Question

A reaction is 50 % complete in 2 hours and 75 % complete in 4 hours. The order of the reaction is?
A. 0
B. 1
C. 2
D. 3

Answer 1

The Order of Reaction refers to the power dependence of the rate on the concentration of each reactant.
- In this question, we need to determine the half-life of the reaction. If the half-life of the reaction is proportional to the initial concentration of the reactant, the reaction is of zero order. If the half time is constant throughout, that is, it is independent of the initial concentration, then the reaction is of first order. For a second order reaction, half-life is inversely proportional to the initial concentration. For a third order reaction, half-life is inversely proportional to the square of the initial concentration.

Complete Solution :
The reaction goes to 50% completion in the first 2 hours. If the initial concentration is A, it becomes half of it, that is, $\dfrac{A}{2}$ in 2 hours.
Then, in the next 2 hours, it becomes $\dfrac{A}{4}$ from $\dfrac{A}{2}$ which means that it again got reduced by half in 2 hours.
This implies that the half-life of the reaction is 2 hours, which is constant. Half-life is constant in the first order reaction.
This in turn means that ${{t}_{1/2}}$ is independent of concentration. Hence, the order of reaction is first order reaction.
So, the correct answer is “Option B”.

Note: For a zero order reaction, the rate of the reaction is independent of the concentration of the species, whereas for a first-order reaction, the rate is dependent on the concentration of a single species. Similarly, for second order reactions, the rate is dependent on the concentration of two species and so on.
- The half-life of a chemical reaction is defined as the time taken for the concentration of a given reactant participating in the reaction to reach 50% of its initial concentration that is the time taken for the reactant concentration to reach half of the initial value. It is usually denoted by the symbol '${{t}_{1/2}}$' and is standardly expressed in seconds.