Chemical Kinetics - Result Question 10
11. The reaction, $2 X \rightarrow B$ is a zeroth order reaction. If the initial concentration of $X$ is $0.2 M$, the half-life is $6 h$. When the initial concentration of $X$ is $0.5 M$, the time required to reach its final concentration of $0.2 M$ will be
( 2019 Main, 11 Jan II)
(a) $7.2 h$
(b) $18.0 h$
(c) $12.0 h$
(d) $9.0 h$
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Answer:
Correct Answer: 11. (b)
Solution:
- For zero order reaction,
$ \left[A _0\right]-\left[A _t\right]=k t $
where, $\left[A _0\right]=$ initial concentration
$\left[A _t\right]=$ final concentration at time ’ $t$ '
$k=$ rate constant
Also, for zero order reaction, $t _{1 / 2}=\frac{\left[A _0\right]}{2 k}$
Given, $t _{1 / 2}=6 h$ and $\left[A _0\right]=0.2 M$
$ \begin{aligned} & \therefore \quad 6=\frac{0.2}{2 k} \ & \text { or, } \quad k=\frac{0.2}{2 \times 6}=\frac{1}{60} \end{aligned} $
Now, from Eq. (i)
$ \left[A _0\right]-\left[A _t\right]=k t $
Given, $\left[A _0\right]=0.5 M,\left[A _t\right]=0.2 M$
$\begin{aligned} \therefore \quad 0.5-0.2 & =\frac{1}{60} \times t \quad\left[\because k=\frac{1}{60}\right] \\ 0.3 & =\frac{1}{60} \times t \\ t & =0.3 \times 60=18 \mathrm{~h}\end{aligned}$
BETA
