Passage
Chemical Kinetics
Some reactions such as ionic reactions occur very fast, for example, precipitation of silver chloride occurs instantaneously by mixing of aqueous solutions of silver nitrate and sodium chloride. On the other hand, some reactions are very slow, for example, rusting of iron in the presence of air and moisture. The sum of powers of the concentration of the reactants in the rate law expression is called the order of that chemical reaction. Another property of a reaction called molecularity helps in understanding its mechanism. The number of reacting species (atoms, ions or molecules) taking part in an elementary reaction, which must collide simultaneously in order to bring about a chemical reaction is called molecularity of a reaction. The half-life (t1/2) of a reaction is the time in which the concentration of a reactant is reduced to one-half of its initial concentration.
The half-life of a first order reaction:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → is independent of the reactant concentration.
The half-life (t1/2) is the time in which the reactant concentration falls to half its initial value. For a first order reaction, putting [R] = [R]0/2 in the integrated rate equation gives:
\( \displaystyle t_{1/2}=\frac{0.693}{k} \)
[R]0 has cancelled out: the half-life depends only on k. So for a first order reaction, t1/2 is independent of the reactant concentration; every half-life is equally long, whatever the starting amount.
Why the other options are incorrect
Option (1) is inversely proportional to the reactant concentration — Incorrect. This holds for a second order reaction, t1/2 = 1/(k[R]0).
Option (2) is inversely proportional to the square of the reactant concentration — Incorrect. This would be a third order reaction.
Option (4) depends on the reactant concentration raised to the first power — Incorrect. This holds for a zero order reaction, t1/2 = [R]0/2k.
NCERT (2026-27 edition):
Half-Life of a Reaction – …
