Write the rate law and use units of rate

Rate of reaction always has units of concentration per unit time: $\text{Rate} = \frac{\text{molarity}}{\text{time}} = M\,s^{-1}$

First-order reaction

For a first-order reaction: $\text{Rate} = k[A]$

Therefore, $k = \frac{\text{Rate}}{[A]} = \frac{M\,s^{-1}}{M} = s^{-1}$

So, the unit of rate constant for a first-order reaction is: $s^{-1} \quad \text{or} \quad \text{sec}^{-1}$

Zero-order reaction

For a zero-order reaction: $\text{Rate} = k[A]^0 = k$

Hence, the unit of $k$ is same as the unit of rate: $k = M\,s^{-1}$

So, the unit of rate constant for a zero-order reaction is: $M\,\text{sec}^{-1}$

Match with options

Required order: first-order, zero-order

• First-order: $\text{sec}^{-1}$
• Zero-order: $M\,\text{sec}^{-1}$

This matches Option A.

Comparison with stored answer

Stored correct answer: A

My derived answer: A

So, they agree.