ExamBro
ExamBro
KCET · Chemistry · Chemical Kinetics

The time required for \(60 \%\) completion of a first order reaction is \(50 \mathrm{~min}\).
The time required for \(93.6 \%\) completion of the same reaction will be

  1. A \(100 \mathrm{~min}\)
  2. B \(83.8 \mathrm{~min}\)
  3. C \(50 \mathrm{~min}\)
  4. D \(150 \mathrm{~min}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(150 \mathrm{~min}\)

Step-by-step Solution

Detailed explanation

Time for \(60 \%\) completion \(=50 \mathrm{~min}\) for first order reaction.
Time required for \(93.6 \%\) completion \(=\) ? \(k=\frac{2.303}{50} \log \frac{a}{a-0.6 a} \Rightarrow k=\frac{2.303}{50} \log \frac{a}{0.4 a}\) \(k=\frac{2.303}{50} \log 2.5\)
Also, \(k=\frac{2.303}{x} \log \frac{a}{a-.936 a}\)
\(\therefore \frac{2.303 \log 2.5}{50}=\frac{2.303}{x} \log \frac{a}{0.064 a}\)
\(x=50 \times \frac{\log \frac{1000}{64}}{\log 2.5}\)
\(=50 \times \frac{\log 15.625}{\log 2.5}=\frac{1.19 \times 50}{0.398}=\frac{59.5}{0.398}\)
\(=150 \mathrm{~min}\)