Read the passage given below and answer the questions based on it.
The rate of a reaction is concerned with decrease in concentration of reactants or increase in concentration of products per unit time. It can be expressed as instantaneous rate at a particular instant of time and average rate over a large interval of time. A number of factors such as temperature, concentration of reactants and catalyst affect the rate of a reaction. Mathematical representation of rate of a reaction is given by rate law. It has to be determined experimentally and cannot be predicted. Order of a reaction with respect to a reactant is the power of its concentration which appears in the rate law equation. Molecularity is defined only for an elementary reaction. Molecularity and order of an elementary reaction are the same.
75% of a first-order reaction was completed in 32 minutes. 50% of the reaction was completed in
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 16 minutes
For a first order reaction, the half-life does not depend on the starting concentration:
\( \displaystyle t_{1/2}=\frac{0.693}{k} \)
So the same time is needed to go from 100% to 50% as from 50% to 25%. When 75% of the reaction is complete, 25% of the reactant is left, which is two half-lives:
\( \displaystyle 100\%\xrightarrow{t_{1/2}}50\%\xrightarrow{t_{1/2}}25\% \)
The same result from the integrated rate equation:
\( \displaystyle t_{75\%}=\frac{2.303}{k}\log\frac{100}{25}=\frac{2.303\times0.602}{k}=\frac{1.386}{k}=2\,t_{1/2} \)
\( \displaystyle t_{1/2}=\frac{32\ \mathrm{min}}{2}=16\ \mathrm{min} \)
So 50% of the reaction is completed in 16 minutes.
NCERT (2026-27 edition):
Half-Life of a Reaction – …
Note: The same/similar question has been asked in different years by NTA as per the details given below:
| 2026 | 2025 | 2024 | 2023 | 2022 |
|---|---|---|---|---|
| – | – | 15-05 S1 | – | 21-08 S2 |