Question

In first order reaction, the concentration of the reactant decreases from ${\rm{0}}{\rm{.8}}\;{\rm{M}}$to ${\rm{7}}{\rm{.5}}\;{\rm{minutes}}$ ${\rm{0}}{\rm{.4}}\;{\rm{M}}$ in ${\rm{15}}\;{\rm{minutes}}$. The time taken for the concentration to change from ${\rm{0}}{\rm{.1}}\;{\rm{M}}$ to${\rm{0}}{\rm{.025}}\;{\rm{M}}$ is:
A) ${\rm{30}}\;{\rm{minutes}}$
B) ${\rm{60}}\;{\rm{minutes}}$
C) ${\rm{7}}{\rm{.5}}\;{\rm{minutes}}$
D) ${\rm{15}}\;{\rm{minutes}}$

Answer 1

We know that if in any reaction, our concentration becomes exactly half in the given time then that time is known as the half-life period of that reaction. The concentration decreases from ${\rm{0}}{\rm{.8}}\;{\rm{M}}$to ${\rm{0}}{\rm{.4}}\;{\rm{M}}$, so actually in our question half-life order is given.

Complete answer:
Let a first order reaction in which A is converted to B. First at the start of the reaction the concentration is ${\rm{0}}{\rm{.4}}\;{\rm{M}}$ but after ${\rm{15}}\;{\rm{minutes}}$ its concentration becomes ${\rm{0}}{\rm{.4}}\;{\rm{M}}$
$A \to B\\\ t = 0\,\,\,\,\,\,\,\,0.{\rm{8}}\;{\rm{M}}\\\ t = 15\,\,\,\,\,\,0.4\;{\rm{M}}$
Since our concentration is exactly half in ${\rm{15}}\;{\rm{minutes}}$then in reaction,
${t_{\dfrac{1}{2}}} = 15\;{\rm{minutes}}$

Hence the correct answer is option is A.

Note: In these first order reactions, the rate of the reaction is proportional to the first power of the concentration of the reactant R. The half-life of a reaction is the time in which the concentration of a reactant is reduced to one half of its initial concentration. It is represented as ${t_{\dfrac{1}{2}}}$. ${t_{\dfrac{1}{2}}}$for a zero-order reaction is directly proportional to the initial concentration of the reactants and inversely proportional to the rate constant. for a first order reaction, half-life period is constant, i.e., it is independent of initial concentration of the reacting species. The half-life of a first order equation is readily calculated from the rate constant and vice versa. There are various examples of first order reaction; the hydrolysis of acetylsalicylic acid and the reaction of t-butyl bromide with water to give t-butanol, hydrolysis of cisplatin.