📚Study Guide: Kinetics
Unit 5: Kinetics
Chemical kinetics investigates the rates of chemical reactions and the molecular-level factors that govern them. Understanding kinetics allows chemists to control reaction speeds for industrial processes, biological systems, and environmental applications. This unit covers the methods for measuring reaction rates, the factors affecting rate (concentration, temperature, surface area, catalysts), and the collision model, which states that reactions occur when particles collide with sufficient energy (activation energy, Ea) and proper orientation. Rate laws express the mathematical relationship between reactant concentration and reaction rate; students must be able to determine reaction orders and rate constants from initial rate data or integrated rate laws. The method of initial rates involves comparing experiments where one reactant's concentration changes while others are held constant. Integrated rate laws allow students to calculate concentration changes over time and determine half-lives. The Arrhenius equation connects temperature to the rate constant, revealing that increasing temperature exponentially increases reaction rate by increasing the fraction of molecules with energy >= Ea. Reaction mechanisms, including elementary steps, molecularity, and the rate-determining step, provide a molecular explanation for rate laws. Catalysts increase reaction rates by providing alternative reaction pathways with lower activation energies without being consumed. On the AP exam, kinetics appears in both multiple-choice and free-response questions, frequently requiring graphical analysis, experimental design, and mechanistic reasoning.
Key Concepts
- Reaction Rate: The change in concentration of reactants or products per unit time. Rate can be expressed as -delta[Reactant]/delta t or +delta[Product]/delta t. Rates decrease as reactants are consumed.
- Collision Model: For a reaction to occur, molecules must collide with sufficient energy (>= Ea) and proper orientation. Increasing temperature increases collision frequency and the fraction of molecules exceeding Ea.
- Rate Laws: Rate = k [A]^m [B]^n. The exponents (m, n) are reaction orders determined experimentally, not from stoichiometric coefficients. The overall order is the sum of individual orders. The rate constant k is temperature-dependent.
- Integrated Rate Laws: Zero order: [A]t = -k t + [A]0 (graph [A] vs t is linear). First order: ln[A]t = -k t + ln[A]0 (graph ln[A] vs t is linear). Second order: 1/[A]t = k t + 1/[A]0 (graph 1/[A] vs t is linear).
- Half-Life: For a first-order reaction, t1/2 = 0.693/k and is independent of initial concentration. For zero-order, t1/2 = [A]0/(2k). For second-order, t1/2 = 1/(k [A]0).
- Reaction Mechanisms: A series of elementary steps that sum to the overall reaction. The rate-determining step (slowest step) determines the rate law. Intermediates are produced and consumed within the mechanism.
- Catalysts: Increase reaction rate by lowering activation energy. Homogeneous catalysts are in the same phase as reactants; heterogeneous catalysts are in a different phase (usually solid).
Vocabulary
- Activation Energy (Ea): The minimum energy required for a chemical reaction to occur; the energy barrier between reactants and products.
- Rate-Determining Step: The slowest step in a reaction mechanism; it limits the overall reaction rate and determines the rate law.
- Intermediate: A species that is formed in one elementary step and consumed in a subsequent step; it does not appear in the overall balanced equation.
- Molecularity: The number of molecules participating as reactants in an elementary step (unimolecular, bimolecular, termolecular).
- Reaction Order: The exponent to which a reactant concentration is raised in the rate law; indicates how rate depends on that reactant's concentration.
- Rate Constant (k): The proportionality constant in the rate law; its value depends on temperature and the specific reaction but not on concentrations.
Essential Formulas
- Rate = k [A]^m [B]^n
- Zero Order: [A]t = -k t + [A]0; slope = -k; t1/2 = [A]0/(2k)
- First Order: ln[A]t = -k t + ln[A]0; slope = -k; t1/2 = 0.693/k
- Second Order: 1/[A]t = k t + 1/[A]0; slope = k; t1/2 = 1/(k [A]0)
- Arrhenius Equation: k = A e^(-Ea/(R T))
- Two-Point Arrhenius: ln(k2/k1) = (Ea/R)(1/T1 - 1/T2)
- R = 8.314 J/(mol K)
Common Mistakes
- Using Stoichiometry for Rate Law Exponents: Reaction orders must be determined experimentally from initial rate data. They are often equal to stoichiometric coefficients only for elementary steps.
- Confusing Rate and Rate Constant: The rate of reaction changes as concentrations change. The rate constant k is constant at a given temperature.
- Assuming All First-Order Reactions Have Constant Half-Life: Only first-order reactions have a half-life independent of initial concentration. Zero and second-order half-lives depend on [A]0.
- Including Intermediates in Rate Laws: The rate law should be written in terms of reactants (or products), not intermediates. If the mechanism proposes an intermediate in the rate-determining step, substitute its concentration using the pre-equilibrium approximation.
AP Exam Strategies
- Use the Method of Initial Rates: To find reaction order, divide the rate of one experiment by another where only one reactant concentration changes. The exponent equals the ratio of the logs of the rates divided by the ratio of the logs of the concentrations.
- Identify Linear Plots: If [A] vs t is linear -> zero order. If ln[A] vs t is linear -> first order. If 1/[A] vs t is linear -> second order. Use this to determine order from graphical data.
- Draw and Label Energy Diagrams: For catalyzed vs uncatalyzed reactions, draw two curves with the catalyzed pathway having a lower Ea peak. Label reactants, products, Ea, and delta H.
- Relate Mechanism to Rate Law: If the rate law is Rate = k [A][B], the rate-determining step likely involves one A and one B (bimolecular collision).
Real-World Applications
- Haber-Bosch Process: Iron catalysts lower the activation energy for ammonia synthesis, enabling mass production of fertilizers that sustain global agriculture.
- Food Preservation: Refrigeration slows bacterial growth and enzymatic reactions by reducing kinetic energy and the fraction of molecules exceeding activation energy.
- Catalytic Converters: Heterogeneous catalysts (platinum, palladium, rhodium) in car exhaust systems accelerate the conversion of toxic NOx, CO, and unburned hydrocarbons into N2, CO2, and H2O.