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
    ${\left( {14} \right)^2}$

Answer

Correct option: B.
$42$
b
$t _{1 / 2}=14 \,sec =\frac{\operatorname{ln} 2}{k} \ldots .[$ half-life for $1^{ st}$ order reaction] $k=\frac{\operatorname{In} 2}{14}-(1)$

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 $(2)$,

$\frac{\operatorname{In} 2}{14}=\frac{1}{t} \operatorname{In}(2)^3=\frac{3}{t} \operatorname{In}(2)$

$\frac{1}{14}=\frac{3}{t}$

$t=42 \,sec$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free