Question

What is the concentration of A after \[25\] min?
A.$0.5M$
B.$0.368M$
C.$0.135M$
D.$0.223M$

Answer 1

Hint: We know that the 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.

Complete answer:
In order to answer this question, to calculate the required time as per the question, we will first apply the first order reaction formula to find the rate constant of the reaction, and then we will apply the first order equation to find the concentration. Integrated Rate Law for a First-Order Reaction Integrated rate expressions can be used to derive the rate constant of a reaction in an experimental setting. 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. Here we have ${{K}_{1}}=0.04{{\min }^{-1}}.$
Thus, to find the concentration of A after $25$ min is given by: $\left[ A \right]=\left[ A_{o}^{{}} \right]{{e}^{-{{K}_{1}}t}}$ the differential rate rule for a first-order reaction must be rearranged as follows in order to obtain the integral form of the rate expression for the first-order reaction.
On substitution we get; $\left[ A \right]=\left[ 1.0M \right]{{e}^{-0.04\times 25}}=0.368M$
Therefore, the correct answer is option B.

Note:
Remember that the time for half reaction for a first order reaction is independent of initial concentration of reactants. All radioactive decay is a first order reaction. All first order reactions must follow the form of rate law for all time instants.