Introductory description

To provide the student with a quantitative appreciation of four branches of physical chemistry:

1. Quantum mechanics
2. Kinetics
3. Thermodynamics
4. Spectroscopy

The Maths skills component provides the mathematical learning support for the Year 1 modules and more advanced modules in Years 2/3/4, enabling students to solve problems in the main branches of chemistry. The mathematical skills taught allow students to understand the concepts behind much of chemistry and allow the processing of their own data.

The majority of the module content is drawn from components of A-level syllabuses. As such, most students will already be familiar with some aspects of the module syllabus, but the pattern of familiarity will be heterogeneous across the class. The primary aim of the module is to equip all students with the necessary mathematical skills to succeed in their chemistry degree at Warwick. The module is structured to allow individual students to concentrate their time on those areas of the module with which they are unfamiliar.

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

The module will be taught in distinct sections. Here follows an illustrative syllabus for each section of the module.

Quantum Mechanics

• TOPIC 1: General concepts: What is quantum mechanics, and why do we need it?
• TOPIC 2: Fundamental principles of quantum mechanics: Postulates, Hamiltonians and operators.
• TOPIC 3: Solvable systems
  o Solvable system I: Particle in a box
  o Solvable system II: Free-particle motion
  o Solvable system III: Harmonic oscillator
  o Solvable system IV: Rigid rotor
  o Solvable system V: One-electron systems
• TOPIC 4: Spin and many-electron systems

Kinetics

• TOPIC 1: Reaction potential energy surfaces and kinetics at the molecular level
• TOPIC 2: Rates of reaction and rate laws
• TOPIC 3: Determining the rate law from experimental data
• TOPIC 4: Multistep reactions including unimolecular, bimolecular, enzyme and chain reactions
• TOPIC 5: Temperature dependence of reaction rates

Thermodynamics

• TOPIC 1 : Foundations: ideal gas, enthalpy and entropy
• TOPIC 2 : Chemical equilibrium, liquids and gases in equilibrium, vapour pressure
• TOPIC 3 : Phase diagrams of pure substances
• TOPIC 4 : The thermodynamic description of mixtures
• TOPIC 5 : The First, Second and Third Laws of thermodynamics

Spectroscopy

• TOPIC 1. Properties of electromagnetic radiation
• TOPIC 2. The H-atom spectrum and the Rydberg equation
• TOPIC 3. Factors influencing transition intensities
• TOPIC 4. Rotational spectroscopy
• TOPIC 5. Vibrational spectroscopy

An example Maths skills syllabus may include elements from the following:
Perform routine algebraic manipulations.
Manipulation of units and dimensions.
Solve simple equations.
Understand the basis of differential calculus, be able to differentiate and, find maxima and minima.
Integrate functions and solve simple differential equations.
Determine the limits of simple functions.
Manipulate logarithmic and exponential functions.
Introduction to error propagation.
Perform routine trigonometric manipulations.
Expand simple series.
Manipulate complex numbers, vectors, and matrices.

Learning outcomes

By the end of the module, students should be able to:

• Understand core concepts in physical chemistry, spanning thermodynamics, kinetics, quantum mechanics, and spectroscopy.
• Apply core concepts from physical chemistry in a range of exercises, often mathematically based.
• Use physical chemistry concepts to understand and explain practical science problems and applications.
• Tackle physical chemistry concepts of similar complexity and depth on the periphery of, or even outside, the syllabus.
• Perform routine algebraic manipulations. Solve simple equations, including both quadratic and simultaneous. Manipulate logarithmic functions and powers. Determine the limiting values of functions.
• Differentiate functions and find maxima and minima. Integrate functions and solve simple differential equations.
• Perform routine trigonometric manipulations. Expand simple series. Manipulate complex numbers and matrices. Solve simple eigenvalue problems
• Become familiar with the use of a range of general IT software packages and coding.
• Be able to use a range of chemical software, plus access relevant databases to support their practical chemistry.

Indicative reading list

Core textbook:
Physical Chemistry, P.W. Atkins and J. de Paula (Oxford University Press) 


Further (non-compulsory) reading:

THERMODYNAMICS:
Physical Chemistry: A Molecular Approach, D. A. McQuarrie and J. D. Simon (University Science Books)

KINETICS:

Reaction Kinetics, M. J. Pilling and P. W. Seakins (Oxford University Press)

QUANTUM MECHANICS:
Molecular Quantum Mechanics, P. W. Atkins (Oxford University Press)
Physical Chemistry: A Molecular Approach, D. A. McQuarrie and J. D. Simon (University Science Books)

SPECTROSCOPY:
Modern Spectroscopy, J. M. Hollas (Wiley)
Symmetry and Spectroscopy, D. C. Harris & M. D. Bertolucci (Oxford University Press)

Maths skills component:
Maths for Chemists, 2nd Ed., M. Cockett and G. Doggett, RSC Publishing.
Foundation Maths, 4th Ed., A. Croft and R. Davison, Pearson Prentice Hall.
Calculus with Analytical Geometry, 2nd Ed., G. F. Simmons, McGraw Hill.

Subject specific skills

Numeracy
Problem solving
Organisation and time management

Transferable skills

Numeracy
Problem solving
Organisation and time management