Chemical Kinetics

Characteristics of composite reaction

  • A composite reaction consists of multiple elementary reactions
  • It can involve both forward and reverse reactions
  • The rate of a composite reaction is determined by the slowest elementary reaction, also known as the rate-determining step
  • The overall reaction order is the sum of the individual reaction orders
  • The rate constant for a composite reaction can be determined using the rate expression for the rate-determining step

Rate Laws and Rate Equations

Determining the rate law for a reaction

  • The rate law for a reaction can be determined experimentally by measuring the initial rates at different concentrations of reactants
  • The rate law expresses the relationship between the rate of a reaction and the concentrations of the reactants
  • The general form of a rate law is: rate = k[A]^m[B]^n
  • The exponents m and n are the reaction orders with respect to reactants A and B, respectively
  • The overall reaction order is the sum of the reaction orders: m + n

Integrated Rate Laws

Relating concentration and time

  • Integrated rate laws relate the concentration of reactants or products to the reaction time
  • There are different integrated rate laws based on the order of the reaction
  • Zero-order reaction: [A] = [A]₀ - kt
  • First-order reaction: ln[A] = -kt + ln[A]₀
  • Second-order reaction: 1/[A] = kt + 1/[A]₀

Half-Life

Time required for reaction completion

  • The half-life of a reaction is the time required for the concentration of a reactant to decrease by half
  • The half-life depends on the order of the reaction
  • For zero-order reactions, the half-life is given by: t₁/₂ = [A]₀/2k
  • For first-order reactions, the half-life is given by: t₁/₂ = ln(2)/k
  • For second-order reactions, the half-life is given by: t₁/₂ = 1/k[A]₀

Collision Theory

Factors affecting reaction rate

  • Collision theory explains how chemical reactions occur at the molecular level
  • According to the theory, for a reaction to occur, reactant molecules must collide with the correct orientation and sufficient energy
  • Factors that affect reaction rate include:
    • Concentration: Increasing reactant concentration increases the collision frequency
    • Temperature: Higher temperature increases the kinetic energy of molecules, leading to more frequent successful collisions
    • Surface area: Increasing surface area of reactants increases the likelihood of collisions
    • Catalysts: Catalysts lower the activation energy of a reaction, increasing the rate without being consumed

Activation Energy

Energy required to start a reaction

  • Activation energy (Ea) is the minimum energy required for a reaction to occur
  • The energy profile diagram represents the change in energy during a reaction
  • The reactants must overcome the activation energy barrier to form the transition state
  • Higher activation energy leads to slower reactions
  • Catalysts lower the activation energy, increasing the rate of the reaction

Arrhenius Equation

Expressing dependence of rate constant on temperature

  • The Arrhenius equation relates the rate constant (k) of a reaction to the temperature (T)
  • The equation is given by: k = Ae^(-Ea/RT)
  • A is the pre-exponential factor or frequency factor, which represents the frequency of successful collisions
  • R is the gas constant (8.314 J/mol·K)
  • T is the absolute temperature (in Kelvin)
  • Ea is the activation energy

Reaction Mechanisms

Step-by-step sequence of reactions

  • A reaction mechanism explains the step-by-step sequence of elementary reactions that lead to the overall reaction
  • Reaction intermediates are formed and consumed during the reaction
  • Elementary reactions can be reversible or irreversible
  • The rate-determining step is the slowest step in the mechanism and determines the overall rate of the reaction
  • Rate laws can be derived for individual steps based on their molecularity

Rate-Determining Step

Slowest step in the mechanism

  • The rate-determining step is the slowest step in the reaction mechanism
  • It determines the overall rate of the reaction
  • The reactants involved in the rate-determining step appear in the rate law
  • The rate constant for the rate-determining step can be determined experimentally using the rate expression
  • It is important to identify the rate-determining step to understand the factors that influence the reaction rate

Chemical Kinetics

  • A composite reaction consists of multiple elementary reactions
  • It can involve both forward and reverse reactions
  • The rate of a composite reaction is determined by the slowest elementary reaction
  • The overall reaction order is the sum of the individual reaction orders
  • The rate constant for a composite reaction can be determined using the rate expression for the rate-determining step

Rate Laws and Rate Equations

  • The rate law for a reaction can be determined experimentally
  • It expresses the relationship between the rate and the concentrations of the reactants
  • The general form of a rate law is: rate = k[A]^m[B]^n
  • The reaction orders (m and n) can be determined by experimental data
  • The overall reaction order is the sum of the reaction orders

Integrated Rate Laws

  • Integrated rate laws relate the concentration of reactants or products to the reaction time
  • Different integrated rate laws exist for different reaction orders
  • Zero-order reaction: [A] = [A]₀ - kt
  • First-order reaction: ln[A] = -kt + ln[A]₀
  • Second-order reaction: 1/[A] = kt + 1/[A]₀

Half-Life

  • The half-life of a reaction is the time required for the concentration of a reactant to decrease by half
  • The half-life depends on the order of the reaction
  • Zero-order reaction: t₁/₂ = [A]₀/2k
  • First-order reaction: t₁/₂ = ln(2)/k
  • Second-order reaction: t₁/₂ = 1/k[A]₀

Collision Theory

  • Collision theory explains how chemical reactions occur at the molecular level
  • Reactant molecules must collide with correct orientation and sufficient energy for a reaction to occur
  • Factors affecting reaction rate include concentration, temperature, surface area, and catalysts
  • Increasing concentration increases collision frequency
  • Higher temperature increases kinetic energy of molecules, leading to more frequent successful collisions

Collision Theory (continued)

  • Increasing surface area of reactants increases the likelihood of collisions
  • Catalysts lower activation energy of a reaction, increasing the rate without being consumed
  • According to collision theory, an effective collision must occur with sufficient energy and correct orientation
  • Not all collisions result in a reaction, only those with enough energy and proper orientation are effective

Activation Energy

  • Activation energy (Ea) is the minimum energy required for a reaction to occur
  • The energy profile diagram shows the change in energy during a reaction
  • Reactants must overcome the activation energy barrier to form the transition state
  • Higher activation energy leads to slower reactions
  • Catalysts lower the activation energy, increasing the rate of the reaction

Arrhenius Equation

  • The Arrhenius equation relates rate constant (k) to the temperature (T)
  • The equation is: k = Ae^(-Ea/RT)
  • A is the frequency factor, representing the frequency of successful collisions
  • R is the gas constant (8.314 J/mol·K)
  • T is the absolute temperature (in Kelvin)

Reaction Mechanisms

  • A reaction mechanism explains the step-by-step sequence of elementary reactions that lead to the overall reaction
  • Reaction intermediates are formed and consumed during the reaction
  • Elementary reactions can be reversible or irreversible
  • The rate-determining step is the slowest step in the mechanism and determines the overall rate
  • Rate laws can be derived for individual steps based on their molecularity

Collision Theory continued

  • According to collision theory, an effective collision must occur with sufficient energy and correct orientation
  • Not all collisions result in a reaction, only those with enough energy and proper orientation are effective ++++

Activation Energy

  • Activation energy (Ea) is the minimum energy required for a reaction to occur
  • The energy profile diagram shows the change in energy during a reaction
  • Reactants must overcome the activation energy barrier to form the transition state
  • Higher activation energy leads to slower reactions
  • Catalysts lower the activation energy, increasing the rate of the reaction ++++

Arrhenius Equation

  • The Arrhenius equation relates rate constant (k) to the temperature (T)
  • The equation is: k = Ae^(-Ea/RT)
  • A is the frequency factor, representing the frequency of successful collisions
  • R is the gas constant (8.314 J/mol·K)
  • T is the absolute temperature (in Kelvin) ++++

Reaction Mechanisms

  • A reaction mechanism explains the step-by-step sequence of elementary reactions that lead to the overall reaction
  • Reaction intermediates are formed and consumed during the reaction
  • Elementary reactions can be reversible or irreversible
  • The rate-determining step is the slowest step in the mechanism and determines the overall rate
  • Rate laws can be derived for individual steps based on their molecularity ++++

Elementary Reactions

  • Elementary reactions are the individual steps in a reaction mechanism
  • They involve a small number of reactant molecules or ions
  • Elementary reactions are often described using molecularity, which refers to the number of molecules or ions participating in the reaction
  • Examples: unimolecular, bimolecular, and termolecular elementary reactions ++++

Rate-Determining Step

  • The rate-determining step is the slowest step in the reaction mechanism
  • It determines the overall rate of the reaction
  • The reactants involved in the rate-determining step appear in the rate law
  • The rate constant for the rate-determining step can be determined experimentally using the rate expression
  • It is important to identify the rate-determining step to understand the factors that influence the reaction rate ++++

Rate Constant

  • The rate constant (k) is a proportionality constant that relates the rate of a reaction to the concentrations of the reactants
  • It reflects the probability of successful collisions with proper orientation and sufficient energy
  • The value of k depends on the specific reaction and conditions
  • The units of k depend on the overall reaction order, and can be determined experimentally ++++

Reaction Order

  • The reaction order determines how the rate of a reaction depends on the concentrations of the reactants
  • It can be determined experimentally by measuring the initial rates at different concentrations
  • The reaction order can be zero, first, second, or a fraction
  • It is represented by an exponent in the rate law: rate = k[A]^m[B]^n
  • The overall reaction order is the sum of the reaction orders ++++

Rate Law and Rate Equation

  • The rate law expresses the relationship between the rate of a reaction and the concentrations of the reactants
  • It is determined experimentally by measuring the initial rates at different concentrations
  • The rate law can be derived by comparing the rate expressions for different reactions
  • The rate equation is the mathematical expression of the rate law, including the specific values of the rate constant and reaction orders ++++

Integrated Rate Law

  • The integrated rate law relates the concentrations of reactants or products to the reaction time
  • It can be derived from the rate law by integrating and solving the resulting differential equation
  • The integrated rate law depends on the order of the reaction
  • Different forms of the integrated rate law exist for zero-order, first-order, and second-order reactions