Under certain conditions, the bromination of cyclohexene follows an unusual rate law:

b. What is the kinetic order with respect to bromine?

Verified step by step guidance

1. Step 1: Understand the rate law provided in the problem. The rate law is given as rate = k_r[cyclohexene][Br2]^2, where k_r is the rate constant, [cyclohexene] is the concentration of cyclohexene, and [Br2] is the concentration of bromine.
2. Step 2: Recall the definition of kinetic order with respect to a reactant. The kinetic order is the exponent of the concentration term for that reactant in the rate law. It indicates how the rate of reaction depends on the concentration of that reactant.
3. Step 3: Identify the exponent of [Br2] in the rate law. In this case, the exponent of [Br2] is 2, as shown in the rate law.
4. Step 4: Conclude that the kinetic order with respect to bromine (Br2) is determined by this exponent. Therefore, the kinetic order with respect to bromine is 2.
5. Step 5: Note that the overall reaction order can be calculated by summing the exponents of all reactants in the rate law, but for this specific question, we are only concerned with the kinetic order of bromine.

Key Concepts

Kinetics of Reactions

Chemical kinetics is the study of the rates of chemical reactions and the factors that affect them. It involves understanding how concentration, temperature, and catalysts influence the speed of a reaction. In this case, the rate law indicates how the concentration of reactants affects the rate of bromination of cyclohexene.

Rate Law

A rate law expresses the relationship between the rate of a chemical reaction and the concentration of its reactants. It is typically formulated as rate = k[A]^m[B]^n, where k is the rate constant, and m and n are the orders of the reaction with respect to reactants A and B. The given rate law for the bromination of cyclohexene shows that the reaction is second order with respect to bromine.

Order of Reaction

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 reaction changes with varying concentrations of reactants. In this scenario, the rate law suggests that the reaction is first order with respect to cyclohexene and second order with respect to bromine, meaning that doubling the concentration of bromine will quadruple the reaction rate.