Mathematics for Chemists: a Study Guide

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, 2 nd 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 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 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 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