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

Q. The rate of a first-order reaction is 0.04 mol litre

^{1}

sec

^{^{- 1}}

at 10 minute and 0.03 mol litre

^{1}

at 20 minute after initiation. Find the half-life of the reaction.

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

The correct option is D 24.1 s K=2.30310×log0.040.03 =2.303×0.12410 (t12=0.693k) ∴ t12=2.303×0.301×102.303×0.124 =24.27s ∴ t12≈24.1 seconds

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

The correct option is D
24.1 s

$K = \frac{2.303}{10} \times l o g \frac{0.04}{0.03}$

$= \frac{2.303 \times 0.124}{10} (t_{\frac{1}{2}} = \frac{0.693}{k})$

$∴ t_{\frac{1}{2}} = \frac{2.303 \times 0.301 \times 10}{2.303 \times 0.124}$

$= 24.27 s$

$∴ t_{\frac{1}{2}} \approx 24.1 seconds$