Question

Write the unit of (i) second order reaction and (ii) zero order reaction.

Hint:

Quick rule: Unit of rate constant = $(\text{mol L}^{-1})^{1-n}\text{ s}^{-1}$. For first order ($n=1$), unit becomes s$^{-1}$.

Answer 1

Concept: The units of the rate constant ($k$) depend on the overall order of the reaction ($n$). From the rate law: \[ \text{Rate} = k[\text{Concentration}]^n \] Since rate has units of mol L$^{-1}$ s$^{-1}$, the unit of $k$ becomes: \[ \text{Unit of } k = (\text{mol L}^{-1})^{1-n}\text{ s}^{-1} \]
Step 1: Second order reaction ($n=2$). Substitute $n = 2$: \[ (\text{mol L}^{-1})^{1-2}\text{ s}^{-1} = (\text{mol L}^{-1})^{-1}\text{ s}^{-1} \] \[ = \text{L mol}^{-1}\text{ s}^{-1} \]
Step 2: Zero order reaction ($n=0$). Substitute $n = 0$: \[ (\text{mol L}^{-1})^{1-0}\text{ s}^{-1} = \text{mol L}^{-1}\text{ s}^{-1} \] For zero-order reactions, the unit of rate constant is the same as the unit of rate.
Step 3: Final answers.

• Second order reaction: $\mathbf{L\ mol^{-1}\ s^{-1}}$
• Zero order reaction: $\mathbf{mol\ L^{-1}\ s^{-1}}$