Rate of a particular reaction is represented by
\(\text{Rate = }K[A]^0[B]^{2}\)
The unit of rate constant \(K\) in this case will be
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(mol^{-1}L\, \ sec^{-1}\)
The order of a reaction is the sum of the powers of the concentration terms in the rate law. Here
Rate = k[A]0[B]2, so the order = 0 + 2 = 2 (second order).
For a reaction of order n, the units of k are (concentration)1−n time−1:
\( \displaystyle k = \frac{\text{Rate}}{[B]^2} = \frac{\text{mol L}^{-1}\ \text{s}^{-1}}{(\text{mol L}^{-1})^2} = \text{mol}^{-1}\ \text{L s}^{-1} \)
So the unit of k is mol−1 L s−1.
Why the other options are incorrect
Option (2) \(mol\, \ L^{-1}sec^{-1}\) — Incorrect. This is the unit of k for a zero order reaction (it is also the unit of rate itself).
Option (3) \(sec^{-1}\) — Incorrect. This is the unit of k for a first order reaction.
Option (4) \(mol^{-2}L^2sec^{-1}\) — Incorrect. This is the unit of k for a third order reaction, (mol L−1)−2 s−1.
NCERT (2026-27 edition):
Order of a Reaction (Table 3.3: Units of rate constant)
| Reaction | Order | Units of rate constant |
|---|---|---|
| Zero order reaction | 0 | mol L–1 s–1 |
| First order reaction | 1 | s–1 |
| Second order reaction | 2 | mol–1 L s–1 |