Read the passage carefully and answer the questions.
The chemical reactions proceed at different rates which depend on various factors like concentration, temperature, etc. Rate law is an expression which relates the rate of reaction with concentration of various reacting species in the reaction. For a first order reaction, the concentration of the reactant after time \( t \) is related with its initial concentration by the relation, \( C = C_0e^{-kt} \). The rate constants for different orders have different expressions. For a first order reaction, \( k =\frac{2.303}{t}\log\frac{a}{a-x} \), where \( a \) is the initial concentration and \( x \) is the extent of reaction.
The quantity k in a rate law expression is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → independent of reactant 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) directly proportional to concentration of reactants. — Incorrect. It is the rate that rises with concentration (for a reaction of order above zero); k does not.
Option (2) inversely proportional to concentration of reactants. — Incorrect. Raising the concentrations does not lower k; the ratio of rate to the concentration terms stays fixed.
Option (3) doubled on increasing the concentration by 10 times. — Incorrect. A tenfold change in concentration leaves k unchanged. The rate constant of many reactions nearly doubles for a 10 °C rise in temperature, which is a different factor altogether.
Note: The same/similar question has been asked in different years by NTA as per the details given below:
| 2026 | 2025 | 2024 | 2023 | 2022 |
|---|---|---|---|---|
| – | 26-05 S2 14-05 S1 | – | – | – |