The equilibrium constant for some reactions are given below against each of the reaction
(i) `2N_(2)+5O_(2)hArr2N_(2)O_(5) , K=5xx10^(-27)`
(ii) `N_(2)+O+(2)hArr2NO , K=2xx10^(-15)`
(iii) N_(2)+2O_(2)hArr2NO_(2) , K=1.5xx10^(-29)`
Which of the following statement is correct

Options

A. The least stable oxide is `NO_(2)`
B. The most stable oxide is `NO`
C. The stability order is `N_(2)O_(5)gtNO_(2)gtNO`
D. The stablity order is `NO_(2)gtNOgtN_(2)O_(5)`

Answer

To determine which statement is correct regarding the stability of the products based on the given equilibrium constants, we will analyze the reactions and their respective equilibrium constants step by step.

### Step-by-Step Solution:

1. **Identify the Reactions and Equilibrium Constants**:
- (i) \( 2N_2 + 5O_2 \rightleftharpoons 2N_2O_5 \), \( K = 5 \times 10^{-27} \)
- (ii) \( N_2 + O_2 \rightleftharpoons 2NO \), \( K = 2 \times 10^{-15} \)
- (iii) \( N_2 + 2O_2 \rightleftharpoons 2NO_2 \), \( K = 1.5 \times 10^{-29} \)

2. **Analyze the Equilibrium Constants**:
- The equilibrium constant \( K \) indicates the extent of the reaction at equilibrium. A smaller \( K \) value suggests that the reaction favors the reactants, meaning less product is formed and the product is less stable.
- Conversely, a larger \( K \) value indicates that the reaction favors the products, meaning more product is formed and the product is more stable.

3. **Compare the Values of \( K \)**:
- For \( K = 5 \times 10^{-27} \) (reaction i), the product \( N_2O_5 \) is less stable.
- For \( K = 2 \times 10^{-15} \) (reaction ii), the product \( NO \) is more stable than \( N_2O_5 \).
- For \( K = 1.5 \times 10^{-29} \) (reaction iii), the product \( NO_2 \) is the least stable among all.

4. **Determine Stability Order**:
- From the values of \( K \):
- \( NO_2 \) (K = \( 1.5 \times 10^{-29} \)) is the least stable.
- \( N_2O_5 \) (K = \( 5 \times 10^{-27} \)) is more stable than \( NO_2 \).
- \( NO \) (K = \( 2 \times 10^{-15} \)) is the most stable.

5. **Conclusion**:
- The stability order from least stable to most stable is:
- \( NO_2 < N_2O_5 < NO \)
- Therefore, the statement that \( NO_2 \) is the least stable oxide is correct.