Rate of reaction
Consider a general reaction: aA + bB → cC + dD
where a, b, c and d are the stoichiometric coefficients of reactants and products. The rate expression for this reaction is Rate ∝ [A]x[B]y
where exponents x and y may or may not be equal to the stoichiometric coefficients (a and b) of the reactants. Above equation can also be written as Rate = k[A]x[B]y
Sum of these exponents, i.e., 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.
\( \displaystyle -\frac{d[\mathrm{R}]}{dt}=k[\mathrm{A}]^x[\mathrm{B}]^y \)
The above equation is known as differential rate equation, where k is a proportionality constant called rate constant. The equation, which relates the rate of a reaction to concentration of reactants is called rate law or rate expression.
In the rate law expression reaction rate is given in terms of molar concentration of reactants with each term raised to some power, which may or may not be same as the stoichiometric coefficient of the reacting species in a balanced chemical equation. For example:
2NO2(g) + O2(g) → 2NO3(g)
The rate of this reaction is measured as a function of initial concentrations either by keeping the concentration of one of the reactants constant and changing the concentration of the other reactant or by changing the concentration of both the reactants. The results obtained are tabulated in table below:
| Experiment | Initial [NO2]/mol L−1 | Initial [O2]/mol L−1 | Initial rate of formation of [NO3]/mol L−1s−1 |
| 1 | 0.25 | 0.25 | 0.090 |
| 2 | 0.50 | 0.25 | 0.360 |
| 3 | 0.25 | 0.50 | 0.180 |
| 4 | 0.50 | 0.50 | 0.720 |
Which of the following are the units of rate constant for second order reaction?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 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 (1) and (4). Option (2) is the zero order unit, which leaves Option (3).
Why the other options are incorrect
Option (1) mol−1 L s — Incorrect. Time appears as s instead of s−1; no rate constant has this unit.
Option (2) mol L−1s−1 — Incorrect. This is the unit of k for a zero order reaction (n = 0).
Option (4) mol−1 L−1s — Incorrect. Both the volume and the time powers are wrong; it is not the unit for any order.
Note 1: It seems that there is a mistake in the original NTA paper, which prints 2NO2(g) + O2(g) → 2NO3(g) when it should read 2NO(g) + O2(g) → 2NO2(g).
NCERT (2026-27 edition):
Order of a Reaction – …
Note 2: 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 S2 11-05 S1 | – | – | – | – |