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Q. The half life of a first order reaction is $2000$ years. If the concentration after $8000$ years is $0.02\, M$, then the initial concentration was :

NEETNEET 2022Chemical Kinetics

Solution:

$k =\frac{2.303}{ t } \log \frac{[ A ]_0}{[ A ]_{ t }}$
$\frac{0.693}{2000}=\frac{2.303}{8000} \log \frac{[ A ]_0}{0.02}$
$\therefore[ A ]_0=0.32 \,M$