🧤Physical Chemistry I Unit 11 – Introduction to Chemical Kinetics

Key Concepts and Definitions

• Chemical kinetics studies the rates of chemical reactions and the factors influencing these rates
• Reaction rate measures the change in concentration of reactants or products per unit time
• Rate law expresses the relationship between the reaction rate and the concentrations of reactants
• Rate constant quantifies the speed of a reaction at a given temperature
• Reaction order determines how the concentration of each reactant affects the rate of the reaction
• Elementary step represents a single molecular event in a reaction mechanism
• Molecularity refers to the number of reactant molecules involved in an elementary step (unimolecular, bimolecular, or termolecular)
• Activation energy is the minimum energy required for reactants to overcome and initiate a chemical reaction

Reaction Rates and Rate Laws

• Reaction rates can be expressed as the change in concentration of a reactant or product over time ($\frac{-\Delta[A]}{\Delta t}$ or $\frac{\Delta[B]}{\Delta t}$)
• Rate laws are mathematical expressions that relate the reaction rate to the concentrations of reactants
  • General form: Rate = $k[A]^m[B]^n$, where $k$ is the rate constant, $[A]$ and $[B]$ are reactant concentrations, and $m$ and $n$ are the reaction orders
• Reaction orders can be determined experimentally by measuring the reaction rate at different initial concentrations of reactants
• Zero-order reactions have rates independent of reactant concentrations (Rate = $k$)
• First-order reactions have rates proportional to the concentration of one reactant (Rate = $k[A]$)
• Second-order reactions have rates proportional to the square of the concentration of one reactant or the product of the concentrations of two reactants (Rate = $k[A]^2$ or Rate = $k[A][B]$)
• Pseudo-first-order reactions occur when one reactant is in large excess, making its concentration effectively constant throughout the reaction

Factors Affecting Reaction Rates

• Temperature increases reaction rates by providing more energy for reactants to overcome the activation energy barrier
  • Arrhenius equation relates the rate constant to temperature: $k = Ae^{-E_a/RT}$, where $A$ is the pre-exponential factor, $E_a$ is the activation energy, $R$ is the gas constant, and $T$ is the absolute temperature
• Concentration of reactants affects reaction rates according to the rate law
  • Increasing the concentration of reactants generally increases the reaction rate
• Pressure influences the rates of gas-phase reactions by altering the frequency of molecular collisions
• Catalysts accelerate reactions by providing an alternative pathway with a lower activation energy
  • Homogeneous catalysts are in the same phase as the reactants (enzymes in biochemical reactions)
  • Heterogeneous catalysts are in a different phase from the reactants (solid catalysts in gas-phase reactions)
• Surface area of solid reactants affects the reaction rate by determining the number of available active sites for the reaction to occur

Reaction Mechanisms

• Reaction mechanisms describe the sequence of elementary steps leading from reactants to products
• Elementary steps are single molecular events that occur in a single collision
  • Unimolecular steps involve one reactant molecule (isomerization or dissociation)
  • Bimolecular steps involve the collision of two reactant molecules (most common)
  • Termolecular steps involve the simultaneous collision of three reactant molecules (rare)
• Rate-determining step is the slowest elementary step in a reaction mechanism and determines the overall rate of the reaction
• Intermediates are species formed in one elementary step and consumed in a subsequent step
  • Steady-state approximation assumes that the concentration of intermediates remains constant throughout the reaction
• Pre-equilibrium approximation applies when an initial reversible step reaches equilibrium much faster than the subsequent rate-determining step
• Molecularity of an elementary step can be determined from the balanced chemical equation for that step

Experimental Methods in Kinetics

• Spectroscopic techniques monitor the concentration of reactants or products over time
  • UV-Vis spectroscopy measures the absorption of light by reactants or products
  • Infrared spectroscopy detects changes in the vibrational frequencies of molecules
• Stopped-flow methods rapidly mix reactants and measure the concentration changes on a millisecond timescale
• Flash photolysis initiates reactions using a short pulse of light and monitors the concentration changes using spectroscopic techniques
• Isotopic labeling uses radioactive or stable isotopes to track the progress of a reaction
• Pressure measurements can be used to monitor gas-phase reactions by detecting changes in the total pressure of the system
• Calorimetry measures the heat released or absorbed during a reaction, which can be related to the reaction rate

Mathematical Models and Equations

• Integrated rate laws express the concentration of a reactant or product as a function of time for different reaction orders
  • Zero-order: $[A]_t = [A]_0 - kt$
  • First-order: $\ln[A]_t = \ln[A]_0 - kt$ or $[A]_t = [A]_0e^{-kt}$
  • Second-order: $\frac{1}{[A]_t} = \frac{1}{[A]_0} + kt$
• Half-life is the time required for the concentration of a reactant to decrease by half
  • For first-order reactions, the half-life is independent of the initial concentration: $t_{1/2} = \frac{\ln 2}{k}$
• Collision theory explains reaction rates in terms of the frequency and energy of molecular collisions
  • Arrhenius equation relates the rate constant to the activation energy and temperature
• Transition state theory describes the formation of an activated complex between reactants, which can then decompose into products
  • Eyring equation relates the rate constant to the thermodynamic properties of the transition state

Applications in Real-World Processes

• Enzyme kinetics studies the rates of biochemical reactions catalyzed by enzymes
  • Michaelis-Menten equation describes the relationship between the reaction rate and substrate concentration for enzyme-catalyzed reactions
• Atmospheric chemistry involves the study of kinetics of reactions in the Earth's atmosphere
  • Ozone depletion and formation of photochemical smog are examples of atmospheric chemical processes
• Combustion kinetics deals with the rates of fuel oxidation reactions in engines and power plants
• Polymerization kinetics describes the rates of polymer formation reactions, which are important in the production of plastics and other materials
• Kinetics of drug absorption, distribution, metabolism, and excretion (ADME) is crucial in the development of pharmaceuticals
• Corrosion kinetics studies the rates of metal degradation reactions, which are important in materials science and engineering

Common Pitfalls and Misconceptions

• Confusing reaction rate with the extent of reaction
  • Reaction rate refers to the speed of the reaction, while the extent of reaction describes how much reactant has been consumed or product formed
• Assuming that the rate law can always be determined from the balanced chemical equation
  • The rate law must be determined experimentally, as it may not match the stoichiometry of the overall reaction
• Neglecting the role of intermediates in reaction mechanisms
  • Intermediates can have a significant impact on the overall reaction rate and mechanism
• Overestimating the effect of concentration on reaction rates
  • While increasing concentration generally increases reaction rates, the relationship is not always linear and depends on the specific rate law
• Misinterpreting the meaning of the rate constant
  • The rate constant is not the same as the reaction rate; it is a proportionality constant that relates the rate to the concentrations of reactants
• Ignoring the importance of temperature in reaction kinetics
  • Temperature has a significant effect on reaction rates, as described by the Arrhenius equation
• Confusing the order of a reaction with the molecularity of an elementary step
  • The order of a reaction is an experimentally determined quantity, while the molecularity refers to the number of reactant molecules involved in an elementary step