In a first order decomposition reaction, the time taken for the...

In a first order decomposition reaction, the time taken for the decomposition of reactant to one fourth and one eighth of its initial concentration are

t_1

and

t_2(s)

, respectively. The ratio

t_1 / t_2

will :

Options

A $\frac{4}{3}$
B $\frac{3}{2}$
C $\frac{3}{4}$
D $\frac{2}{3}$

Correct answer

D. $\frac{2}{3}$

Step-by-step solution

For

\mathrm{I}^{\text{st }}

order reactionWhen

\mathrm{C}_{\mathrm{t}}=\mathrm{Co} / 4

\begin{aligned}& \mathrm{t}_1=2 \mathrm{t}_{50 \%}. \& \text{ when } \mathrm{C}_{\mathrm{t}}=\mathrm{Co} / 8 \& \mathrm{t}_2=3 \mathrm{t}_{50 \%} \& \text{ so } \frac{\mathrm{t}_1}{\mathrm{t}_2}=\frac{2}{3}\end{aligned}

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