Which of the following oxides of nitrogen will be the most stable one ?

Options

A. `2NO_2(g) hArr N_2(g) + 2O_2(g) , K = 6.7 xx 10^(16) mol. 1^(-1)`
B. `2NO(g) hArr N_2(g) + O_2(g) , K = 2.2 xx 10^30 mol.1^(-1)`
C. `2N_2O_5(g) hArr 2N_2(g) + 5O_2(g), K = 1.2 xx 10^(34) mol.l^(-1)`
D. `2N_2O (g) hArr 2N_2(g) + O_2(g), K =3.5 xx 10^33 mol.l^(-1)`

Answer

To determine which oxide of nitrogen is the most stable, we can follow these steps:

### Step 1: Understand the Concept of Stability in Chemical Reactions
Stability of a compound is often related to its tendency to decompose. A more stable compound will have a lower tendency to decompose, which means that the backward reaction (the decomposition reaction) is less favorable.

### Step 2: Analyze the Equilibrium Constant
The equilibrium constant (K) for a reaction is defined as the ratio of the concentration of products to the concentration of reactants at equilibrium. For a reaction:
\[ A \rightleftharpoons B \]
The equilibrium constant is given by:
\[ K = \frac{[B]}{[A]} \]

### Step 3: Relate Equilibrium Constant to Stability
For the backward reaction (decomposition), we can express it as:
\[ B \rightleftharpoons A \]
The equilibrium constant for the backward reaction (Kb) is the reciprocal of K:
\[ K_b = \frac{[A]}{[B]} = \frac{1}{K} \]
This means that a lower value of K indicates a higher value of Kb, suggesting that the backward reaction is more favorable, leading to greater stability of the compound.

### Step 4: Compare the Given Options
We need to compare the equilibrium constants of the given oxides of nitrogen. The oxide with the lowest equilibrium constant (K) will be the most stable because it indicates that the backward reaction is favored.

### Step 5: Identify the Correct Option
After analyzing the equilibrium constants provided for the different nitrogen oxides, we find that the oxide with the lowest equilibrium constant is option 1. Therefore, the most stable oxide of nitrogen is nitrogen dioxide (NO2).

### Conclusion
The most stable oxide of nitrogen among the given options is nitrogen dioxide (NO2).

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