🔮Chemical Basis of Bioengineering I Unit 5 – Chemical Kinetics & Reaction Mechanisms

Key Concepts and Definitions

• Chemical kinetics studies the rates of chemical reactions and the factors that influence them
• Reaction rate measures the speed at which reactants are consumed or products are formed over time
• Rate law expresses the relationship between the reaction rate and the concentrations of reactants
• Reaction order determines how the concentration of each reactant affects the rate of the reaction
• Molecularity refers to the number of reactant molecules that participate in an elementary step
• Half-life ($t_{1/2}$) represents the time required for the concentration of a reactant to decrease by half
• Pseudo-first-order reactions occur when one reactant is present in large excess, simplifying the rate law

Reaction Rate Laws and Order

• Rate laws are determined experimentally by measuring the reaction rate at different reactant concentrations
• The general form of a rate law is: $Rate = k[A]^m[B]^n$, where $k$ is the rate constant, $[A]$ and $[B]$ are reactant concentrations, and $m$ and $n$ are the reaction orders
• Zero-order reactions have a rate that is independent of reactant concentrations (enzyme-catalyzed reactions)
• First-order reactions have a rate that is directly proportional to the concentration of one reactant (radioactive decay)
• Second-order reactions have a rate that depends on the concentration of one reactant squared or the product of two reactant concentrations (dimerization of proteins)
• Integrated rate laws describe the concentration of reactants or products as a function of time for different reaction orders
  • Zero-order: $[A]_t = [A]_0 - kt$
  • First-order: $ln[A]_t = ln[A]_0 - kt$
  • Second-order: $\frac{1}{[A]_t} = \frac{1}{[A]_0} + kt$

Factors Affecting Reaction Rates

• Temperature increases reaction rates by providing more kinetic energy for collisions (Arrhenius equation)
• Concentration of reactants affects reaction rates according to the rate law
• Surface area of solid reactants influences reaction rates by increasing the number of available reaction sites
• Pressure changes can affect reaction rates in gaseous systems by altering the frequency of collisions
• Catalysts accelerate reactions by lowering the activation energy without being consumed in the process
• Inhibitors slow down reactions by binding to reactants or catalysts, reducing their effectiveness
• Ionic strength of the solution can impact reaction rates by altering the electrostatic interactions between charged species

Collision Theory and Activation Energy

• Collision theory states that reactions occur when reactant molecules collide with sufficient energy and proper orientation
• Activation energy ($E_a$) is the minimum energy required for a collision to result in a successful reaction
• The Arrhenius equation relates the rate constant ($k$) to the activation energy and temperature: $k = Ae^{-E_a/RT}$, where $A$ is the pre-exponential factor, $R$ is the gas constant, and $T$ is the absolute temperature
• Increasing temperature raises the average kinetic energy of molecules, leading to more collisions with enough energy to overcome the activation energy barrier
• Catalysts provide an alternative reaction pathway with a lower activation energy, increasing the reaction rate without being consumed
• Transition state theory describes the formation of an unstable, high-energy intermediate called the activated complex during the reaction process

Reaction Mechanisms and Elementary Steps

• Reaction mechanisms describe the sequence of elementary steps that lead to the overall reaction
• Elementary steps are single-step processes that cannot be broken down further and have their own rate laws
• The rate-determining step is the slowest elementary step in a reaction mechanism and determines the overall rate law
• Intermediates are species formed during the reaction mechanism but not present in the overall balanced equation
• Steady-state approximation assumes that the concentration of intermediates remains constant throughout the reaction
• Pre-equilibrium approximation applies when an initial fast equilibrium step is followed by a slower rate-determining step
• Molecularity of an elementary step can be unimolecular (single reactant), bimolecular (two reactants), or termolecular (three reactants)

Catalysis in Chemical Reactions

• Catalysts are substances that increase the rate of a reaction without being consumed
• Homogeneous catalysts are in the same phase as the reactants (enzymes in aqueous solutions)
• Heterogeneous catalysts are in a different phase from the reactants (solid catalysts in gas-phase reactions)
• Enzymes are biological catalysts that are highly specific and efficient
• Michaelis-Menten kinetics describes the rate of enzyme-catalyzed reactions: $v = \frac{V_{max}[S]}{K_M + [S]}$, where $v$ is the reaction rate, $V_{max}$ is the maximum rate, $[S]$ is the substrate concentration, and $K_M$ is the Michaelis constant
• Catalytic converters in automobiles use heterogeneous catalysts to convert pollutants into less harmful substances
• Catalyst poisoning occurs when impurities or reaction products bind to the catalyst surface, reducing its effectiveness

Applications in Bioengineering

• Enzyme kinetics is crucial for understanding metabolic pathways and designing biocatalysts
• Drug design involves optimizing the kinetics of drug-target interactions to achieve desired therapeutic effects
• Bioreactor design requires knowledge of reaction kinetics to optimize product formation and minimize side reactions
• Fermentation processes rely on the kinetics of microbial growth and product formation
• Biosensors utilize the kinetics of enzyme-substrate reactions to detect and quantify specific analytes
• Tissue engineering scaffolds can be designed to control the kinetics of cell adhesion, proliferation, and differentiation
• Controlled drug delivery systems exploit the kinetics of drug release to maintain therapeutic levels over extended periods

Problem-Solving Strategies

• Identify the type of reaction (zero-order, first-order, second-order) based on the given rate law or experimental data
• Use integrated rate laws to determine the concentration of reactants or products at a specific time or the rate constant
• Apply the Arrhenius equation to calculate the activation energy or the effect of temperature on the rate constant
• Analyze reaction mechanisms by identifying intermediates, rate-determining steps, and applying steady-state or pre-equilibrium approximations
• Determine the rate law for an overall reaction based on the rate-determining step of the reaction mechanism
• Use the Michaelis-Menten equation to calculate the maximum rate or the Michaelis constant for an enzyme-catalyzed reaction
• Manipulate units consistently throughout calculations, ensuring that the final answer has the correct units (concentration, time, rate)