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Calculate the time needed for reactant to decompose $99.9 \%$ if rate constant of first order reaction is 0.576 minute $^{-1}$.
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Verified Answer
The correct answer is:
12 minutes
$99.9 \%$ of the reaction is complete.
So, if $[A]_0=100$, then $[A]_{\mathrm{t}}=100-99.9=0.1$
$$
\begin{aligned}
\mathrm{t} & =\frac{2.303}{\mathrm{k}} \log _{10} \frac{[\mathrm{A}]_0}{[\mathrm{~A}]_4} \\
& =\frac{2.303}{0.576} \log _{10} \frac{100}{0.1}=\frac{2.303}{0.576} \log _{19}(1000) \\
& =\frac{2.303}{0.576} \times 3 \\
& =11.99 \approx 12 \text { minutes }
\end{aligned}
$$
So, if $[A]_0=100$, then $[A]_{\mathrm{t}}=100-99.9=0.1$
$$
\begin{aligned}
\mathrm{t} & =\frac{2.303}{\mathrm{k}} \log _{10} \frac{[\mathrm{A}]_0}{[\mathrm{~A}]_4} \\
& =\frac{2.303}{0.576} \log _{10} \frac{100}{0.1}=\frac{2.303}{0.576} \log _{19}(1000) \\
& =\frac{2.303}{0.576} \times 3 \\
& =11.99 \approx 12 \text { minutes }
\end{aligned}
$$
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