Q127 / 200 · MHT CET - Medical 2026 (24 April Shift 2) · Chemistry
Which of the statement is correct regarding the half-life of a first-order reaction?
- AIt depends on the initial concentration of reactants
- Correct answerBIt is independent of the initial concentration of reactants
- CIt increases with increasing concentration of product
- DIt decreases with increasing initial concentration of reactants.
Solution
For a first-order reaction, the integrated rate law is given by:
$k = \dfrac{2.303}{t} \log \dfrac{[A]_0}{[A]}$
At half-life, $t = t_{1/2}$ and $[A] = \dfrac{[A]_0}{2}$. Substituting these values:
$k = \dfrac{2.303}{t_{1/2}} \log 2$
$t_{1/2} = \dfrac{0.693}{k}$
The expression for the half-life of a first-order reaction does not contain the initial concentration term $[A]_0$. Thus, the half-life is independent of the initial concentration of the reactants.
Answer: It is independent of the initial concentration of reactants
$k = \dfrac{2.303}{t} \log \dfrac{[A]_0}{[A]}$
At half-life, $t = t_{1/2}$ and $[A] = \dfrac{[A]_0}{2}$. Substituting these values:
$k = \dfrac{2.303}{t_{1/2}} \log 2$
$t_{1/2} = \dfrac{0.693}{k}$
The expression for the half-life of a first-order reaction does not contain the initial concentration term $[A]_0$. Thus, the half-life is independent of the initial concentration of the reactants.
Answer: It is independent of the initial concentration of reactants
Hence, the correct answer is option: 'B'.