Read the passage carefully and answer the Questions.
The concentration dependence of the rate of a reaction is called the differential rate equation. It is not always convenient to determine the instantaneous rate, as it is measured by calculating the slope of the tangent at point 't' in the concentration vs time plot. This makes it difficult to determine the rate and hence the order of the reaction. This difficulty is overcome by integrating the differential rate equation. This integrated rate equation gives a direct relation between concentrations at different times and the rate constant. The integrated rate equations are different for the reactions having different reaction orders.
The rate constant of a reaction is \( 2.1\, mol\, L^{-1}s^{-1} \). What is the order of the reaction?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Zero order
The rate of a reaction is the change in concentration per unit time, so the unit of rate is always mol L−1 s−1.
For a reaction of order n:
\( \displaystyle \text{Rate}=k[\text{A}]^{n},\quad k=\frac{\text{Rate}}{[\text{A}]^{n}} \)
\( \displaystyle \text{Unit of }k=\frac{\mathrm{mol\,L^{-1}\,s^{-1}}}{(\mathrm{mol\,L^{-1}})^{n}}=(\mathrm{mol\,L^{-1}})^{1-n}\,\mathrm{s^{-1}} \)
Zero order (n = 0):
\( \displaystyle \text{Unit of }k=(\mathrm{mol\,L^{-1}})^{1}\,\mathrm{s^{-1}}=\mathrm{mol\,L^{-1}\,s^{-1}} \)
Third order (n = 3):
\( \displaystyle \text{Unit of }k=(\mathrm{mol\,L^{-1}})^{-2}\,\mathrm{s^{-1}}=\mathrm{mol^{-2}\,L^{2}\,s^{-1}} \)
The given rate constant, 2.1 mol L−1 s−1, has the same unit as the rate itself. So the reaction is zero order.
Shortcut: When k has the same unit as the rate (mol L−1 s−1), the rate does not depend on concentration, so the order is zero.
Why the other options are incorrect
Option (2) First order — Incorrect. The unit of k would be s−1.
Option (3) Second order — Incorrect. The unit of k would be mol−1 L s−1.
Option (4) Third order — Incorrect. The unit of k would be mol−2 L2 s−1.
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 |
|---|---|---|---|---|
| 18-05 S1 | 29-05 S1 | – | – | – |