If the rate expression for a reaction is $\frac{\mathrm{dx}}{\mathrm{dt}}=K{\left[A\right]}^{\frac{1}{2}}{\left[B\right]}^{\frac{3}{2}},$the overall order of the reaction is

From the rate law, the rate expression of a reaction is  $\frac{\mathrm{dx}}{\mathrm{dt}}=K{\left[A\right]}^{\frac{1}{2}}{\left[B\right]}^{\frac{3}{2}},$

Then the sum of the powers are raised to the concentrations of the reactants is called an order. It is denoted by the letter “n”. To the given reaction,

$\mathrm{n}=\frac{1}{2}+\frac{3}{2}=\frac{4}{2}=2$

Therefore, order of the reaction is 2.