Question

The reaction \[A + 3B \to 2C\] obeys the rate equation:
\[{\text{Rate = k[A}}{{\text{]}}^{\dfrac{{\text{1}}}{{\text{2}}}}}{{\text{[B]}}^{\dfrac{{\text{3}}}{{\text{2}}}}}\]
The order of the reaction is?

Answer 1

Hint: In order to find the order of the rate equation given,
i.e., \[{\text{Rate = k[A}}{{\text{]}}^{\dfrac{{\text{1}}}{{\text{2}}}}}{{\text{[B]}}^{\dfrac{{\text{3}}}{{\text{2}}}}}\], we must first know what an order of the reaction is the sum of the exponents of the concentrations of all the reactants.

Complete Solution :
Let us first understand what the rate of the reaction is. Rate is defined as the speed with which the formation of the product from the reactants can take place in a chemical reaction. Rate of the reaction is given as follows:
\[{\text{Rate = k[A}}{{\text{]}}^a}{{\text{[B]}}^b}\]
Where [A] and [B] are concentrations of the reactants A and B. The exponents a and b are the orders of the reactants A and B respectively.
Now let us see what an order of a reaction is. Order of the reaction is the sum of the exponents of the concentrations of all the reactants.
Let us see some of the characteristics of the order of reaction:
- Order of a reaction will give the number of species whose concentration can affect the reaction rate directly.
- Order can be obtained by adding the powers of concentration terms which are present in the rate equation.
- The order of a reaction can be in the integral form, fractional form or even zero value.
- Order of reaction can be obtained with the help of the reactant concentration and not the product concentration.
The rate of the reaction is given as
\[{\text{Rate = k[A}}{{\text{]}}^{\dfrac{{\text{1}}}{{\text{2}}}}}{{\text{[B]}}^{\dfrac{{\text{3}}}{{\text{2}}}}}\]
From the above rate, we have to add the powers of the concentration in order to obtain the product.
\[Order = \dfrac{1}{2} + \dfrac{3}{2} = 2\]
So, the correct answer is “Order of reaction is 2”.

Note: Order of the reaction can be determined by different methods such as
- Integral method.
- Graphical method.
- Differential method.