Question

In a first order reaction the concentration of the reactant decreases from $ 0.8 $ M to $ 0.4 $ M in $ 15 $ minutes. The time taken for the concentration to change from $ 0.1M $ to $ 0.025 $ M is?
(A) $ 30 $ minutes
(B) $ 60 $ minutes
(C) $ 7.5 $ minutes
(D) $ 15 $ minutes

Answer 1

Hint :To proceed with this question, first we will understand the term or the meaning of the first order reaction. Also don’t forget to keep in mind the half-life period, it plays an important role in determining the concentrations and the time of reductions of the reactant at a particular rate.

Complete Step By Step Answer:
So, a first order reaction can be defined as the reaction which depends on the concentration of one of the reactants i.e. a unimolecular reaction.
So, moving ahead with our question:
As we are given that the concentration of the reactant decreases from $ 0.8 $ M to $ 0.4 $ M in $ 15 $ minutes i.e. the concentration of the reactant decreases to its half concentration in the $ 15 $ minutes. Thus, we can say, it is the half-life period.
So, the half-life period i.e. $ {T_{\dfrac{1}{2}}} $ $ = $ $ 15 $ Minutes.
Therefore, by using the concept of half-life:
For the concentration to change from $ 0.1M $ to $ 0.025 $ M requires two half-life.
So, our required time will be $ 2 \times {T_{\dfrac{1}{2}}} $
I.e. by putting the values: $ 2 \times 15 $
 $ = 30 $ Minutes.
Thus, the correct answer is option A. i.e. $ 30 $ Minutes. Therefore, the time taken for the concentration to change from $ 0.1M $ to $ 0.025 $ M is $ 30 $ minutes.

Note :
There are some important facts that we should recall about the half-life of the first order reaction. So half-life is the time taken by the chemical species i.e. reactant to decrease its concentration to the half of its initial concentration. And the half-life of the first order reaction is independent of the concentration of the reactant and is constant over time.