The quantity k in a rate law expression _____

The correct answer is Option (4) → is independent of concentration

In a rate law the rate constant k is the proportionality constant between the rate and the concentration terms:

    \( \displaystyle \text{Rate} = k\,[\mathrm{A}]^{x}[\mathrm{B}]^{y} \)

    \( \displaystyle k = \frac{\text{Rate}}{[\mathrm{A}]^{x}[\mathrm{B}]^{y}} \)

When the concentrations change, the rate changes by the same factor as the denominator, so their ratio k stays the same. k is the rate when every concentration is 1 mol L⁻¹. It depends on the nature of the reaction, the temperature (Arrhenius equation, \( k = A\,e^{-E_a/RT} \)) and the presence of a catalyst, but it is independent of the concentration of the reactants.

Why the other options are incorrect

• Option (1) is independent of temperature — Incorrect. k depends strongly on temperature, as the Arrhenius equation \( k = A\,e^{-E_a/RT} \) shows; for many reactions it nearly doubles for a 10 °C rise.

• Option (2) is called the Arrhenius constant — Incorrect. k is called the rate constant. In the Arrhenius equation it is A that is called the Arrhenius factor or frequency factor (pre-exponential factor).

• Option (3) is dimensionless — Incorrect. The unit of k depends on the order of the reaction, (mol L⁻¹)¹⁻ⁿ s⁻¹: for example mol L⁻¹ s⁻¹ for zero order and s⁻¹ for first order.

Note: The same/similar question has been asked in different years by NTA as per the details given below: