Chemical Kinetics - Rate equations and examples

  • Chemical kinetics is the study of the rates at which chemical reactions occur.
  • Rate equations describe the relationship between the rate of a reaction and the concentrations of the reactants.
  • The rate equation for a reaction can be determined experimentally.

Determining the Rate Equation

  • The rate equation for a reaction can be determined by the method of initial rates.
  • In the method of initial rates, the initial concentrations of the reactants are varied and the initial rate of reaction is measured.
  • By comparing the initial rates for different reactant concentrations, we can determine the rate equation.

Rate Laws

  • The rate equation is often expressed as a rate law, which relates the rate of the reaction to the concentrations of the reactants.
  • The rate law is determined by the experimentally determined rate equation.
  • The rate law can be used to predict the rate of the reaction at any given set of reactant concentrations.

Rate Constants

  • The rate equation also includes a rate constant, which is specific for a given reaction at a specific temperature.
  • The rate constant is determined experimentally and varies with temperature.
  • The rate constant is affected by factors such as concentration, temperature, and catalysts.

Reaction Orders

  • The reaction order for a reactant is determined by the exponent to which its concentration is raised in the rate law.
  • The overall reaction order is the sum of the individual reaction orders.
  • The reaction order determines how the rate of reaction changes with changing reactant concentrations.

Zero-Order Reactions

  • In a zero-order reaction, the rate of reaction is independent of the reactant concentration.
  • The rate law for a zero-order reaction is:
    • Rate = k, where k is the rate constant.
  • Example: Decomposition of hydrogen peroxide in the presence of a catalyst.

First-Order Reactions

  • In a first-order reaction, the rate of reaction is directly proportional to the reactant concentration.
  • The rate law for a first-order reaction is:
    • Rate = k[A], where k is the rate constant and [A] is the concentration of reactant A.
  • Example: Radioactive decay.

Second-Order Reactions

  • In a second-order reaction, the rate of reaction is proportional to the square of the reactant concentration.
  • The rate law for a second-order reaction is:
    • Rate = k[A]^2, where k is the rate constant and [A] is the concentration of reactant A.
  • Example: Reaction between two different reactants.

Reaction Half-Life

  • The half-life of a reaction is the time it takes for half of the reactant to be consumed.
  • The half-life of a reaction can be determined from the rate constant.
  • The half-life of a reaction depends on the reaction order.

Slide 11

Factors Affecting Reaction Rate

  • Concentration: Increasing the concentration of reactants increases the rate of reaction.
  • Temperature: Increasing the temperature increases the rate of reaction by providing more energy for successful collisions.
  • Catalysts: Catalysts increase the rate of reaction by lowering the activation energy required for the reaction to occur.
  • Surface area: Increasing the surface area of reactants increases the rate of reaction by providing more area for collisions to occur.

Slide 12

Collision Theory

  • According to collision theory, for a reaction to occur:
    • Reactant particles must collide with each other.
    • The collisions must occur with sufficient energy (activation energy) to break bonds.
    • The collisions must occur with the proper orientation.
  • Only a small fraction of collisions have enough energy to react, known as the effective collisions.
  • Increasing the concentration of reactants or the temperature increases the frequency of effective collisions.

Slide 13

Reaction Mechanisms

  • Reactions often occur through a series of intermediate steps, known as reaction mechanisms.
  • The overall rate of reaction is determined by the slowest step in the mechanism, known as the rate-determining step.
  • The rate law is based on the stoichiometry and rate-determining step.

Slide 14

Rate-Determining Step

  • The rate-determining step is the slowest step in a reaction mechanism.
  • It determines the overall rate of the reaction.
  • The rate law is based on the reactants and products involved in the rate-determining step.

Slide 15

Integrated Rate Laws

  • Integrated rate laws describe how the concentration of a reactant changes over time.
  • The integrated rate law for a reaction depends on the reaction order.

Slide 16

Zero-Order Integrated Rate Law

  • For a zero-order reaction, the integrated rate law is:
    • [A]t = [A]0 - kt, where [A]t is the concentration of reactant A at time t, [A]0 is the initial concentration, k is the rate constant, and t is time.

Slide 17

First-Order Integrated Rate Law

  • For a first-order reaction, the integrated rate law is:
    • ln[A]t = -kt + ln[A]0, where [A]t is the concentration of reactant A at time t, [A]0 is the initial concentration, k is the rate constant, and t is time.

Slide 18

Second-Order Integrated Rate Law

  • For a second-order reaction, the integrated rate law is:
    • 1/[A]t = kt + 1/[A]0, where [A]t is the concentration of reactant A at time t, [A]0 is the initial concentration, k is the rate constant, and t is time.

Slide 19

Half-Life of a Reaction

  • The half-life of a reaction is the time it takes for the concentration of a reactant to decrease by half.
  • The half-life can be calculated using the integrated rate law.
  • The half-life depends on the reaction order.

Slide 20

Example: Reaction Order and Half-Life

  • Consider a first-order reaction with a rate constant of 0.05 s^-1.
  • If the initial concentration of the reactant is 2.0 M, what is the half-life of the reaction?
  • Using the first-order integrated rate law: ln[A]t = -kt + ln[A]0
  • At half-life, [A]t = [A]0/2
  • ln(2[A]0/[A]0) = -0.05t + ln[A]0
  • ln(2) = -0.05t
  • t = ln(2)/0.05
  • t ≈ 13.86 seconds

Slide 21

Arrhenius Equation

  • The Arrhenius equation relates the rate constant of a reaction to the temperature and activation energy.
  • The equation is: k = Ae^(-Ea/RT)
  • Where k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.

Slide 22

Catalysis

  • Catalysts are substances that increase the rate of a reaction by providing an alternative mechanism with a lower activation energy.
  • Homogeneous catalysts are in the same phase as the reactants.
  • Heterogeneous catalysts are in a different phase than the reactants.
  • Catalysts are not consumed in the reaction and can be reused.

Slide 23

Enzymes

  • Enzymes are biological catalysts that increase the rates of chemical reactions in living organisms.
  • Enzymes lower the activation energy required for a reaction to occur.
  • Enzymes are specific to certain substrates and exhibit high catalytic efficiency.
  • Enzymes can be affected by factors such as pH, temperature, and inhibitors.

Slide 24

Reaction Mechanism and Catalysis

  • Catalysts accelerate reactions by providing an alternative reaction pathway with a lower activation energy.
  • The catalyst interacts with the reactants to form an intermediate complex.
  • The intermediate complex then breaks down to form the products and regenerate the catalyst.

Slide 25

Rate-Determining Step in Catalysis

  • In catalysis, the rate-determining step may change.
  • The rate-determining step is the slowest step in the reaction mechanism.
  • Adding a catalyst may change the rate-determining step and increase the overall rate of reaction.

Slide 26

Effect of Temperature on Reaction Rates

  • Increasing the temperature increases the kinetic energy of the reactant particles.
  • This leads to an increase in the frequency and energy of collisions between reactant particles.
  • Thus, increasing the temperature generally increases the rate of reaction.

Slide 27

Effect of Concentration on Reaction Rates

  • Increasing the concentration of reactants increases the frequency of collisions.
  • This leads to a higher likelihood of effective collisions and an increase in the rate of reaction.
  • The rate of reaction is directly proportional to the concentration of reactants.

Slide 28

Effect of Surface Area on Reaction Rates

  • Increasing the surface area of solid reactants increases the number of exposed particles available for reaction.
  • This increases the frequency of collisions between reactant particles and results in a higher rate of reaction.
  • Examples include grinding a solid into a powder or using a catalyst with a high surface area.

Slide 29

Effect of Pressure on Reaction Rates

  • Increasing the pressure of gaseous reactants increases the concentration of reactant particles.
  • This increases the frequency of collisions and leads to a higher rate of reaction.
  • Pressure affects the rate of reaction for reactions involving gaseous reactants only.

Slide 30

Summary

  • Chemical kinetics studies the rates at which reactions occur.
  • The rate equation and rate law describe the relationship between reactant concentrations and the rate of reaction.
  • The rate constant, reaction orders, and reaction mechanisms are important concepts in chemical kinetics.
  • Factors such as concentration, temperature, and catalysts affect the rate of reaction.
  • Temperature affects the rate by increasing the kinetic energy of the reactant particles.
  • Concentration and surface area affect the rate by increasing collision frequency.
  • Catalysis provides an alternative pathway with a lower activation energy for reactions to occur.