Question

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

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

Answer 1

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

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 minutes, [A] = 0.08
$\therefore$
$K=\frac{0.1-0.08}{10}$
$K=2\times {10}^{-3}Mmi{n}^{-1}$

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

$t_c=50min$

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

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