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Q.
Half life of a First order reaction is 45 minutes. How long does it need to complete 99.9% of the reaction?
NTA AbhyasNTA Abhyas 2020Chemical Kinetics
Solution:
$t _{1 / 2}=45$ minutes
For 1st order reaction $t _{1 / 2}=\frac{0.693}{ k }$
$ \therefore k =\frac{0.693}{45} min ^{-1}=0.0154 min ^{-1} $
Again for 1st order reaction we have
$ k =\frac{2.303}{ t } \log \left[\frac{100}{100-99.9}\right] $
(considering original concentration to be 100)
$ t =\frac{2.303}{ k } \log \left[\frac{100}{0.1}\right] $
$ t=\frac{2.303}{0.0154} \log 1000 $
$t=\frac{2.303}{0.0154} \times 3=448.636$ minutes
$ t =7 \frac{3}{10} \text { hours. } $