Consider the diagram that follows, which represents two steps in an overall reaction. The red spheres are oxygen, the blue ones nitrogen, and the green ones fluorine. (d) Write the rate law for the overall reaction if the first step is the slow, rate-determining step. [Section 14.6]

Verified step by step guidance

1. Identify the reactants and products in the first step of the reaction. The first step involves two molecules of O2 reacting to form an intermediate.
2. Recognize that the first step is the slow, rate-determining step. This means the rate law for the overall reaction will be based on this step.
3. Write the rate law for the first step. Since the first step involves two O2 molecules, the rate law will be rate = k[O2][O2] or rate = k[O2]^2.
4. Note that the rate constant (k) is specific to the rate-determining step and the concentrations of the reactants involved in this step.
5. Combine the information to write the overall rate law for the reaction, which is determined by the slowest step: rate = k[O2]^2.

Key Concepts

Rate-Determining Step

The rate-determining step is the slowest step in a reaction mechanism that dictates the overall reaction rate. It acts as a bottleneck, meaning that the speed of the entire reaction cannot exceed the speed of this step. Understanding which step is rate-determining is crucial for writing the rate law, as it involves the concentrations of the reactants in that specific step.

Rate Law

The 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 rate law can be derived from the rate-determining step, highlighting the reactants involved and their respective stoichiometric coefficients.

Elementary Reactions

Elementary reactions are single-step processes that occur in a reaction mechanism. Each elementary reaction has a specific rate law that can be directly derived from its molecularity, which is the number of reactant molecules involved. Understanding elementary reactions is essential for analyzing complex reactions, as they provide insight into how individual steps contribute to the overall reaction mechanism.