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  4. For the first order reaction half-life is 14 sec, the time required for the initial concentration to reduce to 1/8 of its value is

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Q. For the first order reaction half-life is $14\, \sec$, the time required for the initial concentration to reduce to $1/8$ of its value is

J & K CETJ & K CET 2007Chemical Kinetics

Solution:

$N=N_{0} \times\left(\frac{1}{2}\right)^{n}$
$\frac{1}{8} N_{0}=N_{0} \times\left(\frac{1}{2}\right)^{n}$
$n=3$
$T=n \times t_{1 / 2}$
$=3 \times 14=42\, s$