Chemical Kinetics

  • Temperature dependence of reaction rate

Introduction

  • Chemical kinetics studies the rate of chemical reactions
  • Reaction rate is influenced by various factors, including temperature

Temperature dependence of reaction rate

  • As temperature increases, reaction rate generally increases
  • This is explained by the Arrhenius equation:
    • k = A * e^(-Ea/RT)
      • k: rate constant
      • A: pre-exponential factor
      • Ea: activation energy
      • R: gas constant
      • T: temperature in Kelvin

Activation energy

  • Activation energy is the minimum energy required for a reaction to occur
  • High activation energy indicates a slow reaction rate
  • Low activation energy indicates a fast reaction rate
  • Example: burning a piece of paper requires activation energy in the form of a flame

Effect of temperature on activation energy

  • Increasing temperature decreases the effective activation energy
  • This is due to more reactant molecules having sufficient energy to overcome the activation energy barrier
  • Example: heating a substance increases its reactivity

Boltzmann distribution

  • The energy distribution of a system of particles is described by the Boltzmann distribution
  • Higher temperatures result in a broader distribution of energy levels
  • Example: gas molecules at higher temperatures have a wider range of kinetic energies

Collision theory

  • Reactions occur when reactant molecules collide with sufficient energy and proper orientation
  • Increasing temperature increases the frequency of collisions between reactant molecules
  • Example: increasing temperature causes more gas molecules to move faster and collide with each other more frequently

Effect of temperature on reaction rate

  • The rate constant (k) in the Arrhenius equation increases exponentially with temperature
  • Higher temperatures result in greater average kinetic energy of reactant molecules
  • Example: at higher temperatures, more collisions occur with sufficient energy to overcome the activation barrier

Rate-determining step

  • The slowest step in a reaction is called the rate-determining step
  • Increasing temperature can increase the rate of the rate-determining step
  • Example: in a multi-step reaction, if one of the steps has a higher activation energy, increasing temperature can speed up that step

Conclusion

  • Temperature has a profound effect on the rate of chemical reactions
  • Increasing temperature generally increases reaction rate
  • This can be explained by the Arrhenius equation and the concepts of activation energy, collision theory, and the Boltzmann distribution
  1. Factors Affecting Reaction Rate
  • Apart from temperature, other factors can also influence the rate of a chemical reaction
  • Concentration of reactants
  • Surface area of reactants
  • Catalysts
  • Presence of light
  1. Concentration of Reactants
  • Increasing the concentration of reactants usually increases the reaction rate
  • Higher concentration means more particles available for collision
  • Example: In a reaction A + B → C, doubling the concentration of A and B will double the reaction rate
  1. Surface Area of Reactants
  • Increasing the surface area of reactants increases the reaction rate
  • More exposed surface allows for more frequent collisions
  • Example: Finely powdered magnesium reacts with oxygen at a faster rate compared to a solid magnesium ribbon
  1. Catalysts
  • Catalysts are substances that increase the reaction rate without being consumed in the reaction
  • They provide an alternative reaction pathway with lower activation energy
  • Example: The enzyme catalase speeds up the decomposition of hydrogen peroxide into water and oxygen
  1. Presence of Light
  • Some reactions are influenced by the presence of light
  • Light can act as a catalyst or provide energy to initiate the reaction
  • Example: Photosynthesis in plants requires light as an energy source for the production of glucose
  1. Rate Law and Reaction Order
  • The rate law of a reaction shows the mathematical relationship between the rate of reaction and the concentrations of reactants
  • The reaction order is the exponent to which the concentration is raised in the rate law equation
  • Example: For the reaction A + 2B → C, if the rate is proportional to [A]²[B], then the reaction order is 2 with respect to A and 1 with respect to B
  1. Rate Constant and Half-Life
  • The rate constant (k) is a proportionality constant in the rate law equation
  • The rate constant changes with temperature and represents the speed at which reactants are converted into products
  • The half-life of a reaction is the time taken for half of the reactants to be consumed
  • Example: The half-life of a first-order reaction remains constant, while the half-life of a second-order reaction increases as the concentration decreases
  1. Collision Theory Revisited
  • The collision theory helps understand the factors influencing reaction rate
  • For a reaction to occur, molecules must collide with sufficient energy and in the correct orientation
  • Increasing the concentration or temperature increases the likelihood of such collisions
  • Example: In a gas-phase reaction, increasing the pressure increases the concentration and leads to more frequent collisions
  1. Arrhenius Equation Revisited
  • The Arrhenius equation explains the temperature dependence of reaction rate
  • It relates the rate constant (k) to the activation energy (Ea) and temperature (T)
  • Example: For a reaction with a large Ea value, even a small increase in temperature can significantly increase the reaction rate
  1. Temperature and Reaction Rate Summary
  • Temperature affects the reaction rate by influencing the average kinetic energy and collision frequency of reactant molecules
  • Higher temperatures generally result in faster reaction rates due to increased energy and more frequent collisions
  • The Arrhenius equation describes the exponential relationship between rate constant, temperature, and activation energy
  • Understanding the temperature dependence of reaction rates is crucial for studying and predicting chemical reactions.
  1. Reaction Mechanisms
  • Reactions often involve multiple steps before the final products are formed
  • These individual steps are collectively known as the reaction mechanism
  • Example: The reaction mechanism for the formation of ozone involves a series of reactions between oxygen molecules
  1. Elementary Reactions
  • Elementary reactions are individual steps in a reaction mechanism
  • They occur in a single step without any intermediates
  • Example: The elementary reaction for the formation of water is the combination of hydrogen and oxygen molecules
  1. Rate-determining Step
  • The rate-determining step is the slowest step in a reaction mechanism
  • It determines the overall rate of the reaction
  • Example: In a multi-step reaction, if the first step is slower than the subsequent steps, it will be the rate-determining step
  1. Intermediate Species
  • Intermediate species are formed and consumed during a reaction but do not appear in the overall reaction equation
  • They are usually short-lived and exist momentarily
  • Example: In the reaction between ozone and nitric oxide, the nitrogen dioxide molecule is an intermediate species
  1. Reaction Intermediates
  • Reaction intermediates are stable species that are produced and consumed during a reaction
  • They are typically present in sufficient concentrations to be detected and characterized
  • Example: In the reaction between hydrogen peroxide and iodide ions, iodine is a reaction intermediate
  1. Molecularity and Rate Law
  • Molecularity refers to the number of reactant particles involved in an elementary reaction
  • The molecularity determines the form of the rate law for that step
  • Example: In a unimolecular reaction, the rate law will depend only on the concentration of one reactant
  1. Rate-determining Step and Rate Law
  • The rate law for an overall reaction is determined by the rate-determining step
  • The rate law for the rate-determining step becomes the rate law for the overall reaction
  • Example: If the rate-determining step is a bimolecular reaction, the rate law will depend on the concentrations of two reactants
  1. Catalysis and Reaction Rate
  • Catalysts increase the reaction rate by providing an alternative reaction pathway with lower activation energy
  • They are not consumed in the reaction and can be reused
  • Example: Platinum is a catalyst in the reaction between hydrogen and oxygen to form water
  1. Homogeneous and Heterogeneous Catalysts
  • Homogeneous catalysts are in the same phase as the reactants
  • Heterogeneous catalysts are in a different phase from the reactants
  • Example: In the Haber-Bosch process, iron acts as a heterogeneous catalyst for the synthesis of ammonia
  1. Enzymes as Biological Catalysts
  • Enzymes are biological catalysts that increase the rate of biochemical reactions in living organisms
  • They are highly specific and work under physiological conditions
  • Example: The enzyme amylase catalyzes the hydrolysis of starch into glucose in the human digestive system