What are the units of rate constant for a second order reaction?

The correct answer is Option (2) → mol⁻¹ L s⁻¹

The rate of a reaction is the change in concentration per unit time, so its unit is always mol L⁻¹ s⁻¹. For a reaction of order n:

    \( \displaystyle \text{Rate}=k[\mathrm{A}]^n \quad\Rightarrow\quad k=\frac{\text{Rate}}{[\mathrm{A}]^n} \)

    \( \displaystyle \text{Unit of } k=\frac{\mathrm{mol\,L^{-1}\,s^{-1}}}{(\mathrm{mol\,L^{-1}})^n}=(\mathrm{mol\,L^{-1}})^{1-n}\,\mathrm{s^{-1}} \)

Second order (n = 2):

    \( \displaystyle \text{Rate}=k[\mathrm{A}]^2 \)

    \( \displaystyle \text{Unit of } k=\frac{\mathrm{mol\,L^{-1}\,s^{-1}}}{(\mathrm{mol\,L^{-1}})^2}=\frac{\mathrm{mol\,L^{-1}\,s^{-1}}}{\mathrm{mol^2\,L^{-2}}}=(\mathrm{mol\,L^{-1}})^{1-2}\,\mathrm{s^{-1}}=\mathrm{mol^{-1}\,L\,s^{-1}} \)

So the unit of the rate constant for a second order reaction is mol⁻¹ L s⁻¹ (also written L mol⁻¹ s⁻¹).

Shortcut: Every rate constant carries the time unit s⁻¹, which rules out Options (3) and (4) with s⁻². Option (1) is the zero order unit, which leaves Option (2).

Why the other options are incorrect

• Option (1) mol L⁻¹ s⁻¹ — Incorrect. This is the unit of k for a zero order reaction (n = 0).

• Option (3) mol⁻² L s⁻² — Incorrect. The time unit of a rate constant is always s⁻¹, never s⁻², and the concentration part does not match any order.

• Option (4) mol⁻² L⁻¹ s⁻² — Incorrect. Both the time power and the concentration part are wrong; it is not the unit for any order.

NCERT (2026-27 edition):
Order of a Reaction – …

Note: The same/similar question has been asked in different years by NTA as per the details given below: