Chemical Kinetics

• Activation Energy
• Rate of Reaction
• Factors Affecting the Rate of Reaction
• Collision Theory
• Effect of Temperature on Reaction Rate

Activation Energy

• Definition: The minimum energy required for a chemical reaction to occur
• Symbol: Ea
• Depends on the nature of the reactants and the reaction pathway
• Determines the rate of reaction
• Usually expressed in units of kilojoules per mole (kJ/mol)

Rate of Reaction

• Definition: The change in concentration of reactants or products per unit time
• Measured in units of molarity per second (M/s)
• Can be determined by monitoring the disappearance of reactants or the appearance of products
• Influenced by the concentration of reactants, temperature, and the presence of a catalyst
• Rate equation represents the relationship between the rate of reaction and the concentration of reactants

Factors Affecting the Rate of Reaction

• Nature of Reactants: Different compounds react at different rates due to their chemical properties
• Concentration: Increasing the concentration of reactants increases the rate of reaction (as per the rate equation)
• Temperature: Higher temperatures increase the kinetic energy of particles, leading to more collisions and faster reaction rates
• Catalyst: Catalysts lower the activation energy, increasing the rate of reaction without being consumed in the process
• Physical State: Reactants in the dissolved or gaseous state typically react faster than solids

Collision Theory

• States that for a chemical reaction to occur:
  • Reactant particles must collide with sufficient energy (equal to or greater than the activation energy)
  • Reactant particles must collide in the correct orientation
• Only a small fraction of collisions lead to a reaction due to insufficient energy or unfavorable orientation
• Increasing the number of collisions increases the chances of successful collisions and, therefore, the rate of reaction

Effect of Temperature on Reaction Rate

• Increasing the temperature:
  • Increases the kinetic energy of particles
  • Increases the number of particles with energy equal to or greater than the activation energy
  • Increases the frequency of successful collisions
  • Increases the rate of reaction
• Temperature is a crucial factor affecting reaction rate, as small changes in temperature can lead to significant changes in rate

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Order of Reaction

• Definition: The sum of the exponents in the rate equation (determines the dependence of the rate on the concentration of reactants)
• Zero Order: Rate is independent of reactant concentration (rate = k)
• First Order: Rate is directly proportional to the concentration of one reactant (rate = k[A])
• Second Order: Rate is directly proportional to the square of the concentration of one reactant or the product of the concentrations of two different reactants (rate = k[A]^2 or rate = k[A][B])
• Overall Order: Sum of the exponents in the rate equation

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Integrated Rate Laws

• Differential Rate Law: Describes how the rate of a reaction changes with time (differentiates rate equations)
• Integrated Rate Law: Describes how the concentration of a reactant changes with time (integrates rate equations)
• Can be represented as equations, graphs, or mathematical formulas
• Provides a relationship between time and reactant concentration
• Can be used to determine reaction orders and rate constants

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Half-Life

• Definition: The time taken for the concentration of a reactant to decrease by half
• Symbol: t1/2
• Half-life depends on the order of reaction
• Zero Order: t1/2 = [A]0 / 2k
• First Order: t1/2 = 0.693 / k
• Second Order: t1/2 = 1 / (k[A]0)

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Arrhenius Equation

• Relates the rate constant of a reaction to temperature
• k = A * e^(-Ea/RT)
• k: Rate constant
• A: Pre-exponential factor (frequency factor) - a constant that depends on collision frequency and orientation
• Ea: Activation energy
• R: Gas constant (8.314 J/(mol*K))
• T: Temperature in Kelvin (K)
• As temperature increases, the rate constant and the rate of reaction increase slide-11

Chemical Kinetics - Activation Energy

• Activation Energy:
  • Definition: The minimum energy required for a chemical reaction to occur.
  • Symbol: Ea.
• Factors affecting activation energy:
  • Nature of reactants: Different compounds have different activation energies.
  • Reactant concentration: Higher concentration can increase the effective collision rate, lowering the activation energy.
  • Temperature: Higher temperatures increase the kinetic energy of particles, increasing the proportion with sufficient energy to overcome the activation energy.
• Activation Energy Diagram:
  • Represents the energy changes during a chemical reaction.
  • Reactants start with energy equal to or higher than Ea.
  • Transition state occurs at the maximum energy point.
  • Products form with lower energy than the reactants. slide-12

Chemical Kinetics - Rate of Reaction and Rate Equation

• Rate of Reaction:
  • Definition: The change in concentration of reactants or products per unit time.
  • Measured in units of molarity per second (M/s).
• Rate equation (rate law):
  • Represents the relationship between the rate of reaction and the concentration of reactants.
  • General form: rate = k[A]^m[B]^n
  • k: Rate constant
  • A, B: Concentrations of reactants
  • m, n: Reaction orders for each reactant.
• Determining reaction orders:
  • Method of initial rates or graphical analysis. slide-13

Chemical Kinetics - Factors Affecting Rate of Reaction

• Nature of Reactants’ Properties:
  • Reactants with higher reactivity tend to have faster reaction rates.
  • Reactants with stronger bonds require more energy and have slower reaction rates.
• Concentration of Reactants:
  • Increasing reactant concentration increases the rate of reaction (according to the rate equation).
• Temperature:
  • Higher temperatures increase the kinetic energy of particles, leading to more collisions and faster reaction rates.
• Catalysts:
  • Substances that speed up a reaction without being consumed.
  • Lower the activation energy.
• Physical State:
  • Gaseous and dissolved reactants typically react faster than solids due to increased particle motion. slide-14

Chemical Kinetics - Collision Theory

• Collision Theory:
  • States that for a chemical reaction to occur:
    • Reactant particles must collide with sufficient energy (equal to or greater than the activation energy).
    • Reactant particles must collide in the correct orientation.
  • Only a small fraction of collisions leads to a reaction due to insufficient energy or unfavorable orientation.
• Factors affecting collision rate:
  • Concentration of reactants: Higher concentration increases the chance of collisions.
  • Temperature: Higher temperatures increase the kinetic energy and collision frequency.
• Effectively increasing the number of collisions can increase the rate of reaction. slide-15

Chemical Kinetics - Effect of Temperature on Reaction Rate

• Increasing Temperature:
  • Increases the kinetic energy of particles.
  • Increases the number of particles with energy equal to or greater than the activation energy.
  • Increases the frequency of successful collisions.
  • Increases the rate of reaction.
• Temperature is a crucial factor affecting reaction rate.
• Small changes in temperature can lead to significant changes in rate.
• Example: Combustion reactions generally occur faster at higher temperatures. slide-16

Chemical Kinetics - Order of Reaction

• Order of Reaction:
  • Definition: The sum of the exponents in the rate equation.
  • Zero Order: Rate is independent of reactant concentration (rate = k).
  • First Order: Rate is directly proportional to the concentration of one reactant (rate = k[A]).
  • Second Order: Rate is directly proportional to the square of the concentration of one reactant or the product of the concentrations of two different reactants (rate = k[A]^2 or rate = k[A][B]).
  • Overall Order: Sum of the exponents in the rate equation.
• Example: For the reaction A + B → C, rate = k[A][B] represents a second-order reaction. slide-17

Chemical Kinetics - Integrated Rate Laws

• Differential Rate Law:
  • Describes how the rate of a reaction changes with time.
  • Differentiates rate equations.
• Integrated Rate Law:
  • Describes how the concentration of a reactant changes with time.
  • Integrates rate equations.
• Provides a relationship between time and reactant concentration.
• Can be represented as equations, graphs, or mathematical formulas.
• Useful for determining reaction orders and rate constants. slide-18

Chemical Kinetics - Half-Life

• Half-Life:
  • Definition: The time taken for the concentration of a reactant to decrease by half.
  • Symbol: t1/2.
  • Half-life depends on the order of the reaction.
• Zero Order Half-Life:
  • t1/2 = [A]0 / 2k
• First Order Half-Life:
  • t1/2 = 0.693 / k
• Second Order Half-Life:
  • t1/2 = 1 / (k[A]0)
• Example: If the half-life of a first-order reaction is 10 seconds, after 20 seconds, the reactant concentration will be 1/4 of the initial concentration. slide-19

Chemical Kinetics - Arrhenius Equation

• Arrhenius Equation:
  • Relates the rate constant of a reaction to temperature.
  • k = A * e^(-Ea/RT)
  • k: Rate constant
  • A: Pre-exponential factor (frequency factor) - a constant that depends on collision frequency and orientation.
  • Ea: Activation energy
  • R: Gas constant (8.314 J/(mol*K))
  • T: Temperature in Kelvin (K)
• As temperature increases, the rate constant and the rate of reaction increase.
• Example: The Arrhenius equation explains why food spoils faster at higher temperatures. slide-21

Chemical Equilibrium

• Definition: A state in which the forward and reverse reactions occur at equal rates
• Dynamic equilibrium: Reactants and products are continuously interchanging, but the concentrations remain constant
• Equilibrium constant (Kc): Quantifies the ratio of the concentrations of products to reactants at equilibrium
• Expression: Kc = [Products] / [Reactants]
• Relationship between Kc and reaction coefficient: Kc = (C)^c(D)^d / (A)^a(B)^b
• Le Chatelier’s principle: Predicts the effect of changing conditions on an equilibrium system slide-22

Le Chatelier’s Principle

• States that a system at equilibrium will respond to an external stress by shifting in a direction to restore equilibrium
• Changes in concentration:
  • Increasing reactant concentration shifts the equilibrium towards the products
  • Increasing product concentration shifts the equilibrium towards the reactants
• Changes in pressure (for gaseous reactions):
  • Increasing pressure shifts the equilibrium towards the side with fewer moles of gas
  • Decreasing pressure shifts the equilibrium towards the side with more moles of gas
• Changes in temperature:
  • Increasing temperature shifts the equilibrium in the endothermic direction
  • Decreasing temperature shifts the equilibrium in the exothermic direction slide-23

Factors Affecting Equilibrium

• Concentration:
  • Altering the concentration of reactants or products can change the equilibrium position
• Pressure (for gaseous reactions):
  • Changing the pressure by altering the volume or number of moles of gas affects equilibrium if the number of moles changes
• Temperature:
  • Changing the temperature shifts the equilibrium position according to the reaction’s enthalpy change (ΔH)
• Catalysts:
  • Catalysts do not affect the position of equilibrium but can increase the speed at which equilibrium is achieved slide-24

Equilibrium Expressions for Reactions

• General Reaction: aA + bB ⇌ cC + dD
• Equilibrium constant expression: Kc = ([C]^c [D]^d) / ([A]^a [B]^b)
• Kc: Equilibrium constant
• : Concentration of substance X
• a, b, c, d: Stoichiometric coefficients of the reactants and products
• Example: For the reaction 2A + B ⇌ C, the equilibrium expression is Kc = ([C] / ([A]^2 [B]) slide-25

Calculating Equilibrium Constant (Kc)

• Example:
  • For the reaction N2 (g) + 3H2 (g) ⇌ 2NH3 (g), the equilibrium concentrations are [N2] = 0.10 M, [H2] = 0.30 M, and [NH3] = 0.20 M.
  • Substitute the values into the equilibrium expression: Kc = ([NH3]^2) / ([N2] * [H2]^3)
  • Kc = (0.20)^2 / (0.10 * 0.30^3)
  • Calculate the value of Kc slide-26

Reaction Quotient (Qc)

• Definition: Similar to the equilibrium constant expression, but uses initial or non-equilibrium concentrations of reactants and products
• Compares the relative amounts of reactants and products at any point in a reaction
• If Qc = Kc, the reaction is at equilibrium
• If Qc < Kc, the reaction proceeds in the forward direction
• If Qc > Kc, the reaction proceeds in the reverse direction slide-27

Manipulating Equilibrium Expressions

• Reverse Reaction: If a reaction is reversed, the reciprocal of the original equilibrium constant (Kc) is the new equilibrium constant
• Multiply Reaction by a Constant: If a reaction is multiplied by a constant, raise the original equilibrium constant (Kc) to the power of that constant
• Combined Equilibrium Expressions: If two or more reactions are added or subtracted to determine an overall reaction, the equilibrium constant for the overall reaction is the product or quotient of the equilibrium constants of the individual reactions slide-28

Solubility Equilibrium

• Definition: A specific type of equilibrium that occurs when a sparingly soluble ionic compound dissolves and then re-precipitates in a solution
• Equilibrium constant expression: Ksp = [Cation]^m [Anion]^n
• m, n: Stoichiometric coefficients of the cation and anion in the balanced chemical equation slide-29

Factors Affecting Solubility

• Common Ion Effect: The solubility of a salt is reduced when it is dissolved in a solution that already contains one of its constituent ions
• pH: The solubility of many compounds depends on the pH of the solution
• Temperature: The solubility of most solid solutes increases with increasing temperature slide-30

Acid-Base Equilibrium

• Definition: An acid reacts with a base to form products, and the forward and reverse reactions occur simultaneously
• Equilibrium constant expression: Ka = [H3O+][A-] / [HA]
• Kw: The ion product constant for water (Kw = [H3O+][OH-])
• pKa: The negative logarithm (base 10) of the acid dissociation constant (pKa = -log10 Ka)
• Relationship between pH and pKa: pH = pKa + log10([A-] / [HA])

Chemical Kinetics

• The study of rates of chemical reactions and the factors that influence them.

Reaction Rate

• The speed at which a chemical reaction takes place. Factors affecting reaction rate:

1. Concentration of reactants

2. Temperature

3. Surface area

4. Catalysts

Rate Law

• An equation that relates the reaction rate with the concentrations of reactants.
• General form:
  • Rate = k[A]^m[B]^n Examples:

1. For the reaction A + 2B → C, the rate law is: Rate = k[A][B]^2

Order of Reaction

• The sum of the powers to which all the reactant concentrations are raised in the rate law equation. Examples:

1. Rate = k[A]^2[B] is a second-order reaction.

2. Rate = k[A]^3 is a third-order reaction.

3. Rate = k[NO]^[0.5] is a half-order reaction.

Temperature and Reaction Rate

• Increasing temperature generally increases the reaction rate.
• This is because higher temperature provides more energy to reactant particles, leading to more frequent and energetic collisions.

Activation Energy

• The minimum energy required for a chemical reaction to occur.
• Reaction rate increases with increasing temperature due to more molecules having the required activation energy. Equation:

1. Arrhenius equation: k = A * e^(-Ea/RT)

Concentration and Reaction Rate

• Increasing the concentration of reactants generally increases the reaction rate.
• Higher concentration means more reactant particles, leading to more frequent collisions and a higher chance of effective collisions.

Surface Area and Reaction Rate

• Increasing the surface area of solid reactants increases the reaction rate. Example:

1. Breaking a large brick into small pieces will increase the surface area available for reaction, speeding up the process.

Catalysts

• Substances that increase the rate of a chemical reaction without undergoing permanent changes themselves.
• Catalysts lower the activation energy by providing an alternative reaction pathway. Example:

1. Enzymes are biological catalysts that speed up specific chemical reactions in living organisms.

Catalytic Converter

• A device used in vehicles to reduce air pollution by converting harmful gases into less harmful ones.
• Catalytic converters contain catalysts such as platinum, rhodium, and palladium.
• They facilitate the conversion of harmful pollutants like carbon monoxide, nitrogen oxides, and unburned hydrocarbons into carbon dioxide, nitrogen, and water.

Factors Affecting Reaction Rate (Continued)

• Pressure: Increasing the pressure of gases can increase the reaction rate as it leads to more frequent collisions between gas molecules.
• Presence of Light: Some reactions are accelerated by the presence of light, which provides additional energy to reactant particles.
• Nature of Reactants: Different reactants have different reaction rates due to variations in their chemical properties and molecular structures.
• Presence of Inhibitors: Certain substances, called inhibitors, can slow down or prevent a reaction from taking place by interfering with the reaction mechanism.
• Presence of Radiation: High-energy radiation can induce chemical reactions and increase reaction rates.

Rate Determining Step

• In a multi-step reaction, the slowest step is known as the rate determining step.
• The rate of the overall reaction depends on the rate of this step. Example:

1. For the reaction A + B → C + D, if the formation of C and D is slower than the formation of A and B, the rate determining step is the formation of C and D.

Reaction Mechanism

• The sequence of steps by which a reaction occurs.
• It provides information about the intermediate species, transition states, and reaction pathways. Example:

1. The reaction mechanism for the decomposition of hydrogen peroxide is a two-step process:
   • Step 1: H2O2 → H2O + [O]
   • Step 2: [O] + H2O2 → H2O + O2

Collision Theory

• The collision theory explains how chemical reactions occur and why reaction rates vary. Key Points:
• For a reaction to occur, reactant particles must collide with sufficient energy and proper orientation.
• Only a fraction of collisions result in a reaction, known as effective collisions.
• Increasing the frequency of effective collisions increases the reaction rate.
• Temperature, concentration, and surface area affect the frequency of effective collisions.

Reaction Rate and Molecular Collisions

• Collisions between reactant molecules can be classified as follows:

1. Ineffective Collisions:
   • Collisions where there is insufficient energy or incorrect orientation for reaction to occur.
   • These collisions do not contribute to the reaction rate.

2. Effective Collisions:
   • Collisions where there is sufficient energy and proper orientation for reaction to occur.
   • Only effective collisions result in a reaction and contribute to the reaction rate.

Arrhenius Equation

• The Arrhenius equation relates the rate constant (k) to temperature and activation energy. Equation:
• k = A * e^(-Ea/RT)
  • k: Rate constant
  • A: Pre-exponential factor (frequency factor)
  • Ea: Activation energy
  • R: Gas constant
  • T: Absolute temperature Example:

1. If the activation energy (Ea) of a reaction is high, the reaction rate will be lower compared to a reaction with a lower activation energy.

Integrated Rate Laws

• Integrated rate laws relate the concentration of reactants or products to time. Examples:

1. Zero-order reaction: [A]t = [A]0 - kt

2. First-order reaction: ln[A]t = ln[A]0 - kt

3. Second-order reaction: 1/[A]t = 1/[A]0 + kt

• These equations can be used to determine the orders of reactions experimentally.

Half-Life

• The half-life of a reactant is the time required for the concentration to decrease by half. Equations:

1. Zero-order reaction: t1/2 = [A]0/2k

2. First-order reaction: t1/2 = (0.693)/k

3. Second-order reaction: t1/2 = 1/(k[A]0)

• The half-life remains constant for a first-order reaction but varies with concentration for a second-order reaction.

Catalysts and Reaction Pathways

• Catalysts provide an alternative reaction pathway with lower activation energy.
• They increase the reaction rate without being consumed in the reaction. Example:

1. In the Haber process for the production of ammonia, iron acts as a catalyst to facilitate the reaction between nitrogen and hydrogen.

Summary

• Chemical kinetics studies the rates of reactions and the factors that influence them.
• The rate of a reaction is affected by factors such as temperature, concentration, surface area, and the presence of catalysts.
• The rate law equation relates the reaction rate to the concentrations of reactants.
• The rate determining step is the slowest step in a multi-step reaction.
• Collision theory explains how effective collisions lead to chemical reactions.
• The Arrhenius equation relates the rate constant to temperature and activation energy.
• Integrated rate laws and half-life provide information about the concentration-time relationship in reactions.

Reaction Mechanism (Continued)

• Elementary reactions: The individual steps in a reaction mechanism are called elementary reactions.
• Intermediates: Species that are formed and consumed during the reaction but do not appear in the final reactants/products are called intermediates.
• Rate-determining step: The slowest step in the reaction mechanism determines the overall reaction rate. Example:

1. The reaction mechanism for the decomposition of ozone (O3) involves two elementary reactions:
   • Step 1: O3 → O2 + O
   • Step 2: O2 + O → O3

Arrhenius Equation (Continued)

• The Arrhenius equation shows the relationship between the rate constant (k) and temperature. Equation:
• k = A * e^(-Ea/RT)
  • k: Rate constant
  • A: Pre-exponential factor (frequency factor)
  • Ea: Activation energy
  • R: Gas constant
  • T: Absolute temperature Example:

1. A reaction has an activation energy (Ea) of 50 kJ/mol and a rate constant (k) of 5.0 x 10^(-2) s^(-1) at 298 K. Calculate the rate constant at 350 K.

Integrated Rate Laws (Continued)

• Integrated rate laws provide a mathematical relationship between concentrations and time for different reaction orders. Example:

1. For a first-order reaction, the integrated rate law equation is: ln[A]t = ln[A]0 - kt.

2. Suppose the initial concentration of reactant A is 0.20 M and the rate constant (k) is 0.05 s^(-1). Calculate the concentration of A after 5.0 seconds.

Half-Life (Continued)

• The half-life of a reaction is the time required for the concentration of a reactant to decrease by half. Example:

1. For a second-order reaction, the half-life can be calculated using the equation: t1/2 = 1/(k[A]0).

2. If the initial concentration ([A]0) is 0.10 M and the rate constant (k) is 0.02 M^(-1) s^(-1), calculate the half-life of the reaction.

Reaction Orders

• The reaction order represents the exponent to which the concentration of a reactant is raised in the rate law equation. Examples:

1. For a reaction rate law equation Rate = k[A]^2[B], the reaction is second order with respect to A and first order with respect to B.

2. If the rate law equation is Rate = k[A][B]^3, the reaction is first order with respect to A and third order with respect to B.

Zero-Order Reactions

• In a zero-order reaction, the concentration of reactant has no effect on the reaction rate. Rate Law:
• Rate = k Examples:

1. Decomposition of hydrogen peroxide: 2H2O2 → 2H2O + O2

2. Hydrolysis of sucrose: C12H22O11 + H2O → 2C6H12O6

First-Order Reactions

• In a first-order reaction, the rate of reaction is directly proportional to the concentration of only one reactant. Rate Law:
• Rate = k[A] Examples:

1. Radioactive decay: N(t) = N0 * e^(-kt)

2. Atmospheric ozone formation: O2 + O → O3

Second-Order Reactions

• In a second-order reaction, the rate of reaction is directly proportional to either the concentration of two different reactants or the square of the concentration of a single reactant. Rate Law:
• Rate = k[A][B] (two reactants)
• Rate = k[A]^2 (single reactant) Example:

1. The reaction A + B → C is second order overall with a rate law equation: Rate = k[A][B].

Summary

• Reaction mechanisms involve elementary reactions and intermediates.
• The Arrhenius equation relates the rate constant and activation energy to temperature.
• Integrated rate laws provide mathematical relationships between concentrations and time for different reaction orders.
• Half-life is the time required for the concentration of a reactant to decrease by half.
• Reaction orders represent the exponents in the rate law equation.
• Zero-order reactions have a constant rate, first-order reactions have rate proportional to one reactant concentration, and second-order reactions have rate proportional to two reactant concentrations.

Conclusion

• Chemical kinetics plays a crucial role in understanding the rates of chemical reactions.
• Factors such as temperature, concentration, surface area, and catalysts affect the reaction rates.
• The reaction mechanism and rate-determining step provide insights into the pathways and slowest steps involved in reactions.
• The Arrhenius equation, integrated rate laws, and half-life calculations help in analyzing the kinetics of reactions.
• Understanding these concepts is essential for predicting reaction rates and designing reaction conditions for desired outcomes.