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  4. For a certain first order reaction 32 % of the reactant is left after 570 s. The rate constant of this reaction is . × 10-3 s -1. (Round off to the Nearest Integer). [Given: . log 10 2=0.301, ln 10=2.303]

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Q. For a certain first order reaction $32 \%$ of the reactant is left after $570\,\,s$. The rate constant of this reaction is _____. $\times 10^{-3} s ^{-1}$. (Round off to the Nearest Integer).
[Given : $\left.\log _{10} 2=0.301, \ln 10=2.303\right]$

JEE MainJEE Main 2021Chemical Kinetics

Solution:

For $1^{\text {st }}$ order reaction,

$K =\frac{2.303}{ t } \cdot \log \frac{\left[ A _{0}\right]}{\left[ A _{ t }\right]}=\frac{2.303}{570\, sec } \cdot \log \left(\frac{100}{32}\right)$

$=1.999 \times 10^{-3} sec ^{-1} \approx 2 \times 10^{-3} sec ^{-1}$