Q73 / 180 · NEET 2016 (Phase 1) · Chemistry

The rate of a first-order reaction is $0.04 m o l l^{- 1} s^{- 1}$ at $10$ second and $0.03 m o l l^{- 1} s^{- 1}$ at $20$ seconds after initiation of the reaction. The half-life period of the reaction is:

Correct answer
A
$24.1 s$
B
$34.1 s$
C
$44.1 s$
D
$54.1 s$

Solution

\begin{matrix} R a t e & T i m e \\ 0.04 & 10 \\ 0.03 & 20 \end{matrix}

For first order reaction r

\propto

conc.

\frac{r_{1}}{r_{2}} = \frac{C_{1}}{C_{2}} = \frac{4}{3}

∴ k = \frac{2.303}{t_{2} - t_{1}} \log \frac{C_{1}}{C_{2}}

\Rightarrow \frac{0.693}{t_{1 / 2}} = \frac{2.303}{20 - 10} \log \frac{4}{3}

On solving

t_{1 / 2} = 24.1 s

Hence, the correct answer is option: 'A'.

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