The mathematical expression of the rate of reaction on concentration terms of reactants is known as rate expression or rate equation or rate law.

For reaction \(A + B \rightarrow Products\), the rate equation is

\[rate ­\propto [A] [B]\]

\[rate = K [A] [B]\]

K is known as specific rate constant or rate per unit concentration of the reactants.

Units of rate constant are \((mole)^{1−n} (litre)^{n−1} s^{−1}\).

Rate law for any reaction cannot be predicted by looking at the balanced chemical reaction, that is, theoretically but must be determined experimentally.

Several chemical reactions take place in a sequence

of steps and the overall rate of reaction is governed

by the slowest step.

In certain cases, the slowest or rate-determining step may involve the formation of an unstable intermediate

from the reactant molecules. The total number of reactant molecules taking part in the slowest step may involve the formation of an unstable intermediate. The total number of reactant molecules taking part in the slowest step or limiting step in the formation of intermediate species is known as the molecularity of the reaction.

In a reaction the rate expression is rate = K[A][B]^2/3 , the order of reaction is

5/3

The correct answer is option 3. 5/3.

The order of a reaction refers to the power to which the concentration of a reactant is raised in the rate law. It indicates how the rate of the reaction depends on the concentration of each reactant. For the given reaction:

\(\text{rate} = k[A][B]^{2/3} \)

Here:

\( k \) is the rate constant.

\([A]\) is the concentration of reactant A.

\([B]\) is the concentration of reactant B.

The rate expression tells us how the rate of reaction depends on the concentrations of reactants. To determine the overall order of the reaction, you sum the exponents of the concentration terms:

The order for \([A]\) is 1 (since \([A]\) is equivalent to \([A]^1\)).

The order for \([B]\) is \(\frac{2}{3}\).

The overall order of the reaction is the sum of the individual orders with respect to each reactant:

\(\text{Overall Order} = 1 + \frac{2}{3}\)

\(1 + \frac{2}{3} = \frac{3}{3} + \frac{2}{3} = \frac{5}{3}\)

Therefore, the overall order of the reaction is: 5/3

This means the rate of the reaction is dependent on the concentrations of \( [A] \) and \( [B] \) such that the combined effect of their concentrations is to the power of \( \frac{5}{3} \).