Chemical Kinetics

  • The branch of chemistry that deals with the study of the speed (rate) at which a chemical reaction occurs and the factors that influence it.
  • The rate of a chemical reaction measures how fast the reactants are being consumed or the products are being formed.
  • It is important to understand the factors affecting the rate of a chemical reaction to control and optimize industrial processes.
  • The study of chemical kinetics helps us understand reaction mechanisms and predict reaction rates under different conditions.
  • In this lecture, we will focus on an example to find the relationship between the degree of advancement and the rate of the reaction.

Example Reaction

  • Consider the following reaction: A + B ⟶ C
  • A and B are the reactants, and C is the product.
  • We want to investigate how the rate of this reaction changes as the degree of advancement (extent of reaction) varies.

Degree of Advancement

  • The degree of advancement of a reaction (x) represents the extent to which the reaction has proceeded.
  • A value of x = 0 corresponds to no reaction having occurred, while x = 1 represents complete reaction completion.
  • The degree of advancement can be expressed in terms of concentration or moles, depending on the stoichiometry of the reaction.

Rate of Reaction

  • The rate of a chemical reaction is defined as the change in concentration of reactants or products per unit time.
  • It is usually expressed in terms of the rate or change in concentration of a reactant or product with respect to time.
  • In this example, we will focus on the rate of consumption of reactants rather than the formation of products.

Rate Law

  • The rate of a reaction can be expressed as a mathematical expression called the rate law.
  • The rate law relates the rate of reaction to the concentration of reactants.
  • For the example reaction A + B ⟶ C, the rate law is given by: rate = k[A]^m[B]^n
  • k is the rate constant, and m and n represent the order of the reaction with respect to reactants A and B, respectively.

Determining the Rate Law

  • To determine the rate law, experimental data is collected by varying the initial concentrations of reactants and measuring the corresponding rates.
  • By analyzing the data, the values of the rate constant k, as well as the reaction order m and n, can be determined.
  • Several methods, such as the method of initial rates and graphical analysis, can be used to determine the rate law.

Method of Initial Rates

  • In the method of initial rates, the initial concentrations of reactants are varied while keeping the concentration of other reactants and reaction conditions constant.
  • The initial rate of the reaction is determined for each set of initial concentrations.
  • The data obtained is used to determine the values of the reaction orders m and n by comparing the rates under different conditions.

Graphical Analysis

  • Graphical analysis involves plotting experimental data to determine the rate law.
  • There are different types of graphical plots that can be used depending on the reaction order.
  • For example, if the reaction is first order with respect to both reactants A and B, plotting ln(rate) versus time will give a straight line with slope equal to -k.

Integrated Rate Laws

  • Integrated rate laws are mathematical expressions that relate the concentrations of reactants or products to time.
  • These equations can be derived from the rate law and can be used to determine the concentration of reactants or products at any given time during the reaction.
  • The integrated rate laws depend on the reaction order and are useful for analyzing the kinetics of the reaction.

References

  • Atkins, P., & de Paula, J. (2018). Atkins’ Physical Chemistry. Oxford University Press.
  • Chang, R. (2013). Physical Chemistry for the Chemical Sciences. University Science Books.
  1. Graphical Analysis of Reaction Order
  • Graphical analysis can help determine the reaction order.
  • For a first-order reaction, plotting ln(concentration) versus time gives a straight line with slope equal to -k.
  • For a second-order reaction, plotting 1/concentration versus time gives a straight line with slope equal to k.
  1. Determining the Rate Constant
  • Once the reaction order is determined, the rate constant can be calculated.
  • The rate constant can be found by substituting the reaction order and initial concentrations into the rate law equation and solving for k.
  • The rate constant is usually temperature-dependent and specific to a particular reaction.
  1. Effect of Temperature on Reaction Rate
  • Changing the temperature affects the reaction rate.
  • Increasing the temperature generally increases the rate of reaction.
  • This is because higher temperatures provide more energy to reactant molecules, increasing the probability of successful collisions.
  1. Activation Energy
  • Activation energy is the minimum amount of energy required for a reaction to occur.
  • It is the energy barrier that reactant molecules must overcome to form products.
  • A higher activation energy generally corresponds to a slower rate of reaction.
  1. Arrhenius Equation
  • The Arrhenius equation describes the temperature dependence of the rate constant.
  • It is given by: 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, and T is the temperature in Kelvin.
  1. Effect of Catalysts on Reaction Rate
  • Catalysts are substances that can speed up a reaction without being consumed in the process.
  • They provide an alternative pathway with lower activation energy, allowing more reactant molecules to overcome the energy barrier and participate in the reaction.
  • Catalysts increase the rate of reaction but do not affect the equilibrium position.
  1. Effect of Concentration on Reaction Rate
  • Changing the concentration of reactants can affect the reaction rate.
  • An increase in reactant concentration generally leads to a higher rate of reaction.
  • This is because an increase in concentration results in more collisions among reactant molecules, leading to a greater probability of successful collisions.
  1. Reaction Mechanisms
  • Reaction mechanisms describe the step-by-step sequence of elementary reactions that make up a complex reaction.
  • Elementary reactions are individual steps with their own rate laws.
  • The overall rate law is obtained by adding the rate laws of the elementary reactions, taking into account their stoichiometry.
  1. Rate-Determining Step
  • The rate-determining step is the slowest step in the reaction mechanism.
  • It governs the overall rate of the reaction.
  • The rate law of the rate-determining step is the rate law of the overall reaction.
  1. Factors Affecting Rate of Reaction
  • Besides concentration and temperature, other factors can influence the rate of a reaction.
  • These factors include pressure, surface area, presence of catalysts, and nature of reactants.
  • Understanding these factors is essential for controlling and optimizing chemical reactions in various industrial processes.

Chemical Kinetics

  • The study of the speed (rate) at which a chemical reaction occurs and the factors that influence it.
  • Helps understand reaction mechanisms and predict reaction rates under different conditions.
  • Important for controlling and optimizing industrial processes.

Example Reaction

  • Consider the following reaction: A + B ⟶ C
  • A and B are the reactants, and C is the product.
  • We want to investigate the relationship between the degree of advancement and the rate of this reaction.

Degree of Advancement

  • Degree of advancement (x) represents the extent to which the reaction has proceeded.
  • A value of x = 0 represents no reaction occurred, while x = 1 represents complete reaction completion.
  • Can be expressed in terms of concentration or moles, depending on stoichiometry.

Rate of Reaction

  • Rate of a chemical reaction is the change in concentration of reactants or products per unit time.
  • Usually expressed in terms of rate of consumption of reactants or formation of products.
  • Important to measure and understand to control industrial processes.

Rate Law

  • Rate law expresses the rate of a reaction as a mathematical expression.
  • Relates the rate of reaction to the concentration of reactants.
  • For the example reaction A + B ⟶ C, the rate law is: rate = k[A]^m[B]^n

Determining Rate Law - Method of Initial Rates

  • Vary initial concentrations of reactants while keeping others constant.
  • Determine the initial rate for each set of concentrations.
  • Use data to find the values of reaction order (m and n) by comparing rates.

Determining Rate Law - Graphical Analysis

  • Plot experimental data to determine rate law.
  • Different graphical plots based on reaction order.
  • For a first-order reaction, plot ln(rate) versus time to get a straight line with slope -k.

Integrated Rate Laws

  • Mathematical expressions that relate concentrations or products to time.
  • Derived from rate law and used to determine concentrations at any given time.
  • Depend on reaction order.

Effect of Temperature on Reaction Rate

  • Changing temperature affects reaction rate.
  • Increasing temperature generally increases the rate of reaction.
  • More energy to reactant molecules, increasing probability of successful collisions.

Activation Energy

  • Activation energy is the minimum energy required for a reaction to occur.
  • Energy barrier reactant molecules must overcome to form products.
  • Higher activation energy corresponds to a slower rate of reaction.