Question

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

Answer 1

The concept of half life and kinetics is to be used in this question. The half life of the reaction is needed to be found by analysing the data given in the question, and then a conclusion can be made.

Complete step by step answer:
In order to answer our question, we need to learn about the half life and kinetics of a chemical reaction. Order of reaction is an important parameter for every chemical reaction. It is always determined experimentally and cannot be written from the balanced chemical equation. It may be defined as the sum of exponents or powers that are present in the concentration terms are raised in the rate law expression. If, $Rate=k{{[A]}^{m}}{{[B]}^{n}}$, then:
i. The order of the above reaction is equal to $(m + n)$.
ii. The powers or exponents, i.e., m and n have no relation to the stoichiometric coefficients a and b of the balanced chemical equation.
iii. If the sum of the power is equal to one, the reaction is called first order reaction.
iv. The order of a reaction can also be zero or fractional.
Half life is defined as the time which is needed by the reactants to reduce to half of the initial concentration or it is the time required to complete half of the reaction. It is denoted by ${{t}_{1/2}}$.
Now, let us come to our question. Let the initial concentration be ${{A}_{0}}$. In $2$ hours the concentration becomes half of it i.e $\dfrac{{{A}_{0}}}{2}$ and in the next $2$ hours, the concentration becomes half of $\dfrac{{{A}_{0}}}{2}$ that is $\dfrac{{{A}_{0}}}{4}$. So, we can say that $2$ hours is half life for this reaction and since half life is constant, so we can say that reaction is first order.

So, we obtain option B as the correct option.

Note: In the reaction $C{{H}_{3}}COO{{C}_{2}}{{H}_{5}}+{{H}_{2}}O\to C{{H}_{3}}COOH+{{C}_{2}}{{H}_{5}}OH$, it appears as a second order reaction, but the rate equation is $Rate=k[C{{H}_{3}}COO{{C}_{2}}{{H}_{5}}]$, as concentration of water does not get altered much. Hence it is called a pseudo first order reaction.