Rucete ✏ AP Chemistry In a Nutshell
10. Kinetics
This chapter explores how fast reactions occur, how they are measured, and what factors affect their rates. It also introduces rate laws, mechanisms, and theories explaining molecular interactions during reactions.
Reaction Rates
• Reaction rate is the change in concentration per unit time, with units of mol L⁻¹ s⁻¹.
• Measured using kinetic curves showing concentration vs. time for reactants or products.
• Rate = ΔC / Δt, where ΔC is change in concentration and Δt is change in time.
• Negative sign used for reactants (disappearance); positive for products (appearance).
Stoichiometry and Rates
• Rates for other substances in the reaction can be calculated using stoichiometric ratios.
• Rate of disappearance of C₂H₆ and appearance of H₂O, O₂, CO₂ can be related by balanced equations.
Factors Affecting Reaction Rates
• Concentration: higher concentrations lead to faster reaction rates (more collisions).
• Temperature: higher temperature increases kinetic energy and number of effective collisions.
• Surface area: finely divided solids react faster than large chunks.
• Catalysts: provide alternative pathways with lower activation energy, increasing rate.
Rate Laws and Reaction Order
• General form: Rate = k[A]^x[B]^y...
• k is the rate constant; x, y are determined experimentally, not from the balanced equation.
• Overall order = sum of all exponents in the rate law.
Determining Rate Laws
• Conduct experiments where one reactant concentration changes while others remain constant.
• Use ratios of rates and concentrations to calculate exponents (orders).
• Units of k depend on overall order.
Example of Rate Law Calculation
• If doubling [A] doubles the rate → first-order in A.
• If doubling [B] quadruples the rate → second-order in B.
• Overall order = 1 + 2 = 3.
Effect of Temperature (Arrhenius Equation)
• k = Ae^(-Ea/RT)
• ln k vs. 1/T gives a straight line with slope -Ea/R (Arrhenius plot).
• Higher temperature → greater rate constant → faster reaction.
Zero-Order Reactions
• Rate is independent of concentration: Rate = k
• [A] = [A]₀ – kt
• Half-life: t₁/₂ = [A]₀ / 2k
• Graph of [A] vs. time is a straight line.
First-Order Reactions
• Rate = k[A]
• Integrated form: ln[A] = ln[A]₀ – kt
• Half-life: t₁/₂ = 0.693 / k (constant regardless of [A])
• ln[A] vs. time gives a straight line with slope –k.
Second-Order Reactions
• Rate = k[A]² or Rate = k[A][B]
• Integrated form: 1/[A] = 1/[A]₀ + kt
• Half-life: t₁/₂ = 1 / (k[A]₀)
• Plot of 1/[A] vs. time yields a straight line.
Reaction Mechanisms
• Mechanism = step-by-step sequence of elementary reactions that add up to overall reaction.
• Intermediates appear in steps but not in the overall reaction.
• Rate law depends on the slowest step (rate-determining step).
Elementary Steps
• Unimolecular: one particle decomposes or rearranges (first-order).
• Bimolecular: two particles collide (second-order overall).
• Termolecular: rare, involves three particles simultaneously.
Identifying the Rate-Determining Step
• The slowest step limits the rate of the overall reaction.
• Must match experimental rate law for a proposed mechanism to be valid.
• Fast steps before slow ones often create intermediates.
Catalysis
• Catalysts provide alternative pathways with lower activation energy (Ea).
• Homogeneous catalyst: same phase as reactants (e.g., aqueous acid in ester hydrolysis).
• Heterogeneous catalyst: different phase (e.g., solid catalyst in gas reaction).
• Enzymes: biological catalysts that work under mild conditions with high specificity.
In a Nutshell
Kinetics describes how fast reactions occur and what factors influence their rates. The rate law connects concentration and speed, while temperature affects reaction rates through activation energy. Mechanisms explain how reactions proceed on a molecular level, with catalysts offering more efficient pathways. Understanding kinetics is essential for controlling chemical processes and designing effective reactions.