Chemical Kinetics

  • Integrated rate law for 2nd order reaction

Integrated Rate Law

  • The rate of a chemical reaction is determined by the concentration of reactants.
  • The integrated rate law expresses the relationship between the concentration of reactants and time.
  • The integrated rate law for a second-order reaction is given by: 1/[A]t = kt + 1/[A]o

Relationship between Concentration and Time

  • The integrated rate law shows how the concentration of reactants changes over time.
  • As time increases, the concentration of reactants decreases.
  • The rate constant (k) represents the speed at which the reaction occurs.

Second-Order Reaction

  • A second-order reaction involves two reactants or one reactant with a power of 2 in the rate equation.
  • The rate equation for a second-order reaction is expressed as: Rate = k[A]² or Rate = k[A][B]

Example: Second-Order Reaction

  • Consider the reaction: A + B ⟶ C
  • If the rate equation is given by: Rate = k[A][B], what is the overall order of the reaction?
  • The overall order of the reaction is 2, since the concentrations of both reactants are raised to the power of 1 each.

Determining the Rate constant

  • The rate constant (k) can be determined by using experimental data.
  • By knowing the initial concentration of reactants and measuring the reaction rate at various times, the value of k can be calculated.
  • The units of k will vary depending on the order of the reaction.

Example: Calculating Rate Constant

  • Consider the second-order reaction: 2A ⟶ B
  • The initial concentration of A is 0.10 M and the initial rate of reaction is 0.05 M/s.
  • Using the integrated rate law, we can calculate the rate constant (k): 1/[A]t = kt + 1/[A]o 1/0.05 = k(10) + 1/0.10
  • Solving for k, we find that k = 0.005 M⁻¹s⁻¹.

Half-life of Second-Order Reaction

  • The half-life of a second-order reaction depends on the initial concentration of the reactant.
  • The half-life is the time it takes for the concentration of a reactant to decrease by half.
  • The equation for determining the half-life of a second-order reaction is: t₁/₂ = 1 / (k[A]o)

Example: Half-life Calculation

  • For a second-order reaction with an initial concentration of 0.08 M, the rate constant (k) is 0.003 M⁻¹s⁻¹.
  • Calculating the half-life: t₁/₂ = 1 / (0.003 * 0.08)
  • Therefore, the half-life of this second-order reaction is 4167 s.
  1. Rate Laws for Multiple Steps Reactions
  • Multi-step reactions involve more than one elementary step.
  • The rate law for the overall reaction is determined by the slowest step, also known as the rate-determining step.
  • The rate-determining step is the step with the highest activation energy.
  1. Rate-Determining Step
  • The rate-determining step limits the overall rate of the reaction.
  • The rate law for the rate-determining step determines the overall rate law of the reaction.
  • It is important to identify the rate-determining step in order to understand the kinetics of the reaction.
  1. Determining Rate Law for Multi-step Reactions
  • To determine the rate law for a multi-step reaction, the slowest step must be identified.
  • The rate law for the slowest step is the rate law for the overall reaction.
  • Intermediate species that appear in the mechanism but not in the rate law are called reaction intermediates.
  1. Rate Law and Mechanism
  • The rate law for a multi-step reaction can be determined experimentally.
  • By varying the initial concentrations of the reactants and measuring the reaction rate, the rate law can be deduced.
  • The rate law can help understand the steps involved in the reaction mechanism.
  1. Rate Constants for Multi-step Reactions
  • The rate constants for each step in a multi-step reaction can vary.
  • Using the steady-state approximation, rate constants can be calculated.
  • The rate constant for the rate-determining step is usually the slowest.
  1. Catalysis
  • Catalysis is a process that increases the rate of a reaction.
  • Catalysts provide an alternative pathway with a lower activation energy, allowing the reaction to proceed faster.
  • Catalysts are not consumed in the reaction and can be used multiple times.
  1. Homogeneous Catalysis
  • Homogeneous catalysis involves a catalyst that is in the same phase as the reactants.
  • The catalyst interacts with the reactants, forming an intermediate complex.
  • The intermediate complex then breaks down to regenerate the catalyst and form the products.
  1. Heterogeneous Catalysis
  • Heterogeneous catalysis involves a catalyst that is in a different phase from the reactants.
  • The reactants are adsorbed onto the surface of the catalyst, where the reaction occurs.
  • The products are then desorbed from the catalyst surface.
  1. Enzymes
  • Enzymes are proteins that act as biological catalysts.
  • They increase the rate of biochemical reactions in living organisms.
  • Enzymes are highly specific and can perform complex reactions with high efficiency.
  1. Enzyme Kinetics
  • Enzyme kinetics studies the rate of enzymatic reactions.
  • The Michaelis-Menten equation describes the relationship between enzyme activity and substrate concentration.
  • Enzyme inhibitors can regulate enzyme activity and are important in pharmacology and medicine.
  1. Effect of Temperature on Reaction Rate
  • Temperature is an important factor that affects the rate of a chemical reaction.
  • Increasing the temperature generally increases the rate of reaction.
  • This is because an increase in temperature provides more kinetic energy to the reactant molecules, leading to more frequent and energetic collisions.
  1. Activation Energy
  • Activation energy (Ea) is the minimum amount of energy required for a reaction to occur.
  • The reactant molecules must possess this energy in order to overcome the energy barrier and form the products.
  • Higher activation energy leads to slower reaction rates, while lower activation energy leads to faster reaction rates.
  1. Arrhenius Equation
  • The Arrhenius equation relates the rate constant (k) of a reaction to the temperature (T) and the activation energy (Ea).
  • The equation is given as: k = Ae^(-Ea/RT), where A is the frequency factor and R is the gas constant.
  • The Arrhenius equation helps explain the exponential relationship between reaction rate and temperature.
  1. Catalytic Effect on Reaction Rate
  • Catalysts can decrease the activation energy of a reaction, thereby increasing the reaction rate.
  • This is achieved by providing an alternative reaction pathway with a lower activation energy.
  • Catalysts are not consumed in the reaction and can participate in multiple reactions.
  1. Reaction Rate and Concentration
  • The rate of a reaction is generally proportional to the concentration of reactants.
  • This relationship can be expressed as the rate law, which includes the concentrations of reactants raised to certain powers.
  • The rate law helps determine the order of the reaction and the rate constant.
  1. Effect of Surface Area on Reaction Rate
  • Increasing the surface area of solid reactants can increase the rate of reaction.
  • This is because more surface area allows for more effective collisions between reactant particles.
  • Finely powdered or divided substances have a larger surface area and react more quickly than larger pieces.
  1. Reaction Mechanism
  • The reaction mechanism describes the step-by-step process by which a reaction occurs.
  • It includes the elementary steps, reaction intermediates, and the overall reaction.
  • Understanding the reaction mechanism can provide insights into the rate-determining step and the order of the reaction.
  1. Rate-Determining Step in a Reaction
  • The rate-determining step is the slowest step in the reaction mechanism.
  • It determines the overall rate of the reaction.
  • The rate law for the rate-determining step is the rate law for the overall reaction.
  1. Collision Theory
  • The collision theory explains the process by which molecules react with each other to form products.
  • According to this theory, for a reaction to occur, the reacting molecules must collide in the correct orientation and with sufficient energy.
  • Not all collisions result in a reaction; only those with enough energy (equal to or greater than the activation energy) and correct orientation lead to a successful reaction.
  1. Effect of Concentration on Reaction Rate
  • Increasing the concentration of reactants generally increases the rate of reaction.
  • This is because higher concentrations result in more collisions between reactant particles.
  • More collisions increase the likelihood of effective collisions, leading to a faster reaction rate.