Question:
For a certain first order reaction $32 \%$ of the reactant is left after $570 \mathrm{~s}$. The rate constant of this reaction is $\times 10^{-3} \mathrm{~s}^{-1}$. (Round off to the Nearest $\overline{\text { Integer) }}$.
[Given : $\log _{10} 2=0.301, \ln 10=2.303$ ]
Solution:
For $1^{\text {st }}$ order reaction,
$\mathrm{K}=\frac{2.303}{\mathrm{t}} \cdot \log \frac{\left[\mathrm{A}_{0}\right]}{\left[\mathrm{A}_{\mathrm{t}}\right]}=\frac{2.303}{570 \mathrm{sec}} \cdot \log \left(\frac{100}{32}\right)$
$=1.999 \times 10^{-3} \mathrm{sec}^{-1} \approx 2 \times 10^{-3} \mathrm{sec}^{-1}$
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