bluuebunny/crossref_metadata_2025 huggingface dataset:
The perfect gas
Authors: Atkins Peter , de Paula Julio , Keeler James
Published: September 2023

This chapter discusses an idealized version of a gas, a ‘perfect gas’. It begins by looking at the variables of state, reviewing how the physical state of a gas is described using variables such as pressure and volume, temperature, amount, and intensive and extensive properties. The chapter then considers the equation of state of a perfect gas, which was established by combining a series of empirical laws that arose from experimental observations. These laws can be summarized as Boyle's law, Charles's law, and Avogadro's principle. Boyle's and Charles's laws are strictly true only in the limit that the pressure goes to zero: they are examples of a limiting law, a law that is strictly true only in a certain limit.
Phase diagrams of binary systems: solids
Authors: Atkins Peter , de Paula Julio , Keeler James
Published: September 2023

This chapter assesses phase diagrams of solid mixtures, which are used widely in materials science, metallurgy, geology, and the chemical industry. The phase diagrams of solid mixtures summarize experimental results on the conditions under which the liquid and solid phases of the system are stable, and the composition of these phases. A peritectic line in a phase diagram represents an equilibrium between three phases. At the eutectic composition, the liquid phase solidifies without change of composition. Meanwhile, in congruent melting, the composition of the liquid a compound forms is the same as that of the solid compound. During incongruent melting, a compound melts into its components and does not itself form a liquid phase.
Activities
Authors: Atkins Peter , de Paula Julio , Keeler James
Published: September 2023

This chapter describes how the extension of the concept of chemical potential to real solutions involves introducing an effective concentration called an ‘activity’. In certain cases, the activity may be interpreted in terms of intermolecular interactions; an important example is a solution containing ions. Such solutions often deviate considerably from ideal behaviour on account of the strong, long-range interactions between the charged species. The chapter shows how a model can be used to estimate the deviations from ideal behaviour when the solution is very dilute, and how to extend the resulting expressions to more concentrated solutions. It looks at the Margules equations, the Debye–Hückel theory, and the Debye–Hückel limiting law.
Rotational motion
Authors: Atkins Peter , de Paula Julio , Keeler James
Published: September 2023

This chapter focuses on the concept of rotational motion. It explains that energy and angular momentum for a particle rotating in two- or three-dimensions are quantized and satisfied cyclic boundary conditions, which imply the quantization of angular momentum's magnitude and z-component. The electronic structure of atoms showcases rotational motion because electrons orbit around nuclei and spin on their axis. The chapter details the solutions for the Schrödinger equation and the vector model of angular momentum. It also discusses the concept of space quantization revolving around the quantum mechanical result of a rotating body that may not take up an arbitrary orientation concerning some specified axis.
Hydrogenic atoms
Authors: Atkins Peter , de Paula Julio , Keeler James
Published: September 2023

This chapter details the electronic structure of a hydrogenic atom. It acknowledges how the structure is central to the description of all other atoms, the periodic table, and bonding. Moreover, hydrogenic atoms are important because their Schrödinger equations can be solved exactly, which then involves the separation of the wavefunction into angular and radial parts. The chapter explains that orbitals of a given value of n form a shell of an atom and orbitals of the same shell all have the same energy in hydrogenic atoms. It clarifies that the radial distribution function is the probability density for the distribution of the electron as a function of distance from the nucleus.
Many-electron atoms
Authors: Atkins Peter , de Paula Julio , Keeler James
Published: September 2023

This chapter defines a many-electron atom as an atom or ion with more than one electron. The Schrödinger equation for a many-electron atom is complicated because all the electrons interact with one another. Thus, methods like orbital approximation, Pauli exclusion principle, and Hartree-Fock self-consistent field (HF-SCF) procedure are necessary to find analytical expressions for the orbitals and energies. The chapter elaborates on the origin of the periodicity of atomic properties and the periodic table structure by referencing the quantum mechanical property of electron spin and the concept of the Pauli principle. It also considers the building-up principle as a procedure for predicting the ground state electron configuration of an atom.
Molecular orbital theory: the hydrogen molecule-ion
Authors: Atkins Peter , de Paula Julio , Keeler James
Published: September 2023

This chapter discusses the application of hydrogen molecule-ion in correlation with molecular orbital theory (MO theory). It clarifies that electrons do not belong to particular bonds but spread throughout the entire molecule in MO theory. Valence-bond theory provides the appropriate language widely used in modern discussions of bonding. The chapter then looks into the linear combinations of atomic orbitals while referencing the structures of molecular orbital, bonding orbital, antibonding orbital and σ orbitals. It explains that a molecular orbital in a homonuclear diatomic molecule is labelled either ‘gerade’ (g) symmetry or ‘ungerade’ (u) symmetry, which are all according to its behaviour under inversion symmetry.
Molecular orbital theory: polyatomic molecules
Authors: Atkins Peter , de Paula Julio , Keeler James
Published: September 2023

This chapter covers the concept of polyatomic molecules while considering molecular orbital theory. Polyatomic molecular orbitals spread over the entire molecule and the electrons that occupy them spread like a web over the atoms to bind them all together. Moreover, symmetry considerations play a central role in the construction of the molecular orbitals of polyatomic molecules, because only atomic orbitals of matching symmetry have non-zero overlap and contribute to a molecular orbital. The chapter introduces the Hückel approximation in relation to the construction of π molecular orbital energy level diagrams of conjugated molecules. It also considers the power and speed of computational chemistry.
Rotational spectroscopy
Authors: Atkins Peter , de Paula Julio , Keeler James
Published: September 2023

This chapter focuses on rotational spectroscopy. Despite the limitation of a gas phase-only observation, rotational spectroscopy provides a wealth of information concerning molecules, especially with matters of precise bond lengths, bond angles, and dipole moments. Moreover, microwave spectroscopy can study rotational transitions and monitors the absorption of radiation in the microwave region of the spectrum. The chapter considers the extent of rotational energy levels, gross selection rule, and specific selection rules from microwave spectroscopy. It also explains that nuclear statistics must be taken into account whenever a rotation interchanges equivalent nuclei, referencing the selective existence of rotational states that stems from the Pauli principle.
Vibrational spectroscopy of diatomic molecules
Authors: Atkins Peter , de Paula Julio , Keeler James
Published: September 2023

This chapter tackles the vibrational spectroscopy of diatomic molecules. It explains that one internal mode of motion of a diatomic molecule is its vibration, in which the internuclear separation increases and decreases periodically. Moreover, vibrational transition frequencies are used to determine the strengths and rigidities of bonds. The chapter notes how the vibrational spectrum of a diatomic molecule can be interpreted by using the harmonic oscillator model, with modifications that account for bond dissociation and the coupling of rotational and vibrational motion. It considers how the motion can become anharmonic in the sense that restoring force is no longer proportional to the displacement.
Electron paramagnetic resonance
Authors: Atkins Peter , de Paula Julio , Keeler James
Published: September 2023

This chapter discusses the concept of electron paramagnetic resonance (ESR). ESR, also known as electron spin resonance (ESR), is used to study species that contain unpaired electrons and expressed through the g-value of the radical. While the ESR can be used to study the features of solids and liquids, studying gas-phase samples is complex due to the free rotation of molecules. The chapter looks into the McConnell equation while referencing the hyperfine structure of an EPR spectrum. It explains how hyperfine structure, which is the most important feature of an EPR spectrum, arises from dipole-dipole interactions, Fermi contact interactions, and the polarization mechanism.
The Boltzmann distribution
Authors: Atkins Peter , de Paula Julio , Keeler James
Published: September 2023

This chapter explains how the Boltzmann distribution has been used to predict the populations of states in systems at thermal equilibrium. It considers the calculation of the populations of the energy levels of a system consisting of a large number of non-interacting molecules. The relative populations of energy levels, as opposed to states, must take into account the degeneracies of the energy levels. The chapter mentions that energy levels can be associated with any mode of motion, such as vibration or rotation. Moreover, the principle of equal a priori probabilities assumes that all possibilities for the distribution of energy are equally probable in the sense that the distribution is blind to the type of motion involved.
Molecular partition functions
Authors: Atkins Peter , de Paula Julio , Keeler James
Published: September 2023

This chapter notes how the Boltzmann distribution introduces a quantity known as the molecular partition function, which plays a key role in statistical thermodynamics. It acknowledges how the Boltzmann distribution contains all the information needed to calculate the bulk properties of a system of independent particles. The molecular partition function is an indication of the number of thermally accessible states at the temperature of interest. The chapter details the contributions to the partition function concerning translation, rotation, vibration, and electronic contribution. It then highlights how the notion of symmetry number considers the number of indistinguishable orientations of a symmetrical molecule.
The internal energy and the entropy
Authors: Atkins Peter , de Paula Julio , Keeler James
Published: September 2023

This chapter considers the molecular interpretation of thermodynamic properties, especially concerning internal energy and entropy. Any thermodynamic function can be obtained after the identification of the partition function. Moreover, the calculation of derived functions, like Gibbs energy, will be possible following the identification of internal energy and entropy. The chapter covers the calculation of internal energy, referencing that the total heat capacity of a molecular substance is the sum of the contribution of each mode. It discusses statistical entropy being defined by the Boltzmann formula and expressed through molecular partition function, while residual entropy refers to a non-zero entropy from molecular disorder.
Liquids
Authors: Atkins Peter , de Paula Julio , Keeler James
Published: September 2023

This chapter describes substances that are liquids under normal conditions and chemical reactions that take place in liquids. It emphasizes the importance of being able to describe and understand the structure of the liquid phase and the interface with its vapour. It also looks at the properties of liquids that reflect the short-range order of their molecules in the bulk and the behaviour of their molecules at the mobile surface. The chapter discusses how molecules attract each other when they are less than a few diameters apart but repel each other as soon as they come into contact. It explains that attraction is responsible for the formation of condensed phases and the repulsion is responsible for the fact that liquids have a definite bulk.
Crystal structure
Authors: Atkins Peter , de Paula Julio , Keeler James
Published: September 2023

This chapter discusses the characteristic feature of a crystal, which is the regular arrangement of its constituents. It shows how the regularity of a crystal described in terms of the symmetry of the arrangement and explains how its the arrangements are described quantitatively. It also considers the importance of crystalline solids in many technologies and explores microscopic structures of a crystal in order to account for their mechanical, electrical, optical, and magnetic properties. The chapter analyses the regular arrangement of the atoms in periodic crystals that can be described in terms of unit cells. It explores the internal structure of a crystal, which is a regular array of its atoms, ions, or molecules.
Diffusion-controlled reactions
Authors: Atkins Peter , de Paula Julio , Keeler James
Published: September 2023

This chapter examines reactions in solution that are classified into two types: diffusion-controlled, where the rate is controlled by the frequency with which reactants meet, and activation-controlled, where the accumulation of sufficient energy in a pair of molecules that have met is rate-determining. The rate constants for diffusion-controlled reactions can be expressed quantitatively in terms of the diffusional characteristics of species in liquids. It provides a detailed account of the space- and time-development of products that is obtained by using the diffusion equation. The chapter assesses the rate of a chemical reaction in solution that is controlled either by the rate of diffusion of the reactants or by the activation energy of the step that leads to products. It makes use of the steady-state approximation and draws on Fick's first law of diffusion.
An introduction to solid surfaces
Authors: Atkins Peter , de Paula Julio , Keeler James
Published: September 2023

This chapter provides background on theory relating to the surface of a solid. The surface of a solid has a different structure from a slice through a bulk solid and has various types of imperfections that have a profound effect on how atoms and molecules interact with it. The chapter describes the structure of surfaces, the attachment of molecules to them, and some of the techniques used to study them. It also reviews how molecules are attached to the surface and how it is studied experimentally in order to understand the processes occurring on a solid. The chapter looks at the attachment of molecules to a surface and shows that this is influenced by structural features of the surface, including defects. The chapter draws on results from the kinetic theory of gases.
Processes at electrodes
Authors: Atkins Peter , de Paula Julio , Keeler James
Published: September 2023

This chapter considers the transfer of electrons as a key process at an electrode, which takes place at the interface between a solid surface and an electrolyte. It points out how this process can be modelled by using a version of transition-state theory and lead to an understanding of electron transfer as an activated process. The chapter reviews factors that determine the rate of electron transfer at electrodes that leads to a better understanding of the charging and discharging of batteries, the production of power using solar cells, and manufacturing using electrolysis. It talks about the rate of oxidation and reduction at an electrode that depends on the height of the activation barrier. It also shows how the surface of a solid electrode is in contact with the ions in an electrolyte solution.
Pathogen Genomics
Authors: Chappell Lia , Lindsay Sarah J , Jones Phil , Parkhill Julian , Roberts Jonathan , Holroyd Nancy , Szpak Michal , Gale Francesca
Published: September 2023

This chapter evaluates pathogen genomics. As scientists developed sequencing tools at the end of the 1970s, virus genomes were the first to be tackled, because of their small size. Viruses, and then bacteria, formed the test bed for developments that went on to enable the sequencing of human genomes, but they are also of interest, and of value, in themselves. A pathogen genome tells us a lot about how pathogens grow and interact with their environment. The genome also tells us how the pathogens avoid both our immune systems and the weapons we have developed to overcome them, such as vaccines and antibiotics. Beyond this fundamental information, a genome is also a written record of the evolutionary history of the pathogen. The chapter then looks at metagenomics and how genomics is being used by academics and companies to develop new vaccines and antibiotics in a directed way.
Human Evolution
Authors: Chappell Lia , Lindsay Sarah J , Jones Phil , Parkhill Julian , Roberts Jonathan , Holroyd Nancy , Szpak Michal , Gale Francesca
Published: September 2023

This chapter assesses the role of genomics in studying human evolution. Genome sequences tell us how we differ genetically from other apes, fossils fill in details of some of the extinct species, and ancient DNA (aDNA) can even allow us to read their genome sequences. The Homo sapiens originated in Africa, around 300,000 years ago, and then expanded into most of Asia, Australia, and Europe, as well as the Americas. During these expansions, they mixed with other forms of early human, Neanderthals and Denisovans, so that all non-Africans carry about 2 per cent of Neanderthal DNA, which influences our characteristics such as hair and skin colour, virus resistance, and diabetes risk. Striking examples of local genetic adaptation whose genetic basis is understood are the lighter skin colour seen in Asia and Europe, and the ability of adults in some places, but not others, to digest fresh milk.
Nucleotides and Nucleic Acids: Biology’s Information Stores
Authors: Bowater Richard , Bowater Laura , Husband Tom
Published: September 2023

This chapter examines nucleotides and nucleic acids, which exist in all cells and have been widely studied. Nucleotides play a central role in supplying the energy for many metabolic reactions, and in the storage and use of genetic information: they are key players in passing on genetic material from one generation of cells to the next. They are also involved in controlling how genetic information is used. Meanwhile, nucleic acids are polymers of nucleotides. There are two types: ribonucleic acid (RNA) and deoxyribonucleic acid (DNA). As scientists' understanding of DNA and RNA molecules has developed, the era of molecular biology and, more recently, the era of synthetic biology, emerged. Genetic engineering and gene editing techniques allow the manipulation of genes into novel forms and are fundamental to biotechnology, where biological solutions are applied to some of the major challenges facing humanity.
Metabolism: Transforming Energy and Biomolecules
Authors: Bowater Richard , Bowater Laura , Husband Tom
Published: September 2023

This chapter evaluates the process of metabolism. Although there are many different sets of reactions, or metabolic pathways, involved here, only a small number are fundamental to all cells. The chapter focuses on two metabolic pathways that are particularly well understood by biochemists because of their importance for life: aerobic respiration and photosynthesis. To appreciate cellular metabolism, it is important to understand how energy is transferred between different molecules and converted to different forms. Moving and transforming energy is fundamental to how cells function, and the biochemists that study this topic describe it as bioenergetics. One of the key theoretical concepts that is particularly useful for understanding this biochemical topic is 'free energy'. This concept helps identify whether biochemical reactions are favourable or not. The chapter looks at adenosine triphosphate (ATP), as well as endosymbiosis.
Solving Tomorrow’s Problems: Bioenergy and the Environment
Authors: Bowater Richard , Bowater Laura , Husband Tom
Published: September 2023

This chapter highlights the potential to tackle environmental problems by harnessing human understanding of biochemistry. Biotechnology could help in reducing our crippling dependency on fossil fuels. Biotech, which simply means technology derived from living systems, has already been used to pioneer several different forms of renewable energy. Algae, a diverse group of plant-like organisms, have sparked great interest with their potential to produce carbon-neutral biofuels. Moreover, researchers have been developing artificial photosynthesis, which could also be used to produce alternatives to fossil fuels. Agriculture could also reduce its carbon footprint with help from biotechnology. This field has the potential to produce artificial meat and dairy products, which would reduce our dependence on animals along with our greenhouse gas emissions. Meanwhile, plants have been genetically modified for greater efficiency, to grow in harsh climates, and generally to alleviate the scarcity of food that characterizes a snowballing global population.
Bond Polarization and Electronegativity
Authors: Elliott Mark C.
Published: September 2023

The Purpose of The Exercise

You need to be thinking about the distribution of charge in organic structures. You need to be able to do this no matter how complex the structure. In order to do this, you will need to ‘see’ functional groups even...
Breaking Bonds—Linking Curly Arrows and Molecular Orbitals
Authors: Elliott Mark C.
Published: September 2023

Now we have examined the nature of bonding in organic compounds, we need to revisit the curly arrows from Basics 8, and present them in a more formal way, considering what type of bond is being formed or broken in each case. We...
How Fast Are Reactions?
Authors: Elliott Mark C.
Published: September 2023

We have seen (Basics 13) how to determine whether a reaction is energetically favourable (exothermic). This is important.

We have also looked at reaction profiles (Basics 14), and we have seen that we have an activation ‘barrier’ to reactions....
Drawing Resonance Forms for Carbocations and Carbanions
Authors: Elliott Mark C.
Published: September 2023

The Purpose of The Exercise

We have two very specific goals.

You should be able to draw correct resonance forms that show how a given substituent will ‘interact’ with a given charge.

With suﬃcient practice, you will then be able to visualize the...
Carbocations and Carbanions
Authors: Elliott Mark C.
Published: September 2023

The Most Common Mistake

As we have seen, and will continue to see, most problems arise from a fundamental disconnect between the structures and the words we use to describe them.

Early on you saw that tertiary carbocations are more stable than secondary...
Properties of Stereoisomers
Authors: Elliott Mark C.
Published: September 2023

In Basics 24 we saw some definitions that relate to stereochemistry. These primarily related to the structures of compounds. As we now start to talk about reactivity, we need to introduce definitions that relate to reactions.

We will also take this opportunity to look at...
Stereochemical Aspects of Substitution Reactions
Authors: Elliott Mark C.
Published: September 2023

Right, now we are going to consider the stereochemical outcome of a reaction. There will be words that you associate with a given outcome, but we need to look at the fundamental principles, so we can see when the words apply and when they do...
Substitution Reactions
Authors: Elliott Mark C.
Published: September 2023

The Basics

Good news! There isn’t much here. Once you’ve learned the basics, you probably won’t make too many mistakes with substitution reactions.

Of course, you have two major mechanisms. They have different stereochemical outcomes.

You need to be able to tell, at a glance,...
Substitution with Retention of Configuration
Authors: Elliott Mark C.
Published: September 2023

Since we considered all possible orders of bond formation for nucleophilic substitution in Fundamental Reaction Type 1, perhaps you were not expecting another new mechanism.

Fortunately, this one is only a variation on one of the previous mechanisms. It just happens that the timing...
Bonds Can Rotate
Authors: Elliott Mark C.
Published: September 2023

This chapter highlights molecular models that can be twisted and turned. This provides insight into what might happen in a real molecule. It considers how some compounds prefer to react in specific orientations and how the ease of adopting a particular orientation often determines the reactivity of the compound. It also discusses conformational isomers or conformers which regard a special type of stereoisomer related simply by rotation around single bonds. The chapter reviews the applications of conformational isomerism in substitution reactions and the energy difference between conformers fundamental to E2 elimination reactions. It outlines the fundamental principles of conformational analysis in cyclohexanes to substitution and elimination reactions.
SN2 Substitution Reactions Forming Three-Membered Rings
Authors: Elliott Mark C.
Published: September 2023

As we progress further into the ‘Applications’ chapters, you will find that we need to draw on an increasing number of principles from various sections in order to rationalize or predict the outcome of reactions. This is very common in organic chemistry. In fact, it...
Drawing Cyclohexanes
Authors: Elliott Mark C.
Published: September 2023

The Point of The Exercise

Six‑membered rings are really stable, and that doesn’t just apply to benzene. Nature loves six‑membered rings, and they are found in many biologically active natural products. You need to become good at drawing them.

There are lots of instances where...
Elimination Reactions
Authors: Elliott Mark C.
Published: September 2023

What is Elimination?

The first error, which is more common than you would probably expect, is confusing elimination with substitution.

Here’s the problem. Compounds that undergo elimination reactions do also undergo substitution. Most of the same principles apply, so that the exam questions do look...
Competing SN2 Substitution and E2 Elimination
Authors: Elliott Mark C.
Published: September 2023

Introduction

We have done a lot with SN1 and E1 mechanisms, and it is all good! However, these are the less common mechanisms. Fortunately, we would draw almost identical conclusions about SN2 and E2 mechanisms, and for almost identical reasons.
Acid Catalysis in Organic Reactions Part 2
Authors: Elliott Mark C.
Published: September 2023

Introduction

We started looking at this problem in Basics 22. Now we have looked at the thermodynamics of reactions involving charged species (Basics 35), we can consider the implications of acid catalysis with a strong acid and with a weak acid....

This...
SN2′ Stereochemistry and Conformations
Authors: Elliott Mark C.
Published: September 2023

Introduction

The next problem focuses on key skills, and it introduces one more important idea.

We have been considering shape in reactions throughout. Reactions such as E2 elimination are very clear in the sense that they only proceed through one specific conformational isomer. Other reactions...
Competing SN1 Substitution and E1 Elimination
Authors: Elliott Mark C.
Published: September 2023

Answer 1

In Worked Problem 1, we established that the three carbocations, 12, 13, and 14, are of broadly similar stability, as long as we are considering electronic effects (hyperconjugation).

They are all tertiary carbocations.
Introducing Evolution
Authors: Ingram Neil , Andrews Sylvia Hixson , Still Jane
Published: September 2023

This chapter introduces the theory of evolution, which sparked concepts of competition, struggle, uncertainty, and random chance before it became the major unifying principle of biological sciences. The crucial concept of species is constantly referred to in discussions around this theory. Selection is the driver behind the evolution of species, while natural selection leads to the speciation and extinction of species. The chapter lists the different types of selection: stabilizing selection, sexual selection, disruptive selection, and directional selection. It also highlights the foundational works of Charles Darwin and Gregor Mendel establishing the field of evolution. The birth and death of species, through these works, came to be understood as central to the evolution of life on Earth.
The Birth and Death of Species
Authors: Ingram Neil , Andrews Sylvia Hixson , Still Jane
Published: September 2023

This chapter focuses on the birth and death of species, which has been referred to be the nature of evolution. It also notes the modern classification system based on Linnaeus' Systema Naturae, a framework featuring genus and kingdoms of species. The chapter also notes how reproduction isolation is required for speciation. Genetic isolation is the result of a physical or geographical barrier to gene flow during the process of allopatric speciation. Sympatric speciation is involved in the emergence of hybrids, especially among plant species. Extinction, the chapter explains, is an essential part of evolution as new niches and set of speciation take over.
The Evolution of the Theory: Changing Views
Authors: Ingram Neil , Andrews Sylvia Hixson , Still Jane
Published: September 2023

This chapter discusses the changing views into the development of an evolution theory. Modern Synthesis is a set of tools for thinking which builds a model of the evolving living world. Modern Synthesis emerged from the re-interpretation of Charles Darwin's Origin of Species following the re-discovery of Gregor Mendel's work on genetics and the establishment of August Weismann's cell theory. The chapter notes how natural selection is known to be the main driver of evolutionary change, which is observed through the shifts in allele frequencies in populations. Additionally, behavioural systems, symbolic systems, and epigenetics help explain evolution theory.
Measuring Marine Biodiversity
Authors: Kent Michael
Published: September 2023

This chapter assesses how biodiversity research is carried out scientifically by being quantified. By measuring a component of marine biodiversity, ecologists can postulate hypotheses and make predictions that can be subjected to rigorous scientific testing. Species diversity is the component of marine biodiversity most commonly measured. It can be measured by species richness, a species diversity index, or by species evenness. Environmental DNA is transforming the way species diversity is measured in the marine environment. Genetic diversity is measured in a variety of ways, but one well-tried and tested method is by calculating the heterozygosity index. Meanwhile, ecosystem diversity is most commonly measured in terms of the number and types of ecosystems in a defined area, and marine biodiversity can be measured functionally as well as structurally. The chapter then considers ways of avoiding unintended consequences of measuring biodiversity, including damage to the physical and living environment.
Presenting single-sample data: histograms and boxplots
Authors: Humphreys Rosalind K. , Ruxton Graeme D.
Published: September 2023

This chapter looks at ways for producing clear and effective histograms and boxplots when presenting single-sample data. It explains the advantages and disadvantages of each figure type relative to the other. The customization of histograms primarily revolves around the features of bin size, cell colour, and axis features. Boxplot customization involves adding text labels, changing box colour, and editing axis features. Even though boxplots can give a good sense of data spread, the data may be less intuitive for interpretation due to its whiskers. The chapter then explains the basic code for histograms and boxplots when using R.
Second-order differential equations. Constant coefficients
Authors: Sainsbury Malcolm
Published: September 2023

This chapter tackles second-order differential equations with constant coefficients. It cites as examples the classical equations of motion for the harmonic oscillator and for forced oscillations in mechanical and electrical systems, as well as the Schrödinger equations for the particle in a box and in a ring. The chapter starts off by describing homogenous linear equations and an important property which is called the principle of superposition. It also introduces concepts such as the characteristic equation or auxiliary equation, initial value problem, and boundary conditions. The chapter then looks at inhomogeneous linear equations and shows how to use the method of undetermined coefficients.
Orthogonal expansions. Fourier analysis
Authors: Steiner Erich
Published: September 2023

This chapter introduces the concept of expansion in sets of orthogonal functions. It describes the orthonormal set and the property of completeness. Then it tackles two examples of expansions in Legendre polynomials that are important in potential theory and in scattering theory. The discussion covers the expansion of electrostatic potential. The chapter also explains the Fourier series representation of a function or the expansion of the function in terms of the set of trigonometric functions. Furthermore, it shows how the Fourier series is used to solve the wave equation for the vibrating string for a given set of initial conditions. Lastly, the chapter discusses the Fourier transforms which are essential for the analysis of the results of diffraction experiments and in Fourier transform spectroscopy.
The matrix eigenvalue problem
Authors: Steiner Erich
Published: September 2023

This chapter explains the eigenvalue problem or the determination of the eigenvalues and eigenvectors of a square matrix, which is important in many branches of the physical sciences and engineering. The chapter discusses the properties of eigenvalues and eigenvectors. It has examples showing the normalization of eigenvectors, orthogonalization of vectors, and the Hückel theory of cyclobutadiene. The chapter also tackles matrix diagonalization—touching on the topics of similarity and orthogonal transformations. It further looks at the reduction of quadratic forms to canonical forms. Lastly, it provides a summary of the complex matrices that are important in advanced group theory and in quantum mechanics.
Numerical methods
Authors: Steiner Erich
Published: September 2023

This chapter focuses on the method for obtaining the solution of a mathematical problem in the form of numbers. It discusses the general principles underlying some of the more important numerical methods and treats the simplest ones in detail. The discussion emphasizes that nearly all numerical operations are necessarily accompanied by errors, and the analysis of these errors is an integral part of any numerical method. The chapter lays down the three ways by which errors in numerical computations arise: through mistakes (e.g., bug in a computer program, incorrectly calibrated apparatus), mathematical truncation errors, and rounding errors. It also tackles the solution of ordinary equations, describing the bisection method and Newton-Raphson method. Furthermore, it explains polynomial, linear, quadratic, and spline interpolations. The chapter also explains the Gauss elimination for the solution of linear equations, and the Gauss–Jordan elimination for the inverse of a matrix.
Conceptual toolkit: the molecular principles for understanding proteins
Authors: Price Nicholas C. , Nairn Jacqueline
Published: September 2023

This chapter discusses the principles for understanding the structures and functions of proteins. It begins by reviewing the properties of amino acids, which represent the building blocks of proteins. The chapter looks at the structure of proteins on four levels. The primary structure refers to the sequence of amino acids in the polypeptide chain, i.e. the covalent structure of the protein. The secondary structure refers to the local folding of the polypeptide chain, such that segments of the chain may form helices, strands of sheet, or turns. Meanwhile, the tertiary structure refers to the long-range folding of the polypeptide chain so that portions of the chain that are remote in terms of sequence are brought close together in space. The quaternary structure refers to the association of the individual polypeptide chains in a multi-subunit protein. The chapter then considers the forces contributing to the structures and interactions of proteins.
Calculations in the molecular biosciences
Authors: Price Nicholas C. , Nairn Jacqueline
Published: September 2023

This chapter assesses some general principles important in any calculations involved in studying proteins, and then focuses on how to study the individual components of reactions. This includes the preparation and dilution of solutions and how spectrophotometry can be used to check concentrations in some cases. The chapter considers the Système Internationale (SI) system of units, as well as the concepts of moles and molarity. It is important to note that the term mole can refer to molecules, atoms, subatomic particles, photons, etc. The chapter then describes the behaviour of acids, bases, and buffers, before looking at the specific activities of proteins and the manner in which their purification is recorded. An acid can be defined as a substance which has a tendency to donate H+ ions and a base as a substance which has a tendency to accept H+ ions.
Calculations in the molecular biosciences
Authors: Price Nicholas C. , Nairn Jacqueline
Published: September 2023

This chapter addresses the analysis of some important types of biological processes. It begins by looking at the energetics of processes. In biological systems we deal with two main types of processes, namely chemical reactions in which covalent bonds are broken and made, so that one or more new compounds are made from the starting compounds, and complex formation in which two (or more) compounds can associate reversibly with one another. The science of thermodynamics is concerned with the overall changes in energy when processes occur; it can be used to predict how far a process will proceed, i.e. does the equilibrium lie more towards the side of the products or the reactants? The chapter then discusses binding equilibria; this includes the kinetics of enzyme-catalysed reactions since many of the equations involved are similar. The chapter also considers radioactivity, which is widely used to track specific compounds.
Purification of proteins
Authors: Levinton Jeffrey S.
Published: September 2023

This chapter studies the purification of proteins. The overall aim of any protein purification method is to generate a high yield of pure protein while retaining maximum activity. The chapter begins with an explanation of the basis of separation methods and proceeds to describe a number of purification methods, encompassing a range of starting materials, experimental conditions, and chromatographic methods. For each example of purification, it provides a brief description of the protein along with an outline of the experimental procedures required to purify the protein. Each protein has a unique set of biochemical properties which can be exploited to facilitate its isolation from complex biological sources. The most common biochemical properties that are exploited include surface polarity, molecular mass, and specific binding sites. The chapter then considers precipitation, chromatography, isoelectric focusing, dialysis/ultrafiltration, and centrifugation.
Enzyme activity and mechanism
Authors: Price Nicholas C. , Nairn Jacqueline
Published: September 2023

This chapter illustrates some of the main approaches used to gain an understanding of the mechanism of enzyme action. A complete description of a mechanism involves both kinetic and structural aspects and hence it can be a long process to achieve this goal. The chapter focuses on the kinetic experiments as these are more amenable to routine laboratory investigations. It also looks at some of the structural approaches which can be used, such as the mapping of active sites and identification of amino acids involved in catalysis or binding. There are at least three good reasons why a study of enzyme kinetics is important. Firstly, it is observing the enzyme doing its job, i.e. actually catalysing a reaction. Secondly, it can provide very important information about the mechanism. Thirdly, it helps one to understand the physiological role of the enzyme in an organism.
Binding of ligands to proteins
Authors: Nicholas C. Price , Jacqueline Nairn
Published: September 2023

This chapter reviews some of the experimental methods used to study ligand binding. It begins by looking at the principal equations describing binding of ligands to proteins. Binding data can be analysed to determine the number of ligand binding sites on the protein and the strength of the ligand-protein interaction. Spectroscopic methods are widely used to monitor the binding of ligands to proteins; the only requirement is that there is a spectroscopic signal (of either the ligand or the protein) which changes on complex formation. In the case of multiple ligand binding sites on a protein, it is assumed that the extent of the spectroscopic signal change is proportional to the extent of complex formation. The chapter then considers equilibrium dialysis, filtration, electrophoretic mobility shift assay (EMSA), isothermal titration calorimetry, surface plasmon resonance, and competition assays.
Introduction: The biochemical basis of exercise and sport
Authors: Maughan Ronald J. , Gleeson Michael
Published: September 2023

This introductory chapter provides an overview of the biochemical basis of exercise and sport. All sports activities involve muscular activity, and for each one of us there is an upper limit to our ability to perform any task involving muscular effort. It is these differences in physical capacity between individuals that form the basis of sporting contests as each competitor strives to reach those limits. Understanding the body's responses to exercise is thus important for the athlete who seeks to perform well, but it is also a crucial element in the development of successful physical activity programmes that can tackle the growing prevalence of the diseases that accompany a sedentary lifestyle. The chapter then describes some of the factors that have contributed to the improvement of world records in sports events over the last century. It also looks at the use of performance enhancing drugs by some athletes.
Middle-distance events
Authors: Maughan Ronald J. , Gleeson Michael
Published: September 2023

This chapter evaluates the relative contributions to energy metabolism from phosphocreatine breakdown, anaerobic glycolysis, and carbohydrate oxidation during middle-distance running. Oxidative metabolism makes the major contribution to energy production when the exercise duration exceeds about one to two minutes. However, at least for exercise intensities that can be sustained for less than about ten minutes, the rate at which energy must be supplied to the working muscles exceeds the maximum rate of the oxidative processes. The chapter uses the example of the middle-distance track runner to describe the metabolic processes occurring and to consider the causes of fatigue and potential limitations to performance in events taking place over this time scale. The chapter then looks at the glycolytic pathway and the regulation of glycolysis.
The games player
Authors: Maughan Ronald J. , Gleeson Michael
Published: September 2023

This chapter addresses the activity patterns and work rate in team games. Games such as football, soccer, rugby, hockey, and tennis involve repetitive bouts of high-intensity exercise. Maintaining performance for the full duration of matches is obviously important to success and depends to a large degree on the ability of muscle to recover from the last exercise bout. Compared with continuous exercise activities such as running and cycling, relatively little attention has been directed to the metabolic responses to team games. However, some standardized models of intermittent exercise have been developed in recent years. The chapter describes how these protocols, as well as measurements made during competition itself, have shed some light on the demands of participation on the skeletal muscle recovery processes after intense exercise and their importance for metabolism and performance during one or more subsequent exercise bouts.
Linear functions and curve sketching
Authors: Reed Martin B
Published: September 2023

This chapter discusses the general formula for the function that involves x and various parameters and the shape of the graph of y = f(x). It shows useful points on the graph, such as where it crosses the x- or y-axes and demonstrates how to use information about a particular function to work out the equation of the curve. It also cites some of the physical processes that can be modelled by the function. The chapter mentions the graph-drawing package called FNGraph, which can show the direct and inverse proportion functions, with the constant of proportionality k as a parameter. It considers a function where the output value is the same, that is y stays constant whatever the value of x.
Quadratic and polynomial functions
Authors: Reed Martin B
Published: September 2023

This chapter reviews the independent variable x and a dependent variable y that define two data-points, which can be plotted as two points on a graph, fit a straight line through them, and find the equation of the line. It looks at different forms of the quadratic function, and their graphs. It also describes the shape of a curve called a parabola that concaves upwards. The chapter cites parabolas that occur in real life, such as parabolic reflectors and antennas focus incoming rays of light or waves of sound onto a single point. It considers what happens when a constant of proportionality a is included with the squaring function y = ax2.
Applications of differentiation
Authors: Reed Martin B
Published: September 2023

This chapter reviews differential calculus, which gave a tremendous impetus to the development of both pure and applied mathematics. It covers optimization and polynomial approximation of functions, together with a powerful numerical method for finding roots. It also shows how calculus can provide all the ‘pre-calculus’ results about roots and turning-points for the basic functions, including an analysis of more complicated differentiable functions. The chapter emphasizes the crucial step of interpreting the function or graph in order to extract significant information from which practical conclusions can be drawn. It highlights the use of the function f (x) and its first and second derivatives f '(x) and f ''(x) to identify significant features of the graph of a general smooth function f (x).
Extension: dynamical systems
Authors: Reed Martin B
Published: September 2023

This chapter focuses on dynamical systems, wherein the simplest nonlinear mathematical models could give rise to incredibly complex behaviour. It mentions scientists studying biological and physical processes of nature that were in the forefront of the revolution in mathematics for discovering dynamical systems. It also introduces some basic concepts of complexity theory: equilibria and stability, bifurcations, and chaos. The chapter begins with a brief snapshot of the birth of chaos theory, particularly theories of pattern formation and ecological implications. It cites the truncation error, which is another source of error in numerical methods that happens by approximating the true function by a Taylor series that is truncated after the first two or three terms.