Match List-I and List-II and choose the correct answer from the codes given below the lists :
List-I : $\qquad$$\qquad$ $\qquad$ $\qquad$ $\qquad$ List-II
$(A.) N_2O_3 ightleftharpoons NO + NO_2\quad$ : (i) $k_p = k_c(RT)$
$(B.) 2NH_3 ightleftharpoons N_2 + 3H_2\quad$ : (ii) $k_c = k_p(RT)$
$(C.) 2SO_2 + O_2 ightleftharpoons 2SO_3\quad$ : (iii) $k_c = k_p$
$(D.) N_2 + O_2 ightleftharpoons 2NO\qquad$ (iv) k_p = $k_c(RT)^2$

Question

Accepted Answer

To justify why Option 1 is the correct answer, we need to analyze the relationship between the equilibrium constants $ k_c $ and $ k_p $ for each reaction given in List-I and List-II. The relationship between $ k_c $ and $ k_p $ is determined by the change in the number of moles of gas ($\Delta n$) in the reaction, where:

$$ k_p = k_c(RT)^{\Delta n} $$

Let's evaluate each reaction:

**(A) $ N_2O_3 \rightleftharpoons NO + NO_2 $:**

- The reaction involves the decomposition of $ N_2O_3 $ into $ NO $ and $ NO_2 $.
- The change in moles of gas, $\Delta n$, is $1 + 1 - 1 = 1$.
- Therefore, $ k_p = k_c(RT)^1 = k_c(RT) $.
- This matches with List-II (i).

**(B) $ 2NH_3 \rightleftharpoons N_2 + 3H_2 $:**

- The reaction involves the decomposition of $ NH_3 $ into $ N_2 $ and $ H_2 $.
- The change in moles of gas, $\Delta n$, is $1 + 3 - 2 = 2$.
- Therefore, $ k_p = k_c(RT)^2 $.
- This matches with List-II (iv).

**(C) $ 2SO_2 + O_2 \rightleftharpoons 2SO_3 $:**

- The reaction involves the combination of $ SO_2 $ and $ O_2 $ to form $ SO_3 $.
- The change in moles of gas, $\Delta n$, is $2 - (2 + 1) = -1$.
- Therefore, $ k_p = k_c(RT)^{-1} = \frac{k_c}{RT} $.
- This matches with List-II (ii).

**(D) $ N_2 + O_2 \rightleftharpoons 2NO $:**

- The reaction involves the combination of $ N_2 $ and $ O_2 $ to form $ NO $.
- The change in moles of gas, $\Delta n$, is $2 - (1 + 1) = 0$.
- Therefore, $ k_p = k_c(RT)^0 = k_c $.
- This matches with List-II (iii).

Now, let's verify why the other options are incorrect:

- **Option 2:** Incorrect because it mismatches the reactions with the wrong relationships. For example, it assigns (ii) to reaction (B), which should be (iv).
- **Option 3:** Incorrect because it assigns (iii) to reaction (B), which should be (iv), and (i) to reaction (C), which should be (ii).
- **Option 4:** Incorrect because it assigns (iii) to reaction (A), which should be (i), and (ii) to reaction (C), which should be (iii).

Thus, Option 1 correctly matches each reaction with the appropriate relationship between $ k_c $ and $ k_p $, making it the correct answer.