The units of rate of reaction and rate constant are identical for a

Zero order reaction

The correct answer is Option (2) → Zero order reaction

The unit of the rate constant depends on the overall order of the reaction. Only in zero-order reactions is the rate independent of concentration, making the units of rate and the rate constant identical.

Explanation

Option 1: Fractional order reaction

In fractional order reactions, the rate depends on concentration raised to a fractional power. Therefore, the unit of the rate constant differs from that of the rate and includes concentration terms.

Option 2: Zero order reaction

For a zero order reaction:

$\text{Rate} = k$

Since the rate is independent of concentration, the unit of $k$ is the same as the rate. Thus, both have units of concentration per time.

Option 3: First order reaction

For a first order reaction:

$\text{Rate} = k[A]$

Here, $k$ has units of $\text{time}^{-1}$, which differs from rate units ($\text{concentration/time}$).

Option 4: Second order reaction

For a second order reaction:

$\text{Rate} = k[A]^2$

The unit of $k$ becomes $\text{concentration}^{-1} \text{time}^{-1}$, which is different from the rate.