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.

What is the unit of rate constant for the reaction given in the passage

$s^{-1}$

The correct answer is Option (3) → $s^{-1}$

The units for a rate constant ($k$) depend on the overall order of the reaction. The general formula for the units of $k$ is:

$\text{Unit of } k = (\text{mol L}^{-1})^{1-n} \text{ s}^{-1}$

Where $n$ is the order of the reaction.

Calculation for the Given Reaction

Since the passage states the decomposition of $N_2O_5$ is a first-order reaction ($n = 1$):

Substitute $n = 1$ into the formula:

$\text{Unit of } k = (\text{mol L}^{-1})^{1-1} \text{ s}^{-1}$

Simplify the exponent:

$\text{Unit of } k = (\text{mol L}^{-1})^0 \text{ s}^{-1}$

Any value raised to the power of zero is $1$:

$\text{Unit of } k = 1 \times \text{s}^{-1} = \text{s}^{-1}$