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If the rate constant for a first order reaction is $k$, the time ($t$) required for the completion of 99% of the reaction is given by:
A
$t=0.693/k$
B
$t=6.909/k$
C
$t=4.606/k$
D
$t=2.303/k$
Detailed Solution
For a first order reaction: $k=\frac{2.303}{t}\log\frac{[A]_0}{[A]_t}$
For 99% completion, $\frac{[A]_0}{[A]_t}=\frac{100}{1}$
$k=\frac{2.303}{t}\log10^2=\frac{2.303\times2}{t}$
$t=\frac{4.606}{k}$