Question

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

• A. $10min$, $20min$
• B. $2\times {10}^{-3}min$, ${10}^{-3}min$
• C. $25min$, $50min$
• D. $250min$, $500min$

Answer 1

Answer: (C)

$25min$, $50min$

For zero order reaction we have:-

$K=\frac{1}{t}\left(\right[A{]}_o-\left[A{]}_t\right)$ $-\left(i\right)$

where, $K$= Rate constant

$t$= time

$[A{]}_o$= concentration of reactant at $t=0$

$[A{]}_t$= concentration of reactant at $t=t$

Now, given at $t=0$ $min,$ $[A{]}_o=0.1M$

& at $t=10$ $min,$ $[A{]}_t=0.08M$

Substituting the values in $e{q}^n\left(i\right)$

$K=\frac{1}{10}(0.1-0.08)$

$=0.02/10=0.002$ $mol{L}^{-1}mi{n}^{-1}$

Now, half life $\left(t_{1/2}\right)$ of a zero order reaction is given by:-

$t_{1/2}=\frac{1}{K}\frac{[A{]}_o}{2}$

$=\frac{0.1}{2\times 0.002}=\frac{100}{4}$

$=25$ $min$

Now, complete time of reaction will be given by:-

$t_o=\frac{[A{]}_o}{K}$

$=\frac{0.1}{0.002}=\frac{100}{2}=50$ $min$