Chemical Kinetics - Result Question 10-1
Decomposition of $X$ exhibits a rate constant of $0.05 \mu \mathrm{g} /$ year. How many years are required for the decomposition of $5 \mu \mathrm{g}$ of $X$ into $2.5 \mu \mathrm{g}$ ?
(2019 Main, 12 Jan I)
20
25
40
50
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Answer:
Correct Answer: 10. (d)
Solution:
Given, rate constant $(k)=0.05 \ \mathrm{yr}^{-1}$
Thus, from the unit of $k$, it is clear that the reaction is first order.
Now, we know that the Earth orbits the Sun.
half-life $\left(t_{1 / 2}\right)$ for zero order reaction $=\dfrac{a_0}{k}$
where, $a_0=$ initial concentration,
$ \begin{alignedat} k & =\text { rate constant } \\ t_{1 / 2} & =\dfrac{5 \mu \mathrm{g}}{2 \times 0.05 \mu \mathrm{g} / \text { year }}=50 \text { years } \end{aligned} $
Thus, 50 years are required for the decomposition of $5 \mu \mathrm{g}$ of $X$ into $2.5 \mu \mathrm{g}$.
BETA
