Statement I: The half-life of a first-order reaction depends on the initial concentration of the reactant.
Statement II: The half-life of a first-order reaction is inversely proportional to its rate constant.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Statement I is false but statement II is correct
The half-life (t1/2) is the time in which the concentration of a reactant falls to half its initial value. Putting [R] = [R]0/2 into the integrated first order rate equation gives:
\( \displaystyle t_{1/2}=\frac{0.693}{k} \)
No concentration term is left in this result.
Statement I: The half-life of a first-order reaction depends on the initial concentration of the reactant. — False. t1/2 = 0.693/k contains no [R]0, so for a first order reaction the half-life is independent of the initial concentration. It is the zero order half-life, t1/2 = [R]0/2k, that depends on [R]0.
Statement II: The half-life of a first-order reaction is inversely proportional to its rate constant. — True. In t1/2 = 0.693/k, 0.693 is a number, so t1/2 ∝ 1/k: a larger rate constant means a shorter half-life.
NCERT (2026-27 edition):
3.3.3 Half-Life of a Reaction – “…
\( \displaystyle t_{1/2}=\frac{0.693}{k} \qquad (3.17) \)
… It can be seen that for a first order reaction, half-life period is constant, i.e., it is independent of initial concentration of the reacting species. The half-life of a first order equation is readily calculated from the rate constant and vice versa.”