Mathematics for Chemists: A Study Guide
Much of this material has been developed with support from the Royal Society of Chemistry,
together with advice and help from many colleagues whose contributions are gratefully
acknowledged.
QVAs - Questions with video answers: These are on-line multiple choice questions, with
each question providing a fully worked answer on video.
Keywords: These are suggested ‘search’ terms that can be used to access further
resources in the 'Discover Maths for Chemists' website
Book sections: These are relevant sections in the textbook, Essential Mathematics and
Statistics for Science, 2nd ed, by G Currell and A A Dowman
Notes: This Word document can be edited to provide guidance to specific groups of students
as hard copy or on-line. The resources below are indicative of its possible use, and material
from other sources can be added to match the requirements of particular student cohorts.
Diagnostic Assessment
G Currell, University of the West of England, Bristol
http://calcscience.uwe.ac.uk/w2/sa/saIndex.htm
Guidance: For any questions that you don’t understand, you should seek additional
help/revision by following the on-line feedback guidance given with the answers
Note for incorrect answers:
1 - 28, 31, 32
Revise topics immediately
29, 30, 33 - 40
Topics will be covered in tutorials
Basics
G Currell, University of the West of England, Bristol
http://calcscience.uwe.ac.uk/w2/sg/sgBasics/sgBasics.htm
Keywords: Algebra, BODMAS, indices, powers, fractions
Book sections: 2.1, 2.2, 2.4, 3.1, 3.3
Guidance: These are essential techniques in maths. Check asap that you understand, and
can correctly answer, all the QVA questions. For further guidance - go to Maths Support.
Video tips:
Using the rules of BODMAS
Basic
Using 'powers of ten' for scientific (standard) Basic
notation in a calculator and Excel
Changing ‘powers of ten’
Basic
QVAs:
Number line
Basic
BODMAS rules
Basic
Powers
Basic
Scientific (standard) notation
Basic
Some basic techniques in algebra
Basic
pdf Tutorials:
Powers
Basic
Fractions
Basic
Areas and volumes
Basic
Royal Society of Chemitry
p1
Dr Graham Currell
Rearranging Equations
G Currell, University of the West of England, Bristol
http://discovermaths.rsc.org/Resource/Item/Rearranging%20Equations%20Study%20Guide
Keywords: Rearranging, transposing
Book sections: 3.2, 3.4
Guidance: These are essential techniques in maths. Check asap that you understand, and
can correctly answer, all the ‘Basic’ QVA questions.
Video tips:
SIX rules for rearranging equations
Basic
Using the rules of BODMAS
Basic
Using 'powers of ten' for scientific (standard) Basic
notation in a calculator and Excel
QVAs:
BODMAS rules
Basic
Some basic techniques in algebra
Basic
Rearranging simple equations
Basic
Rearranging pV = nRT
Basic
Substituting values in pV = nRT
Basic
Rearranging more complicated equations
Basic / Intermediate - covered in tutorial
Rearranging exponential equations
Intermediate - covered in later tutorial
Units of Measurement in Science
G Currell, University of the West of England, Bristol and R Wright, University of Nottingham
http://calcscience.uwe.ac.uk/w2/sg/sgUnitsScience/sgUnitsScience.htm
Keywords: Units, SI
Book sections: 2.2
Guidance: This is an essential topic in science. Following the introductory lectures in week
1, check that you understand, and can correctly answer, all the ‘Basic’ QVA questions.
Video introduction:
Units in science
Video tips:
Basic
Various: v1, v2, v3, v4, v5, v6
Basic
QVAs:
Using SI Prefixes
Basic
Basic unit conversion
Basic
Handling ‘power’ units
Basic
Conversion of combined units
Basic
Using ‘units’ to understand equations
Basic / Intermediate - covered in later tutorial
Conversion of units - pV = nRT
Basic
Moles, Concentration and Dilution
G Currell, University of the West of England, Bristol
http://discovermaths.rsc.org/Resource/Item/Moles,%20concentrations%20and%20dilutions
Keywords: moles, grams, molarity, molar, concentration, dilution, propagation of errors
Book sections: 2.3
Guidance: These are essential topics in chemistry. Following the introductory lectures in
week 1, check that you understand, and can correctly answer, all the ‘Basic’ QVA questions.
For further guidance - go to ??.
QVAs:
Moles and grams
Basic
Concentrations
Basic
Dilutions
Basic
Errors in concentration and dilution
Intermediate - covered in later tutorial
Royal Society of Chemitry
p2
Dr Graham Currell
Straight Lines / Linear Regression
G Currell, University of the West of England, Bristol
http://discovermaths.rsc.org/Resource/Item/Linear%20Regression%20Study%20Guide
Keywords:
Book sections: 4.1, 4.2, 4.3
Guidance: These are essential topics in science, and will be revised in term 1.
QVAs:
Straight line relationships
Basic
Using y = mx + c
Basic
Using SLOPE and INTERCEPT
Basic
Straight line analysis of pV = nRT
Basic
Linearization
Intermediate - covered in later tutorial
Linear calibration in science
Intermediate - covered in later tutorial
Downloads:
Excel file: Gas Law Calculation
Logarithms and Exponentials
G Currell, University of the West of England, Bristol
http://calcscience.uwe.ac.uk/w2/sg/sg_LogExps/sg_LogExps.htm
Keywords:
Book sections: 5.1, 5.2
Guidance: These are essential topics in science, and will be revised in term 1.
QVAs:
Powers
Basic
Logarithms and powers of 10 and e
Basic
Properties of logarithms
Basic
Calculations with logs and exponentials
Basic
Rearranging exponential equations
Intermediate - covered in later tutorial
Experimental Error and Uncertainty
G Currell, University of the West of England, Bristol
http://calcscience.uwe.ac.uk/w2/sg/sgUncertaintyError/sgUncertaintyError.htm
Keywords:
Book sections: 1.2, 7.1, 7.2, 8.2, 8.3, 13.3
Guidance:.This is an essential topic at all levels of science.
QVAs:
Experimental variations and errors
Basic/Intermediate
Experimental uncertainty
Intermediate
Combining uncertainties / errors
Intermediate
Errors in concentration and dilution
Intermediate
Downloads:
Excel file:Soil pH Data
Basic/Intermediate
Excel file: Replicate Data
Intermediate
Excel file: Combining Uncertainties
Intermediate
Royal Society of Chemitry
p3
Dr Graham Currell
Data Analysis, Error, and Uncertainty, using Excel
G Currell, University of the West of England, Bristol
http://calcscience.uwe.ac.uk/w2/am/ExcelTuts/ExcelDataUncert.htm
Keywords:
Book sections: 4.2 4.3, 8.2, 8.3, 13.3
Guidance: Using Excel for data analysis is a key skill which develops throughout the course.
Initially, check your understanding and use of Excel by studying the Introduction section.
Introduction
Overview of use of Excel
Basic skills & straight line calculations
Case studies
1. Analysis of replicate data
Basic/Intermediate
2. Analysis of linear data
Intermediate
3. Analysis of linear calibration data
Advanced
Ideal Gas Law: pV = nRT - case study
G Currell, University of the West of England, Bristol and D Read, University of Southampton
http://calcscience.uwe.ac.uk/w2/sg/sgGasLaws/sgGasLaws.htm
Keywords: Ideal gas, Boyles law, Charles law
Book sections: 2.2, 3.2, 4.2, 8.2, 8.3, 13.3
Guidance: These are essential techniques in science. Check asap that you understand, and
can correctly answer, all the Basic QVA questions. For further guidance - go to Maths
Support.
QVAs
Rearrangement of equation
Basic
Substitution of values
Basic
Changing units
Basic
Analysis of a straight line
Intermediate
Experimental uncertainty
Intermediate
Downloads:
Excel file: Gas Law Calculation
Beer-Lambert’s Law - case study
G Currell, University of the West of England, Bristol
http://discovermaths.rsc.org/Resource/Item/Beer-Lambert%20Study%20Guide
Keywords: Beers law, Beer-Lambert law
Book sections: 4.2, 4.3, 13.3
Guidance: This topic will be introduced in module ???
Video answers
Initial evaluation of data (residuals /
Intermediate
correlation coefficient)
Calculation of 'best-estimate' value for
Intermediate
concentration
Calculation of 95% confidence interval for
Advanced
concentration
Royal Society of Chemitry
p4
Dr Graham Currell
Arrhenius Equation - case study
G Currell, University of the West of England, Bristol
http://discovermaths.rsc.org/Resource/Item/Arrhenius%20Study%20Guide
Keywords: Arrhenius,
Book sections: 4.2, 4.3, 5.2
Guidance: This topic will be introduced in module ???
Video answers
Linearising the Arrhenius equation
Intermediate
Using Excel to plot the data and perform a
Intermediate
linear regression to calculate Ea and A
Calibration Standard Solutions - case study
G Currell and K Sudlow, University of the West of England, Bristol
http://calcscience.uwe.ac.uk/w2/sg/sgPrepStandards/sgPrepStandards01.htm
Keywords: Concentration, dilution, uncertainty, error, tolerance
Book sections: 2.3, 8.2, 8.3
Guidance: This topic will be introduced in module ???
Interactive decisions / calculations
1. Concentration of stock solution
Basic
2. Mass of solute required
Basic
3. Dilution required
Intermediate
4. Selecting glassware
Intermediate
5. Overall uncertainty
Advanced
6. Step with greatest uncertainty
Advanced
Downloads
Overall solution (pdf)
Basic/ Intermediate/ Advanced
Excel file: Calculating Uncertainties
Advanced
Royal Society of Chemitry
p5
Dr Graham Currell
Study Guides for using the textbook
Experiment / Research Design - study guide for textbook
G Currell, University of the West of England, Bristol
http://calcscience.uwe.ac.uk/w2/sg/sgExptDesign/spExptDesign.htm
Keywords:
Book sections: Chapters 4, 7 to 15
Guidance: This topic will be a useful reference for an experimental project
Sections
Types of experimentation and research
Intermediate
Type and distribution of data
Intermediate
Linear / non-linear relationships
Intermediate
Handling variations / uncertainties
Intermediate
Design of the experiment and selection of
Intermediate / Advanced
statistical tests/analyses
Presenting data/results
Intermediate
Downloads
Study guide (pdf)
Intermediate / Advanced
Data transformation (pdf)
Advanced
Common statistical tests (pdf)
Advanced
Analysis of Exponential Growth/Decay using Logarithms - study guide for textbook
G Currell, University of the West of England, Bristol
http://calcscience.uwe.ac.uk/w2/sg/sgLogGrowth/spLogGrowth.htm
Keywords: Exponential growth, decay, half life
Book sections: Guidance: This topic occurs in many aspects of science
Sections
Standard exponential growth/decay equation Intermediate
Analysing population/quantity against time
Intermediate
Using Excel to perform the calculations
Intermediate
Downloads
Study guide (pdf)
Intermediate
Royal Society of Chemitry
p6
Dr Graham Currell
Example of reference to other resources:
Simultaneous Equations
M Seery, Dublin Institute of Technology
http://www.mathsforchemistry.info/DMCsimltaneousequations/player.html
Keywords: Simultaneous
Book sections: 3.5
Guidance: These are essential techniques in maths. Check asap that you understand the
two Basic methods of solution.
Video tutorials:
Elimination & substitution solution methods
Basic
Applications in analytical chemistry
Basic / Intermediate
Applications in physical chemistry
Basic / Intermediate
Quiz:
On-line
Basic / Intermediate
Royal Society of Chemitry
p7
Dr Graham Currell