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Question: For reaction \(aA\to xP\), when [A] = 2.2mM, the rate was found to be 2.4 mM\({{s}^{-1}}\). On reduc...

For reaction aA→xPaA\to xP, when [A] = 2.2mM, the rate was found to be 2.4 mMs−1{{s}^{-1}}. On reducing the concentration of A to half, the rate changes to 0.6mMs−1{{s}^{-1}}. The order of reaction with respect to A is:
A.1.5
B.2.0
C.2.5
D.3.0

Explanation

Solution

Before answering this question, we should know about the order of reaction. The relationship between the rate of a chemical reaction and the concentration of the species in that reaction is known as the Order of reaction. The reaction order can be obtained with this expression
r=K[A]x[B]yr=K{{[A]}^{x}}{{[B]}^{y}}

Complete answer:
To find the reaction order, one should know the rate equation of the reaction in the question. The composition of a mixture of all the species can easily be obtained as soon as we know the rate equation.
Generally, The reaction order can be obtained with this expression
r=K[A]x[B]yr=K{{[A]}^{x}}{{[B]}^{y}}
Here r is the rate of reaction
k refers to the rate constant of the reaction
[A] [B] is the concentration of the reactants
x and y are the partial order of the reaction
The overall order of the reaction will be obtained by adding all the partial orders of the reaction.
Rate of reaction = [A] a{{[A]}^{\,a}}
Order of a reaction = a
[A] 1{{[A]}_{\,1}} = 2.2 mM
r1{{r}_{1}}= 2.4 mM s−1{{s}^{-1}}
[A] 2 = 2.22[A]{{\,}_{2}}\,=\,\frac{2.2}{2}
r2= 0.6  or can be written like  2.44{{r}_{2}}=\,0.6\,\,or\,can\,be\,written\,like\,\,\frac{2.4}{4}
So, when the concentration of A is decreased to half, the rate of reaction will get decreased by four times.
Rate of reaction = [A] 2{{[A]}^{\,2}}
So, the Order of reaction will be 2.

Option (B) 2 is correct.

Additional information:
There are many ways to determine reaction order-
Initial Rates Method
Integral Method
Differential method

Note:
Some characteristics of reaction order are-
It shows the number of species in the reaction and the rate of reaction is affected by the concentration of them.
In rate expression, we have to add all the exponents of the concentration terms.
It is independent of all the stoichiometric coefficients related to every species in the balanced reaction.
The concentration of reactant defines the reaction order and not the concentration of the product.
The value of reaction order can be 0, can be an integer, or any fraction too.