🧪AP Chemistry Unit 5 – Kinetics

Key Concepts and Definitions

• Kinetics studies the rates of chemical reactions and the factors that influence them
• Reaction rate measures the change in concentration of a reactant or product per unit time
• Rate law expresses the relationship between the reaction rate and the concentrations of reactants
• Reaction order determines how the concentration of a reactant affects the rate of a reaction
• Elementary step represents a single molecular event in a reaction mechanism
• Molecularity refers to the number of molecules that participate in an elementary step
• Activation energy ($E_a$) is the minimum energy required for reactants to form an activated complex and proceed to products
• Catalyst lowers the activation energy of a reaction without being consumed in the process

Reaction Rates and Rate Laws

• Reaction rate can be determined by measuring the change in concentration of a reactant or product over time
• Rate law takes the general form: $\text{Rate} = k[A]^m[B]^n$, where $k$ is the rate constant, $[A]$ and $[B]$ are reactant concentrations, and $m$ and $n$ are reaction orders
• Reaction order can be zero (rate independent of concentration), first (rate directly proportional to concentration), or second (rate proportional to the square of concentration)
• Rate constant ($k$) is specific to a reaction at a given temperature and includes the frequency factor and activation energy
• Differential rate law expresses the rate in terms of the change in concentration over an infinitesimal time interval
• Integrated rate law relates the concentration of a reactant or product to time, allowing for the determination of the rate constant and half-life
• Method of initial rates involves measuring the initial reaction rate at different initial concentrations to determine the rate law and reaction orders
  • Plot the initial rate versus the concentration of each reactant separately to identify the reaction order with respect to each reactant

Factors Affecting Reaction Rates

• Temperature increases the average kinetic energy of molecules, leading to more frequent and energetic collisions and a higher reaction rate
  • Arrhenius equation relates the rate constant to temperature: $k = Ae^{-E_a/RT}$, where $A$ is the frequency factor, $E_a$ is the activation energy, $R$ is the gas constant, and $T$ is the absolute temperature
• Concentration of reactants affects the reaction rate according to the rate law
  • Higher concentrations result in more frequent collisions and a faster reaction rate
• Surface area of solid reactants influences the reaction rate by determining the number of available reaction sites
  • Smaller particle sizes have a higher surface area to volume ratio, leading to faster reactions (powder vs. chunk)
• Pressure affects the reaction rate for gaseous reactants by altering the frequency of collisions
  • Higher pressure increases the concentration of gas molecules, resulting in more collisions and a faster rate
• Catalysts accelerate reactions by providing an alternative pathway with a lower activation energy
  • Homogeneous catalysts are in the same phase as the reactants (acid-base catalysis), while heterogeneous catalysts are in a different phase (surface catalysis)

Collision Theory and Activation Energy

• Collision theory states that reactions occur when reactant molecules collide with sufficient energy and proper orientation
• Activation energy barrier must be overcome for a reaction to proceed, and the fraction of collisions with enough energy depends on temperature
• Maxwell-Boltzmann distribution describes the distribution of molecular speeds and kinetic energies at a given temperature
  • Higher temperatures shift the distribution towards higher energies, increasing the fraction of molecules with energy greater than the activation energy
• Activated complex (transition state) is a high-energy, unstable intermediate formed when reactants collide with sufficient energy and proper orientation
  • Represents the highest energy point along the reaction coordinate and determines the rate of the reaction
• Potential energy diagram illustrates the energy changes during a reaction, including the activation energy and the overall enthalpy change
  • Exothermic reactions release energy (products have lower potential energy than reactants), while endothermic reactions absorb energy (products have higher potential energy)

Reaction Mechanisms and Rate-Determining Steps

• Reaction mechanism is the sequence of elementary steps that describes how a reaction occurs at the molecular level
• Elementary steps are single molecular events that add up to the overall balanced equation
  • Unimolecular steps involve one molecule (dissociation), bimolecular steps involve two molecules (collision), and termolecular steps involve three molecules (rare)
• Molecularity of an elementary step determines its kinetics and is reflected in the rate law
  • Unimolecular steps have first-order kinetics, bimolecular steps have second-order kinetics, and termolecular steps have third-order kinetics
• Rate-determining step (slowest step) controls the overall rate of a multi-step reaction
  • Reactants must pass through the highest energy transition state, which corresponds to the rate-determining step
• Intermediate is a species formed in one step of a mechanism and consumed in a subsequent step
  • Steady-state approximation assumes that the concentration of an intermediate remains constant during the reaction
• Catalysts participate in the reaction mechanism by providing an alternative pathway with lower activation energy
  • Enzymes are biological catalysts that bind to specific substrates and stabilize the transition state

Integrated Rate Laws and Half-Life

• Integrated rate laws relate the concentration of a reactant or product to time, depending on the reaction order
  • Zero-order: $[A]_t = -kt + [A]_0$, first-order: $\ln[A]_t = -kt + \ln[A]_0$, second-order: $\frac{1}{[A]_t} = kt + \frac{1}{[A]_0}$
• Half-life ($t_{1/2}$) is the time required for the concentration of a reactant to decrease by half
  • For first-order reactions, half-life is independent of initial concentration: $t_{1/2} = \frac{\ln 2}{k}$
• Pseudo-first-order reactions have an excess of one reactant, making the reaction kinetics appear first-order with respect to the limiting reactant
  • Pseudo-rate constant ($k_{\text{pseudo}}$) incorporates the concentration of the excess reactant: $k_{\text{pseudo}} = k[\text{excess}]$
• Radioactive decay follows first-order kinetics, with the decay constant ($\lambda$) related to the half-life: $t_{1/2} = \frac{\ln 2}{\lambda}$
  • Activity of a radioactive sample decreases exponentially with time: $A_t = A_0e^{-\lambda t}$, where $A_0$ is the initial activity

Catalysts and Enzyme Kinetics

• Catalysts accelerate reactions by lowering the activation energy without being consumed
  • Homogeneous catalysts (acid-base) are in the same phase as reactants, while heterogeneous catalysts (surface) are in a different phase
• Enzymes are protein catalysts that bind to specific substrates and stabilize the transition state
  • Active site is the region of an enzyme where the substrate binds and the reaction occurs
• Michaelis-Menten kinetics describes the rate of enzyme-catalyzed reactions
  • Reaction rate depends on the concentration of the enzyme-substrate complex: $v = \frac{v_{\max}[S]}{K_M + [S]}$, where $v_{\max}$ is the maximum rate and $K_M$ is the Michaelis constant
• Lineweaver-Burk plot (double-reciprocal plot) is used to determine $v_{\max}$ and $K_M$ from experimental data
  • Plot $\frac{1}{v}$ versus $\frac{1}{[S]}$ to obtain a straight line with intercepts related to kinetic parameters
• Enzyme inhibitors reduce the activity of enzymes by binding to the active site (competitive) or elsewhere on the enzyme (noncompetitive)
  • Competitive inhibitors increase $K_M$ without affecting $v_{\max}$, while noncompetitive inhibitors decrease $v_{\max}$ without changing $K_M$
• Allosteric regulation involves the binding of effectors at sites other than the active site, leading to conformational changes that alter enzyme activity
  • Positive allosteric effectors increase enzyme activity, while negative allosteric effectors decrease activity

Real-World Applications and Lab Techniques

• Chemical kinetics plays a crucial role in understanding and optimizing various processes, such as chemical synthesis, drug design, and environmental remediation
• Catalytic converters in automobiles use heterogeneous catalysts (platinum, palladium, rhodium) to convert pollutants (CO, NO$_x$, hydrocarbons) into less harmful substances (CO$_2$, N$_2$, H$_2$O)
• Enzyme kinetics is essential for developing new drugs and understanding metabolic pathways
  • Inhibitors can be designed to target specific enzymes involved in disease processes (protease inhibitors for HIV, acetylcholinesterase inhibitors for Alzheimer's)
• Spectrophotometry measures the absorbance of light by a sample to determine the concentration of a reactant or product over time
  • Beer-Lambert law relates absorbance to concentration: $A = \epsilon bc$, where $\epsilon$ is the molar attenuation coefficient, $b$ is the path length, and $c$ is the concentration
• Stopped-flow technique allows for the study of fast reactions by rapidly mixing reactants and measuring the absorbance at short time intervals
  • Useful for investigating enzyme kinetics and fast chemical reactions (protein folding, electron transfer)
• Temperature jump (T-jump) method involves rapidly heating a sample to initiate a reaction and measuring the relaxation of the system to equilibrium
  • Provides information about the activation energy and the rate constants of elementary steps in a reaction mechanism