1. Tardigrade
  2. Question
  3. Chemistry
  4. In the first order reaction, half of the reaction is completed in 100 second. The time for 99 % reaction to occur will be

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. In the first order reaction, half of the reaction is completed in $100$ second. The time for $99\%$ reaction to occur will be

Rajasthan PMTRajasthan PMT 2003Chemical Kinetics

Solution:

Half of the reaction is completed in $100$ second
$\therefore t_{1 / 2}=100 \,sec . $
$\therefore K =\frac{0.693}{100} sec ^{-1}$
For a first order reaction
$K =\frac{2.303}{t} \log \frac{a}{a-x} $
$a=100, \,\,\,x=99, \,\,\,t_{99 \%}=? $
$t_{99 \%}=\frac{2.303}{ K } \log \frac{100}{100-99}$
$=\frac{2.303 \times 100}{0.693} \times \log 100 sec$
$=\frac{2.303 \times 100 \times 2}{0.693}$
$=664.64\, sec$