:** \( K_p = K_c \)

### Summary of Relationships
1. \( N_2O_3 \rightleftharpoons NO + NO_2 \) → \( K_p = K_c (RT) \)
2. \( NH_3 \rightleftharpoons \frac{1}{2} N_2 + \frac{3}{2} H_2 \) → \( K_c = K_p (RT)^{-1} \)
3. \( 2SO_2 + O_2 \rightleftharpoons 2SO_3 \) → \( K_p = K_c (RT)^{-1} \)
4. \( N_2 + O_2 \rightleftharpoons 2NO \) → \( K_p = K_c \)

### Final Matching
- **List-I**:
1. \( N_2O_3 \rightleftharpoons NO + NO_2 \) → Matches with \( K_p = K_c (RT) \)
2. \( NH_3 \rightleftharpoons \frac{1}{2} N_2 + \frac{3}{2} H_2 \) → Matches with \( K_c = K_p (RT)^{-1} \)
3. \( 2SO_2 + O_2 \rightleftharpoons 2SO_3 \) → Matches with \( K_p = K_c (RT)^{-1} \)
4. \( N_2 + O_2 \rightleftharpoons 2NO \) → Matches with \( K_p = K_c \)