In the rate equation

Rate = k [A]^x [B]^y

x and y indicate how sensitive the rate is to the change in concentration of A and B. Sum of these exponents, i.e., x + y gives the overall order of a reaction whereas x and y represent the order with respect to the reactants A and B respectively.

Hence, the sum of powers of the concentration of the reactants in the rate law expression is called the order of that chemical reaction. Order of a reaction can be 0, 1, 2, 3 and even a fraction. A zero-order reaction means that the rate of reaction is independent of the concentration of reactants.

Another property of a reaction called molecularity helps in understanding its mechanism. The number of reacting species (atoms, ions or molecules) taking part in an elementary reaction, which must collide simultaneously in order to bring about a chemical reaction is called molecularity of a reaction.

Calculate the overall order of a reaction which has the following rate expression.

Rate = k[A]^{\(\frac{5}{2}\)}[B]^-1

\(\frac{3}{2}\)

The correct answer is option 3. \(\frac{3}{2}\).

In chemical kinetics, the rate law of a reaction provides a relationship between the reaction rate and the concentration of reactants. The rate law is typically expressed in the form:

\(\text{Rate} = k[A]^m[B]^n \)

where:

\(k\) is the rate constant,

\([A]\) and \([B]\) are the concentrations of the reactants,

\(m\) and \(n\) are the orders of the reaction with respect to each reactant.

Determining Overall Order

The exponent of \([A]\) in the rate law is the order with respect to \([A]\). In this case, it’s \(\frac{5}{2}\). The exponent of \([B]\) in the rate law is the order with respect to \([B]\). In this case, it’s \(-1\).

The overall order of the reaction is the sum of the individual orders with respect to each reactant. For the given rate expression:

\(\text{Rate} = k[A]^{5/2}[B]^{-1}\)

Add the exponents:

\(\text{Overall order} = \frac{5}{2} + (-1)\)

\(\text{Overall order} = \frac{5}{2} - \frac{2}{2} = \frac{3}{2}\)

Exponents in Rate Law: The exponents in the rate law indicate how the rate of the reaction changes with changes in the concentration of each reactant. Positive exponents indicate a direct relationship (rate increases with concentration), while negative exponents indicate an inverse relationship (rate decreases with concentration).

Overall Order: It reflects the combined effect of all reactants on the reaction rate. In this case, the overall order of \(\frac{3}{2}\) suggests that the rate of reaction is influenced in a more complex manner by the concentrations of \([A]\) and \([B]\).

The overall reaction order provides insight into how the rate of reaction is expected to change with varying concentrations of the reactants.