Recall For the hypothetical reaction \\[3 A+2 B \rightarrow 2 C+3 D \\]the rate was experimentally determined to be\\[\text { Rate }=k[\mathrm{A}]^{1}[\mathrm{B}]^{1}\\].What is the order of the reaction with respect to A? With respect to B? What is the overall order of the reaction? Suggest how many molecules each of A and B are likely to be involved in the detailed mechanism of the reaction.

The rate law is an equation that links the reaction rate with the concentrations of the reactants. For the given hypothetical reaction, the rate law is expressed as \[\text{Rate} = k[\text{A}]^{1}[\text{B}]^{1}\], where \(k\) is the rate constant. This equation tells us how the rate of reaction depends on the concentrations of reactants A and B. Each reactant's concentration is raised to an exponent known as the order.

In this example:

• The exponent for [A] is 1, indicating that the reaction rate changes linearly with the concentration of A.
• Similarly, the exponent for [B] is 1, meaning the rate changes linearly with the concentration of B.

The rate law is essential for understanding how different factors affect the speed of a reaction and for predicting how changes in concentrations will impact the reaction rate.

A reaction mechanism describes the step-by-step sequence of elementary reactions by which overall chemical change occurs. Knowing the detailed mechanism is important because it offers insight into which steps are rate-determining.

For our given reaction, \[3 A + 2 B \rightarrow 2 C + 3 D \], the experimentally determined rate law \[\text{Rate} = k[\text{A}]^{1}[\text{B}]^{1}\] suggests that the mechanism involves one molecule of A and one molecule of B in the rate-determining step. This means that despite the overall stoichiometry showing more molecules, the slowest step in the mechanism likely involves just these two reactant molecules.

Understanding the reaction mechanism can help chemists design experiments and catalysts to control and optimize the reaction rate.

The order of reaction refers to the power to which the concentration of a reactant is raised in the rate law. It's crucial because it indicates whether the concentration of a reactant has a linear, quadratic, or higher-order effect on the reaction rate.

For the given reaction:

• The order with respect to A is 1 (first order).
• The order with respect to B is 1 (first order).
• The overall order is the sum of the individual orders, which is 1 + 1 = 2 (second order).

Being first-order with respect to both A and B means that doubling the concentration of either A or B will double the reaction rate, while doubling both will quadruple the rate. Understanding the order of reaction helps in predicting how changes in reactant concentration will affect the speed of the reaction and is vital for the proper design of chemical processes.