CH12002
About
Mathematical Foundations
0.1
Working with Exponentials and Logarithms
0.1.1
Exponential Functions
0.1.2
Logarithmic Functions
0.1.3
Converting Between Exponential and Logarithmic Forms
0.2
Linearising Exponential Equations
0.2.1
General Approach
0.2.2
Example
0.3
Differentiation
0.3.1
Key Results
0.3.2
The Special Property of Exponentials
0.3.3
Example
0.4
Integration
0.4.1
Key Results
0.4.2
Definite Integrals
0.4.3
Example: Solving a Differential Equation by Separation of Variables
0.5
Additional Resources
1
Introduction to Chemical Kinetics
1.1
Why Study Reaction Kinetics?
1.2
Describing How Concentrations Change with Time
1.3
Reaction Rates
1.4
Mass Balance
1.5
Rate Laws
1.6
Elementary Processes
1.7
Complex Reactions
1.8
Units of the Rate Constant
1.9
Key Concepts
2
Integrated Rate Laws
2.1
Zeroth-Order Reactions
2.2
First-Order Reactions
2.3
Second-Order Reactions
2.4
Distinguishing Reaction Orders by Graphical Analysis
2.5
Worked Example: Decomposition of Azomethane
2.6
Reactions with Two Different Reactants
2.7
Key Concepts
3
Methods for Determining Rate Laws from Experimental Data
3.1
The Integral Method
3.1.1
Worked Example: Azomethane Decomposition Revisited
3.2
The Half-Life Method
3.2.1
Worked Example: Azomethane Revisited
3.3
The Isolation Method
3.3.1
Varying the Excess Concentration
3.4
The Differential Method (Initial Rates)
3.4.1
Worked Example: Determining Orders by Comparing Experiments
3.5
Key Concepts
4
Complex Reaction Mechanisms
4.1
Consecutive Reactions
4.1.1
Solving the Rate Equations
4.1.2
The Rate-Determining Step
4.2
Equilibrium Reactions
4.3
Pre-Equilibrium Mechanisms
4.4
Key Concepts
5
The Steady-State Approximation
5.1
The Idea Behind the Steady-State Approximation
5.2
Applying the SSA: A + B ⇌ C → D
5.2.1
Pre-Equilibrium and Irreversible Limits
5.3
A Second Example: A ⇌ B, B + C → D
5.3.1
Concentration-Dependent Limiting Behaviour
5.4
SSA versus Pre-Equilibrium
5.5
Key Concepts
6
Problem-Solving Session
7
Unimolecular and Third-Order Reactions
7.1
The Lindemann–Hinshelwood Mechanism
7.1.1
Separating Activation from Reaction
7.1.2
The Lindemann Rate Law
7.1.3
Pressure Dependence
7.2
Third-Order Reactions and Collision Dynamics
7.2.1
The NO Oxidation
7.2.2
Formation of Ozone: Why a Third Body is Needed
7.3
Key Concepts
8
Binding and Catalysis
8.1
Enzyme Kinetics
8.1.1
The Michaelis–Menten Mechanism
8.1.2
Deriving the Michaelis–Menten Equation
8.1.3
Limiting Cases
8.1.4
The Physical Meaning of
\(K_\mathrm{M}\)
8.1.5
Determining Michaelis–Menten Parameters
8.1.6
Catalytic Efficiency
8.2
The Langmuir Adsorption Isotherm
8.2.1
Limiting Cases
8.3
The Common Pattern: Saturation Kinetics
8.4
Key Concepts
9
Chain Reactions
9.1
The Ozone Layer and CFC-Catalysed Destruction
9.2
The H
2
+ Br
2
Reaction
9.2.1
The Mechanism
9.2.2
Deriving the Rate Law Using the SSA
9.3
Chain Length
9.3.1
Returning to Ozone
9.4
Key Concepts
10
Feedback, Stability, and Explosions
10.1
Why Reactive Intermediates Reach a Steady State
10.2
The General Feedback Equation
10.3
From Straight Chains to Branching Chains
10.4
Positive Feedback and Explosions
10.5
The Hydrogen–Oxygen Explosion
10.5.1
The H
2
/O
2
chain mechanism
10.5.2
Wall termination at low pressure: the first explosion limit
10.5.3
Three-body termination at high pressure: the second explosion limit
10.5.4
The third explosion limit and thermal runaway
10.5.5
The explosion diagram
10.6
Key Concepts
11
Temperature Effects on Reaction Rates
11.1
The Arrhenius Equation
11.2
Extracting Arrhenius Parameters from Data
11.3
What Do
\(E_\mathrm{a}\)
and
\(A\)
Tell Us?
11.4
Reading an Arrhenius Plot: The Sign of
\(E_\mathrm{a}\)
11.5
When the Arrhenius Plot Is Not Linear
Key Concepts
12
Problem-Solving Session
Course Review
From Measurement to Mechanism
A Toolkit with Recurring Structure
Temperature Completes the Picture
Appendices
A
Integrated Rate Law for Two Different Reactants
A.1
Setting Up the Problem
A.2
Solving by Partial Fractions
A.3
The Equal-Concentration Limit
B
Integrated Rate Law for Consecutive Reactions
B.1
Identifying the Standard Form
B.2
Applying the Integrating Factor
B.3
Applying the Initial Condition
B.4
Interpreting the Result
C
Relaxation Methods and the Approach to Equilibrium
C.1
The Approach to Equilibrium
C.2
The Temperature Jump Experiment
C.3
Analysing the Relaxation
C.4
Extracting Individual Rate Constants
D
Why Don’t All Bimolecular Reactions Require a Third Body?
D.1
The Problem: Energy Disposal After Bond Formation
D.2
Why Most Reactions Avoid This Problem
D.3
A Spectrum of Behaviour
E
Translational Kinetic Energy in Sticking Collisions
F
Negative Apparent Orders
F.1
When Increasing a Concentration Slows the Reaction
F.2
Example 1: Product Inhibition in H
2
+ Br
2
\(\rightarrow\)
2HBr
F.3
Example 2: Competitive Adsorption in Surface Reactions
F.4
Recognising Inhibition in Rate Laws
G
Solving the Feedback Equation
G.1
Setting Up the Integral
G.2
Evaluating the Left-Hand Side
G.3
Solving for
\([\mathrm{I}]_t\)
CH12002 Lecture Notes
CH12002 Lecture Notes
Benjamin J. Morgan
2026-03-18
About
These notes accompany the CH12002 lecture course on Chemical Kinetics.