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.