Question

For the zero order reaction $A\to B+C$, initial concentration of ${}^{\prime }{A}^{\prime }$ is $0.1\text{M}$. If ${}^{\prime }{A}^{\prime }$ is $0.08\text{M}$ after $10\text{minutes}$, then the half-life and completion time for the reaction, are respectively:

• A. $25\text{and}50\text{min}$
• B. $50\text{and}100\text{min}$
• C. $70\text{and}35\text{min}$
• D. $150\text{and}300\text{min}$

Answer 1

The correct option is A $25\text{and}50\text{min}$

At the time of completion $\left(t_c\right)$, the reaction is completed which means $[A{]}_t=0$

From integrated law for zero order reaction,
$[A{]}_t=[A{]}_0-Kt.....eqn\left(1\right)$

Substitute value of $[A{]}_t$ in equation (1),
$0=[A{]}_0-K{t}_c$

$t_c=\frac{[A{]}_0}{K}$

Also we know,
$K=\frac{[A{]}_0-[A{]}_t}{t}$
At $10\text{minutes}$, $\left[A\right]=0.08$
$\therefore$
$K=\frac{0.1-0.08}{10}$
$K=2\times {10}^{-3}{\text{M min}}^{-1}$

Thus,
$t_c=\frac{[A{]}_0}{K}$
$\Rightarrow t_c=\frac{0.1\text{M}}{2\times {10}^{-3}{\text{M min}}^{-1}}$

$\Rightarrow t_c=50\text{min}$

Also half life period,
$t_{\frac{1}{2}}=\frac{[A{]}_0}{2K}$
$\Rightarrow t_{\frac{1}{2}}=\frac{0.1M}{2\times 2\times {10}^{-3}{\text{M min}}^{-1}}$

$\Rightarrow t_{\frac{1}{2}}=25\text{min}$