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A first order reaction takes \(40 \mathrm{~min}\) for \(30 \%\) decomposition. Calculate \(t_{1 / 2}{ }^*\)
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Verified Answer
\(30 \%\) decomposition means that \(x=30 \%\) of a \(=0.30 \mathrm{a}\) As the reaction is first order, therefore rate
\(\begin{aligned}
&=\frac{2.303}{t} \log \frac{a}{a-x} \\
&=\frac{2.303}{40 \mathrm{~min}} \times \log \frac{100}{100-30}=8.918 \times 10^{-3} \mathrm{~min}^{-1} . \\
&t_{1 / 2}=\frac{0.693}{k}=\frac{0.693}{8.918 \times 10^{-3} \mathrm{~min}^{-1}}=77.7 \mathrm{~min} .
\end{aligned}\)
\(\begin{aligned}
&=\frac{2.303}{t} \log \frac{a}{a-x} \\
&=\frac{2.303}{40 \mathrm{~min}} \times \log \frac{100}{100-30}=8.918 \times 10^{-3} \mathrm{~min}^{-1} . \\
&t_{1 / 2}=\frac{0.693}{k}=\frac{0.693}{8.918 \times 10^{-3} \mathrm{~min}^{-1}}=77.7 \mathrm{~min} .
\end{aligned}\)
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