Read the passage carefully and answer the questions :

The speed at which a chemical reaction takes place is called the rate of reaction. The rate of reaction depends on various factors like concentration of the reactants, temperature, etc. The relation between the rate of reaction and the concentration of reacting species is represented by the equation r = k[A]x[B]Y, where x and y are the order of the reaction with respect to the reactants A and B, respectively.

The overall order of the reaction is x ++ y. The rate of reaction can also be increased by the use of a catalyst which provides an alternate pathway of lower activation energy. It increases the rate of forward and backward reaction to an equal extent. It does not alter the Gibbs energy of the reaction.

Q) Calculate the order of a reaction whose Rate = k [A] ^1/2 [B]^3/2 

The correct option is second order.

Step-by-step Explanation:

According to the rate law described in the passage, the relationship between the rate of reaction and the concentration of reacting species is represented by the equation:
Rate = k[A]^x[B]^y
where x and y are the orders of the reaction with respect to the reactants A and B, respectively.

The overall order of the reaction is calculated by taking the sum of the exponents of the concentration terms in the rate law equation:
Overall order = x + y

We are given the rate equation:
Rate = k[A]^1/2[B]^3/2

Comparing this with the general formula, we can identify the individual orders:

$$x=\frac{1}{2}$$

and

$$y=\frac{3}{2}$$

Now, we add these two values to find the overall order of the reaction:

$$\text{Overall order}=\frac{1}{2}+\frac{3}{2}$$

Since the fractions have a common denominator of 2, we can add the numerators directly:

$$\text{Overall order}=\frac{1+3}{2}=\frac{4}{2}=2$$

Since the sum of the exponents is 2, the reaction is of the second order.