Introduction to Contextual Maths in Chemistry

Fiona Dickinson, Andrew McKinley

• Publisher: Royal Society of Chemistry
• Year: 2021
• eBook ISBN: 9781839161933
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Chemistry
• Index: Chemistry

CHEMISTRY STUDENT GUIDES. GUIDED BY STUDENTS

For any student who has ever struggled with a mathematical understanding of chemistry, this book is for you.

Mathematics is the essential tool for physical scientists. We know that confidence in using mathematics early on in a chemistry degree builds a solid foundation for further study. However, applying the abstract mathematics taught in schools to chemical phenomena is one of the biggest challenges that chemistry students face.

In this book, we take a 'chemistry-first' approach. We link the mathematics to recognisable chemical concepts, building on high school chemistry, to facilitate deeper understanding. We cover the practical mathematical skills, including representation of data as tables and graphs, and give an overview of error handling in the physical sciences. More advanced mathematical concepts are introduced, using calculus to determine kinetic rate laws, intermolecular forces and in quantifying energetic change in thermodynamics. We also introduce the concept of the complex number and its role in considering quantum wave functions, widely used in computational chemistry.

There are worked examples and problem sets to provide plenty of practise material to build proficiency. We also include insights from real students, which identify common problem areas and provide the prompts that helped them to overcome these.

Chemistry Student Guides are written with current students involved at every stage, guiding the books towards the most challenging aspects of the topic.

CHAPTER

Learning Points: What We'll Cover

• □Notation of functions and inverse functions
• □Higher-order operations: powers, roots, exponentials and logarithms
• □Identifying inverse functions of higher-order operations
• □Strategies for using inverse functions to rearrange equations
• □Dimensional analysis: using units to validate equations and in combining quantities
• □SI base and derived units
• □Scaling factors: both SI and non-SI
• □Interconverting units and identifying a scaling factor

Why This Chapter Is Important

• There is a wealth of mathematical notation which we need to understand to apply the maths in a chemical context.
• The models we use in chemistry are fundamentally mathematical; understanding the mathematical relationships allows us to apply these ideas.
• All these models are represented as equations; being able to rearrange and manipulate them allows us to make predictions and to interpret experimental observations.
• Values are meaningless without a unit; having a consistent and systematic approach to the handling of units means that values can be shared and interpreted with no ambiguity, whether using SI units or quantities which are more manageable in a chemistry context, including dm³ and wavenumbers (cm⁻¹).
• The process of dimensional analysis allows us to determine the appropriate units for our calculated quantities.

The Basics: Mathematical Functions, Rearranging Equations and Handling Units

Chemistry is a physical science; there is a wealth of equations which describe the behaviour of chemical systems. However, very few of these will be in a form which is easily recognisable, or might not have the subject we need in order to carry out the desired calculation. Consequently, we must be able to rearrange equations so that we can ensure that we use the calculations needed to test our reactions against an existing model.

The subject of an equation is the thing you are trying to calculate; it is separated on its own on one side of the equation.

To confidently manipulate these equations, we need to identify mathematical operations and functions, as well as how to un...

Table of contents

• Cover
• Title
• Copyright
• Author Biographies
• Student Contributors
• Preface
• Acknowledgements
• List of Symbols and Their Uses in Chemistry
• Table of Contents
• 1 The Basics: Mathematical Functions, Rearranging Equations and Handling Units
• 2 Probability and Statistics in Chemistry
• 3 Experimental Uncertainty and Significant Figures: What Are the Bounds of Experimental Error?
• 4 Tables and Graphs – Presenting and Analysing Experimental Data
• 5 Trigonometry and Coordinate Systems: Describing Molecular Positions
• 6 Vectors, Directions and Crystal Structures
• 7 Calculus 1, Differentiation: Mean Speeds and Equilibrium Separations
• 8 Calculus 2, Integration: Reaction Kinetics and Rate Laws
• 9 Complex Numbers: Quantum Mechanics and Solving the Schrödinger Equation
• Appendix: The Mathematical Toolkit
• Reading List
• Index