Chemical Kinetics

  • Arrhenius equation
  • Rate of reaction
  • Factors affecting rate of reaction
  • Order of reaction
  • Rate law
  • Integrated rate law
  • Half-life of a reaction
  • Collision theory
  • Activation energy
  • Catalysts

Arrhenius equation

  • Developed by Svante Arrhenius in 1889
  • Relates the rate constant of a reaction to temperature
  • Equation: k = A * e^(-Ea/RT)
    • k is the rate constant
    • A is the pre-exponential factor
    • Ea is the activation energy
    • R is the gas constant
    • T is the absolute temperature

Rate of reaction

  • Defines how fast a reactant is used up or how fast a product is formed
  • Measured in terms of concentration change per unit time
  • Formula: Rate = Δ[A]/Δt = -Δ[B]/Δt = Δ[C]/Δt = -Δ[D]/Δt
  • Δ[A] represents the change in concentration of A over time Δt

Factors affecting rate of reaction

  1. Concentration: Increase in concentration leads to an increase in rate of reaction.
  1. Temperature: Higher temperature increases the kinetic energy of particles, leading to higher collision rate and faster reaction.
  1. Surface area: Larger surface area increases the chances of collisions and therefore the rate of reaction.
  1. Catalysts: Speeds up reaction by providing an alternative pathway with lower activation energy.
  1. Nature of reactants: Different substances have different reaction rates due to their chemical properties.
  1. Pressure (for gaseous reactions): Higher pressure leads to more frequent collisions and faster reaction.

Order of reaction

  • Describes the relationship between the rate of a reaction and the concentrations of the reactants
  • Can be zero, first, second, or higher order
  • Example: A + B → C
    • If the rate solely depends on the concentration of A, it is first-order with respect to A.
    • If the rate is proportional to the concentration of A and B combined, it is second-order overall.

Rate law

  • Mathematical expression that relates the rate of a reaction to the concentrations of the reactants
  • General form: Rate = k[A]^m[B]^n
    • k is the rate constant
    • [A] and [B] are the concentrations of reactants A and B
    • m and n are the orders of reaction with respect to A and B, respectively

Integrated rate law

  • Shows how the concentration of a reactant changes over time
  • Different forms for different orders of reaction
  • Example: For a first-order reaction, integrated rate law is ln[A] = -kt + ln[A₀]
    • [A] is the concentration at time t
    • [A₀] is the initial concentration
    • k is the rate constant

Half-life of a reaction

  • Time taken for the concentration of a reactant to decrease to half its initial value
  • Different for different orders of reaction
  • Example: For a first-order reaction, half-life is t₁/₂ = ln(2)/k
    • t₁/₂ is the half-life
    • k is the rate constant

Collision theory

  • Explains how chemical reactions occur
  • States that reactant particles must collide with sufficient energy and proper orientation for a reaction to occur
  • Effective collisions lead to the formation of products

Activation energy

  • Minimum energy required for reactant particles to undergo a chemical reaction
  • Higher activation energy leads to slower reaction rates
  • Determines the rate at which reactants collide and form products

Catalysts

  • Substances that increase the rate of a reaction without being consumed in the process
  • Provides an alternate reaction pathway with lower activation energy
  • Speeds up reactions without being permanently changed in the process
  1. Rate Determining Step
  • In a multi-step reaction, the slowest step is known as the rate determining step.
  • The rate of the overall reaction is determined by the rate of this step.
  • Usually, this step involves the highest activation energy.
  1. Reaction Mechanism
  • A series of elementary reactions that make up the overall reaction.
  • Each elementary reaction has its own rate law and molecularity.
  • The overall rate law can be determined by the rate-determining step.
  1. Molecularity
  • Refers to the number of molecules or ions involved in an elementary reaction.
  • Unimolecular: Involves the decomposition of one molecule.
  • Bimolecular: Involves collisions between two molecules.
  • Termolecular: Involves simultaneous collision between three molecules.
  1. Rate-determining Step Example
  • Example reaction: A + B → C + D
  • Step 1: A + B → X (fast)
  • Step 2: X → C + D (slow)
  • If the second step is the slowest, it becomes the rate-determining step.
  1. Catalysts in Reactions
  • A substance that increases the rate of a chemical reaction by providing an alternative reaction pathway with lower activation energy.
  • Catalysts are not consumed in the reaction and can be used repeatedly.
  • They increase the rate by providing a different mechanism or by stabilizing transition states.
  1. Homogeneous Catalysts
  • Catalysts that are in the same phase as the reactants.
  • Example: Acid-catalyzed reactions, where the acid is present in the same phase as the reactants.
  • Homogeneous catalysts form an intermediate with the reactants.
  1. Heterogeneous Catalysts
  • Catalysts that are in a different phase than the reactants.
  • Example: Platinum catalyst in the catalytic converter of a car, where the reactants are in the gas phase and the catalyst is in the solid phase.
  • Reactants adsorb onto the catalyst surface, undergo reaction, and then desorb as products.
  1. Enzymes as Catalysts
  • Enzymes are biological catalysts that increase the rate of specific biochemical reactions.
  • They are highly specific and can work under mild conditions.
  • Enzymes lower the activation energy required for a reaction to occur.
  1. Rate Determination Using Initial Rates Method
  • Experimentally determining the rate from the initial concentrations of reactants.
  • Calculate the initial rates based on the concentration change over a short time interval.
  • Comparing the initial rates of different reactions with varying initial concentrations helps determine the rate equation.
  1. Rate Determination Using the Method of Isolation
  • In complex reactions, the reaction of interest is isolated by keeping the concentration of one reactant high while the others remain low.
  • By varying the concentration of the reactant of interest, its effect on the rate can be determined.
  • This method helps determine the order of the reaction with respect to a particular reactant.
  1. Factors Influencing Reaction Rates
  • Concentration: Higher concentration leads to more frequent collisions and faster reaction rates. It follows the rate law equation.
  • Temperature: Increasing temperature increases the kinetic energy of molecules, leading to more energetic collisions and faster reaction rates. Arrhenius equation is used to determine the rate constant.
  • Surface Area: Greater surface area exposes more reactant particles to collisions, resulting in a higher reaction rate.
  • Catalysts: Catalysts increase the rate of reaction by providing an alternate reaction pathway with lower activation energy.
  • Nature of Reactants: Different reactants have different reactivity due to variations in their molecular structures and bond strength.
  1. Reaction Mechanism
  • In complex reactions, multiple steps or intermediates might be involved in the overall reaction.
  • Each step has its own rate law equation and activation energy, which determines the rate of that particular step.
  • The slowest step, known as the rate-determining step, dictates the overall rate of the reaction.
  • Reaction mechanisms help explain the sequence of events that occur during a chemical reaction.
  1. Rate-Determining Step Example
  • A reaction: A + B → C + D
  • Step 1: A + B → X (fast)
  • Step 2: X → C + D (slow)
  • The rate of the overall reaction is determined by the slowest step, which is Step 2 in this case.
  • The rate law equation for the overall reaction can be derived from the rate-determining step.
  1. Molecularity in Elementary Reactions
  • Molecularity refers to the number of molecules or ions involved in an elementary reaction.
  • Unimolecular reactions involve the decomposition of one molecule, while bimolecular reactions involve collisions between two molecules.
  • Termolecular reactions involve the simultaneous collision of three molecules, which is relatively rare due to the low probability of such encounters.
  1. Collision Theory
  • The collision theory explains how chemical reactions occur at the molecular level.
  • To react, molecules must collide with sufficient energy and proper orientation.
  • The energy of collision must exceed the activation energy to break bonds and form new ones.
  • Only a fraction of collisions leads to a successful reaction, known as effective collisions.
  1. Activation Energy
  • Activation energy (Ea) is the minimum energy required for a reaction to proceed.
  • It is the energy barrier that reactant molecules must overcome for a successful reaction.
  • Higher activation energy leads to slower reaction rates, as fewer molecules possess sufficient energy to cross the barrier.
  • Catalysts lower the activation energy by providing an alternative reaction pathway.
  1. Catalysts in Reactions
  • Catalysts increase the rate of a chemical reaction without being consumed in the process.
  • They provide an alternate reaction pathway with lower activation energy, making it easier for reactants to convert into products.
  • Homogeneous catalysts are in the same phase as the reactants, while heterogeneous catalysts are in a different phase.
  • Enzymes are biological catalysts that facilitate biochemical reactions in living organisms.
  1. Rate Determination Using Initial Rates Method
  • The initial rates method involves determining the rate of reaction based on the initial concentrations of reactants.
  • Calculate the initial rates by measuring the concentration change over a short time interval.
  • By comparing the initial rates of different reactions with varying initial concentrations, the rate equation can be determined.
  • This method is useful when the reaction rate is not simply proportional to the concentration of a single reactant.
  1. Rate Determination Using the Method of Isolation
  • In complex reactions, the method of isolation helps determine the effect of a specific reactant on the overall rate.
  • The concentration of the reactant of interest is kept high, while the other reactants are kept at low concentrations.
  • By varying the concentration of the reactant of interest, its influence on the rate can be determined.
  • This method aids in determining the order of the reaction with respect to a particular reactant.
  1. Analysis of Kinetic Data
  • Kinetic data can be analyzed to determine the order of reaction and rate constant.
  • Plotting concentration/time or ln(concentration)/time graphs can help determine the order of reaction.
  • The slope of the graph can provide information about the rate constant or rate law equation.
  • Half-life can be calculated from the rate constant, helping to understand the time required for the concentration to reach half its initial value.