Calculate the time needed for reactant to decompose $99.9 \%$ if rate constant of first order reaction is 0.576 minute $^{-1}$.

Question

Aicharya · Accepted Answer

$99.9 \%$ of the reaction is complete. So, if $[A]_0=100$, then $[A]_{\mathrm{t}}=100-99.9=0.1$ $\begin{aligned} \mathrm{t} & =\frac{2.303}{\mathrm{k}} \log _{10} \frac{[\mathrm{A}]_0}{[\mathrm{~A}]_4} \ & =\frac{2.303}{0.576} \log _{10} \frac{100}{0.1}=\frac{2.303}{0.576} \log _{19}(1000) \ & =\frac{2.303}{0.576} 	imes 3 \ & =11.99 \approx 12 	ext { minutes } \end{aligned}$

Calculate the time needed for reactant to decompose $99.9 \%$ if rate constant of first order reaction is 0…

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