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KCET · Chemistry · Chemical Kinetics

A first order reaction is half completed in \(45 \mathrm{~min}\). How long does it need \(99.9 \%\) of the reaction to be completed ?

  1. A 7.5 Hours
  2. B 10 Hours
  3. C 20 Hours
  4. D 5 Hours
Verified Solution

Answer & Solution

Correct Answer

(A) 7.5 Hours

Step-by-step Solution

Detailed explanation

\(t_{1 / 2}\) for first order reaction is \(45^{\circ} \mathrm{min}\)
\[
t_{1 / 2}=\frac{0.693}{k} \Rightarrow k=\frac{0.693}{I_{1 / 2}}=\frac{0.693}{45}
\]

\[
\begin{aligned}
t & =\frac{2.303}{k} \log \frac{a}{a-x}=\frac{2.303}{0.693} \times 45 \log \frac{100}{0.1} \\
& =448 \text { min } \approx 7.5 \mathrm{hrs} .
\end{aligned}
\]