The rate of a first-order reaction is 0.04\ mol\ l^-1\ s^-1 at 10 seconds and 0.03\ mol\ l^-1\ s^-1 at 20 seconds after initiation of the reaction. The half-life period of the reaction is :

1. 24.1 s

2. 34.1 s

3. 44.1 s

4. 54.1 s

Doubtly Asked 30 Oct 2026 NEET UG 2016 Phase 1 Practice test neet Save WhatsApp Report

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Answer: 1. 24.1 s

Key idea: for a first-order reaction, rate = $k[A]$, so the ratio of rates equals the ratio of concentrations.

$[A]_{10}/[A]_{20}=0.04/0.03=4/3$.

Also $\ln([A]_{10}/[A]_{20}) = k(20-10)$, so

$$k=\frac{\ln(4/3)}{10}=\frac{0.2877}{10}=0.02877\ \mathrm{s^{-1}}$$

$$t_{1/2}=\frac{0.693}{k}=\frac{0.693}{0.02877}\approx 24.1\ \mathrm{s}$$

Doubtly AI · 30 Oct 2026 AI-generated · not yet verified Report

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