Question

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

Answer 1

Hint: First order reaction is the reaction that depends on the concentration of only one reactant. Other reactants can be present, but each will be zero-order. First order reaction is a unimolecular reaction.

Complete step by step solution
In the given question it is said that reaction is a first order reaction and the concentration of the reactant decreased from $ 0.8M $ to $ 0.4M $ in $ 15 $ minutes.
So, at $ t = 0 $ concentration is $ 0.8M $ of the reactant
And at $ t = 15\min $ , concentrate the reactant $ 0.4M $ . We can conclude that concentration is decreased by half at $ t = 15\min $ . So, Half life $ {\left( t \right)_{\dfrac{1}{2}}} $ is $ 15 $ minute.
We have to find the time to decrease the concentration from $ 0.1M $ to $ 0.025M $ . For calculating time we can use the concept of half life.
 $ 0.1M\xrightarrow[{{{\left( t \right)}_{\dfrac{1}{2} = 15\min }}}]{}0.05M\xrightarrow[{{{\left( t \right)}_{\dfrac{1}{2} = 15\min }}}]{}0.025M $
Hence, the total time required to decrease the concentration from $ 0.1M $ to $ 0.025M $ is $ 30\min $ .
Thus, the correct option is $ A. $

Additional Information
The half-life of a reaction $ {\left( t \right)_{\dfrac{1}{2}}} $ is the amount of time needed for a reactant concentration to decrease by half compared to its initial concentration. Its application is used in chemistry and medicine to predict the concentration of a substance over. The half-life of a reaction does not depend upon initial concentration. It depends only on the rate constant.

Note:
Order of a reaction is defined as the number of reactants which determine rate of reaction or number of reactants whose molar mass concentration changes during the chemical reaction or also can be defined as it is the sum of exponents raised on active masses of reactants in a rate law equation.
It is an experimental value, it may be zero, negative, or in fraction and order of a reaction depends upon the temperature, pressure and concentration.