MCQ
For the first order reaction, half life is $14\,sec$. The time required for the initial concentration to reduce to $\frac{1}{8}\,th$ of its value is .......... $\sec$
- A$28$
- ✓$42$
- C${\left( {14} \right)^3}$
- D${\left( {14} \right)^2}$
For $1^{st}$ order reaction, $k=\frac{1}{t} \operatorname{ln} \frac{a_0}{a_t}$
given that $a_t=\frac{a_0}{8}$
$k=\frac{1}{t} \operatorname{ln} \frac{a_0}{a_0 / 8}=>k=\frac{1}{t} \operatorname{In} 8-(2)$
From $(1)$ and $(2)$,
$\frac{\operatorname{In} 2}{14}=\frac{1}{t} \operatorname{In}(2)^3=\frac{3}{t} \operatorname{In}(2)$
$\frac{1}{14}=\frac{3}{t}$
$t=42 \,sec$
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