Question

$25\%$ of a zero order reacton completes in 4 hours. $12.5\%$ of the same reaction completes in:

• A. $6hours$
• B. $4.6hours$
• C. $8hours$
• D. $2hours$

Answer 1

The correct option is D $2hours$

For a zero order reaction,
$\text{Rate constant,}K=\frac{{\left[A\right]}_0-\left[A\right]}{t}$

where,
${\left[A\right]}_0$= initial concentration of reactant
$\left[A\right]$ = concentration of reactant at time 't'
when 25% of a zero order reaction completes,
$\left[A\right]=\frac{75{\left[A\right]}_0}{100}$
$\text{Rate constant,}\left(K\right)=\frac{{\left[A\right]}_0-\frac{75}{100}[A{]}_0}{4}=0.0625[A{]}_0$

When 12.5% of the reaction completes,
$\left[A\right]=\frac{87.5{\left[A\right]}_0}{100}$
$\text{Rate constant,}\left(K\right)=\frac{{\left[A\right]}_0-\frac{87.5}{100}[A{]}_0}{t}$
$t=\frac{{\left[A\right]}_0-\frac{87.5}{100}[A{]}_0}{K}$

$t=\frac{0.125[A{]}_0}{0.0625[A{]}_0}$

$t=2hours$
$\therefore$ hence option D is correct