Reaction Rates and Mechanisms: The Progress of Chemical Reactions

Reaction Rates and Equilibrium

The Progress of Chemical Reactions

Chemical reactions proceed at different rates, and understanding these rates is essential for predicting how quickly products form. The study of reaction rates, or kinetics, involves analyzing how the concentration of reactants affects the speed of a reaction and how reactions progress through various steps.

Rate Laws

Definition and Importance

A rate law is an expression that relates the rate of a chemical reaction to the concentration of its reactants. The rate law helps chemists understand how changes in concentration affect the speed of a reaction and is fundamental for controlling chemical processes.

• General form: For a reaction A → B, the rate can be expressed as the change in concentration of A over time: $\text{rate} = \frac{\Delta [A]}{\Delta t}$

• Proportionality: The rate of disappearance of A is proportional to its concentration: $\frac{\Delta [A]}{\Delta t} \propto [A]$

• Specific rate constant (k): The proportionality can be written as: $\text{rate} = k \times [A]$

• Interpretation of k: A large k means products form quickly; a small k means products form slowly.

Order of Reaction

The order of a reaction is the power to which the concentration of a reactant is raised in the rate law. It is determined experimentally and indicates how the rate depends on reactant concentrations.

• First-order reaction: Rate is directly proportional to the concentration of one reactant. $\text{rate} = k[A]$

• Higher-order reactions: For reactions involving more than one reactant, the rate law is: $\text{rate} = k[A]^x[B]^y$

• Overall order: The sum of the exponents x and y gives the overall order of the reaction.

Determining Reaction Order from Experimental Data

To find the order of a reaction, compare how changes in reactant concentration affect the reaction rate using experimental data.

Trial	Initial [A] (mol/L)	Initial Rate (mol/(L·s))
1	0.050	3.0 × 10–4
2	0.10	12 × 10–4
3	0.20	48 × 10–4

By dividing the rate laws for two trials and solving for the exponent, you can determine the reaction order. For example, if doubling [A] causes the rate to quadruple, the reaction is second order in A.

Reaction Mechanisms

Elementary and Multistep Reactions

A reaction mechanism describes the sequence of steps (elementary reactions) by which a chemical reaction occurs. Most reactions proceed through multiple steps, each with its own energy changes.

• Elementary reaction: A single-step process with one activation energy peak and one activated complex.

• Multistep reaction: Involves two or more elementary steps. The overall reaction is the sum of these steps.

• Intermediate: A species produced in one step and consumed in the next; does not appear in the overall equation.

Energy Profile of Multistep Reactions

The energy profile of a multistep reaction shows multiple peaks (activated complexes) and valleys (intermediates). Each peak represents the energy barrier for a step, and each valley represents an intermediate state.

Rate-Determining Step

In a multistep reaction, the rate-determining step is the slowest step, which limits the overall reaction rate. Increasing the rate of this step increases the rate of the entire reaction.

Key Equations

• $\text{Rate} = \frac{\Delta [A]}{\Delta t} = k \times [A]$

• $\text{Rate} = k[A]^x[B]^y$

Glossary of Terms

• Rate law: An expression relating the rate of a reaction to the concentration of the reactants.

• Specific rate constant (k): A proportionality constant relating the concentrations of reactants to the rate of the reaction.

• First-order reaction: A reaction in which the rate is proportional to the concentration of only one reactant.

• Elementary reaction: A reaction in which reactants are converted to products in a single step.

• Reaction mechanism: A series of elementary reactions that take place during the course of a complex reaction.

• Intermediate: A product of one of the steps in a reaction mechanism; it becomes a reactant in the next step.