The unit of rate constant for first order reaction is

The correct answer is Option (4) → \(s^{-1}\)

The unit of a rate constant follows from the rate law. For a reaction of order n, Rate \( = k[\mathrm{A}]^{n} \), so \( k = \text{Rate}/[\mathrm{A}]^{n} \). The rate always has the unit mol L⁻¹ s⁻¹, and concentration has the unit mol L⁻¹.

For a first order reaction, n = 1:

    \( \displaystyle k = \frac{\text{Rate}}{[\mathrm{A}]} = \frac{\mathrm{mol\,L^{-1}\,s^{-1}}}{\mathrm{mol\,L^{-1}}} = \mathrm{s^{-1}} \)

The concentration units cancel, so a first order rate constant has the unit s⁻¹ (time⁻¹) and does not depend on the unit of concentration.

Shortcut: For order n, the unit of k is \( (\mathrm{mol\,L^{-1}})^{1-n}\,\mathrm{s^{-1}} \). With n = 1 the concentration part has power zero, which leaves s⁻¹.

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, where Rate = k.

• Option (2) \(mol^{-1}\, L\, s^{-1}\) — Incorrect. This is the unit of k for a second order reaction, Rate = k[A]².

• Option (3) \(mol\, s^{-1}\) — Incorrect. This has no volume term, so it is not the unit of a rate constant of any order; rates are measured per unit volume.

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: