Question

Write the order of
a.) r = K [A] ${[B]^{\dfrac{1}{2}}}$
b.) r = K [A] ${[B]^{\dfrac{3}{2}}}$
c.) r = K [A] ${[B]^2}$

Answer 1

Hint: The order of a reaction represents the number of those species whose concentration directly affects the rate of a reaction. It can be calculated by adding the powers of the concentrations of all reactants in rate expression.

Complete step by step solution:
First, let us see what is the order of a reaction and how we can calculate it.
The order of a reaction can be defined as the power dependence of rate on the concentration of the reactants. The order of a reaction actually represents the number of those species whose concentration directly affects the rate of a reaction.
It can be calculated by adding the powers of the concentrations of all reactants in rate expression.
We have been given rate expressions. Now lets us calculate their order as -
The first-rate expression is -
a.) r = K [A] ${[B]^{\dfrac{1}{2}}}$
In this rate expression, the reactant A has power = 1 and B = 1/2
So, order = 1 +$\dfrac{1}{2}$
Order = $\dfrac{3}{2}$
The second rate expression is -
b.) r = K [A] ${[B]^{\dfrac{3}{2}}}$
In this rate expression, the reactant A has power = 1 and B = 3/2
So, order = 1 +$\dfrac{3}{2}$
Order = 2
The third rate expression is -
c.) r = K [A] ${[B]^2}$
In this rate expression, the reactant A has power = 1 and B = 2
So, order = 1 + 2
Order = 3
This way we have found orders of all the reactions.

Note: It must be noted that the order of a reaction can be calculated only from reactants and not from products. The order of a reaction can be positive, zero or in fractions. It can be the whole number only. The order of a reaction is applicable in all chemical reactions.