Read the passage carefully and answer the Questions.

The decomposition of $N_2O_5 (g)$ is given as

$N_2Os (g) → 2NO_2(g) +\frac{1}{2}O_2(g)$

The above reaction is found to be of first order.

Select the correct statement for the half life of the given reaction

Half life is independent of the initial concentration of $N_2O_5$

The correct answer is Option (1) → Half life is independent of the initial concentration of $N_2O_5$

For a first-order reaction, the half-life is given by:

$t_{1/2} = \frac{0.693}{k}$​

From this expression:

• It does not contain the initial concentration of the reactant.
• It is inversely proportional to the rate constant $k$.

 Half life is independent of the initial concentration of N₂O₅ → Correct

 Half life is directly proportional to the initial concentration → Incorrect
 Half life depends on the final concentration of all species → Incorrect
 Half life is directly proportional to the rate constant → Incorrect (it is inversely proportional)