Find the order of reaction having rate constant 1.5 × 10−3 L−1 mol s−…

The correct answer is Option (1) → Zero

The rate of a reaction is the change in concentration per unit time, so its unit is always mol L⁻¹ s⁻¹. The unit of the rate constant k changes with the order, and it can be worked out from the rate law.

For a reaction of order n:

    \( \displaystyle \text{Rate}=k[\mathrm{A}]^{n}\quad\Rightarrow\quad k=\frac{\text{Rate}}{[\mathrm{A}]^{n}} \)

Putting in the units:

    \( \displaystyle \text{Unit of }k=\frac{\mathrm{mol\,L^{-1}\,s^{-1}}}{(\mathrm{mol\,L^{-1}})^{n}}=(\mathrm{mol\,L^{-1}})^{1-n}\,\mathrm{s^{-1}} \)

For a third order reaction (n = 3) the same rule gives:

Third order (n = 3): Rate = k[A]³

    \( \displaystyle \text{Unit of }k=\frac{\mathrm{mol\,L^{-1}\,s^{-1}}}{\mathrm{mol^{3}\,L^{-3}}}=\mathrm{mol^{-2}\,L^{2}\,s^{-1}} \)

The given unit, L⁻¹ mol s⁻¹, is mol L⁻¹ s⁻¹ written in a different order. It is the same as the unit of rate, so the reaction is of zero order.

Shortcut: When k has the same unit as the rate (mol L⁻¹ s⁻¹), the order is zero.

NCERT (2026-27 edition):
Units of Rate Constant – …