Read the Passage carefully and answer the Questions.
Kinetic studies not only help us to determine the rate of a chemical reaction but also describe the conditions by which the reaction rates can be altered. The factors such as concentration, temperature, pressure and catalyst affect the rate of a reaction. The speed of a reaction or the rate of a reaction can be defined as the change in concentration of a reactant or product in unit time.
Rate = \( k [A]^x [B]^y \)
Here k is the rate constant
\( x + y \) gives the overall order of a reaction, whereas x and y represent the order with respect to the reactants A and B, respectively.
The unit of rate constant for first order reaction is
Answer & explanation
Correct answer: option 4
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) \( mol\, L\, s^{-1} \) — Incorrect. In \( (\mathrm{mol\,L^{-1}})^{1-n}\,\mathrm{s^{-1}} \) mol and L always carry opposite powers, so mol L s−1 is not the unit of k for any order.
Option (3) \( L^{-1}\, s^{-1} \) — Incorrect. It has a volume term without the matching mol term, so it does not fit \( (\mathrm{mol\,L^{-1}})^{1-n}\,\mathrm{s^{-1}} \) 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:
| 2026 | 2025 | 2024 | 2023 | 2022 |
|---|---|---|---|---|
| – | 02-06 S2 02-06 S1 | – | – | – |