Study Guide for Finding Rate Laws from Reaction Mechanisms

Understanding Rate Laws from Reaction Mechanisms

Introduction to the Lesson

• The focus of this lesson is on how to derive the rate law associated with chemical reactions from their mechanisms.

Key Concepts

• Rate Law: A mathematical expression that relates the rate of a reaction to the concentration of the reactants.

• Reaction Mechanism: A detailed description of the individual steps that occur during a chemical reaction. Each step in the mechanism reveals how the reactants are converted into products.

Steps to Derive Rate Law from Mechanisms

1. Identify Elementary Steps

   • An elementary step is a single stage of the reaction mechanism that describes one process of breaking bonds, forming bonds, or both.

2. Determine Rate-Determining Step (RDS)

   • The rate-determining step is the slowest step in a reaction mechanism and effectively controls the overall rate of the reaction.

   • If the RDS is simple, it dictates the rate law directly.

3. Write the Rate Law

   • The rate law expression is generally of the form: $\text{Rate} = k [A]^m [B]^n$ where:

     • $k$ = rate constant

     • $[A]$ and $[B]$ = concentrations of reactants

     • $m$ and $n$ = orders of the reaction with respect to each reactant, corresponding to their stoichiometric coefficients in the RDS.

4. Use Intermediates

   • If the RDS involves an intermediate (a species produced in one step and consumed in another), its concentration must be expressed in terms of the concentrations of other reactants.

5. Final Rate Expression

   • After substituting for intermediates, formulate the complete rate law and ensure it reflects the stoichiometry of the RDS.

Example

• Consider a simple two-step reaction:

  • Step 1 (Fast): $A + B \xrightarrow{k_1} C$

  • Step 2 (Slow): $C \xrightarrow{k_2} D$

From the example:

1. Identify the RDS:

   • The slow step is the second step, thus the rate law is based on the concentration of species from this step.

2. Write Rate Law for RDS:

   • $\text{Rate} = k_2 [C]$

3. Substitute for Intermediate If Necessary:

   • If $C$ is an intermediate, express it in terms of $A$ and $B$ using the fast step.

4. Final Rate Law:

   • After performing the substitution, we derive the complete rate law for the reaction.

Conclusion

• Deriving the rate law from a reaction mechanism requires identifying the rate-determining step, writing the associated rate law, and considering any intermediates. Practicing multiple examples is crucial for mastery of this topic.