CLUE: Chemistry, Life, the Universe and Everything PDF

CLUE: Chemistry, Life, the Universe and Everything Melanie M. Cooper & Michael W. Klymkowsky CLUE: Chemistry, Life, the Universe and Everything by Melanie M. Cooper & Michael W. Klymkowsky is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted. CLUE trademark and copyright reserved. CONTENTS Preface to the Reader ix Melanie Cooper and Michael Klymkowsky To the Student xii Melanie Cooper and Michael Klymkowsky Introduction to the Course 1 Melanie Cooper and Michael Klymkowsky 1. Atoms 3 Melanie Cooper and Michael Klymkowsky 1.1 What Do You Think You Know About Atoms? 4 1.2 Atomic Realities and Scientific Theories 6 1.3 Some History of Atomic Theory 9 1.4 Identifying and Isolating Elements 13 1.5 Evidence for Atoms 14 1.6 The Divisible Atom 17 1.7 Interactions Between Atoms and Molecules 22 1.8 Interactions Between Helium Atoms and Hydrogen Molecules 36 2. Electrons and Orbitals 39 Melanie Cooper and Michael Klymkowsky 2.1 Light and Getting Quantum Mechanical 40 2.2 Taking Quanta Seriously 43 2.3 Exploring Atomic Organization Using Spectroscopy[footnote]For a more 45 complex explanation, see: http://www.coffeeshopphysics.com/articles/ 2011-10/30_the_discovery_of_rainbows/[/footnote] 2.4 Beyond Bohr 49 2.5 Organizing Elements: Introduction to the Periodic Table 52 2.6 Orbitals, Electron Clouds, Probabilities, and Energies 55 2.7 Quantum Numbers[footnote]For more information see: 60 http://winter.group.shef.ac.uk/orbitron/AOs/1s/index.html http://www.uark.edu/misc/julio/orbitals/index.html[/footnote] 3. Elements, Bonding, and Physical Properties 66 Melanie Cooper and Michael Klymkowsky 3.1 Elements and Bonding 67 3.2 Elements and Their Interactions 75 3.4 Metals 90 4. Heterogeneous Compounds 95 Melanie Cooper and Michael Klymkowsky 4.1 3D and 2D Representations 95 4.2 Single Bonds and Molecular Shape 104 4.3 Double and Triple Bonds 107 4.4 Bonding in Nitrogen, Oxygen, and Fluorine 110 4.5 Molecular Shapes, Polarity, and Molecular Interactions 118 4.6 Ionic Bonding 125 5. Systems Thinking 131 Melanie Cooper and Michael Klymkowsky 5.1 Temperature 132 5.2 Thinking About Populations of Molecules 134 5.3 Vibrating, Bending, and Rotating Molecules 138 5.4 Open Versus Closed Systems 146 5.5 Thermodynamics and Systems 148 5.6 Back to Phase Changes 155 5.7 Gibbs (Free) Energy to the Rescue 156 6. Solutions 163 Melanie Cooper and Michael Klymkowsky 6.1 What Is a Solution? 164 6.2 Solubility: why do some things form solutions and others not? 166 6.3 Hydrogen Bonding Interactions and Solubility 169 6.4 Gibbs Energy and Solubility 175 6.5 Polarity 177 6.6 Temperature and Solubility 181 7. A Field Guide to Chemical Reactions 185 Melanie Cooper and Michael Klymkowsky 7.1 Collisions and Chemical Reactions 186 7.2 Acid–Base Reactions: A Guide for Beginners 191 7.3 Lewis Acid–Base Reactions 204 7.4 Nucleophiles and Electrophiles 206 7.5 Oxidation–Reduction Reactions 215 7.6 Energy Changes and Chemical Reactions 219 8. How Far? How Fast? 224 Melanie Cooper and Michael Klymkowsky 8.1 What Factors Control Reactions? 225 8.2 Reaction Rates 228 8.3 Kinetics and the Mechanisms of Reactions 232 8.4 Catalysis 241 8.5 Equilibrium 243 8.6 Back to Reaction Mechanisms 256 9. Reaction Systems 260 Melanie Cooper and Michael Klymkowsky 9.1 Systems Composed of One Reaction 261 9.2 Buffered Systems 265 9.3 Amino Acids, Proteins, and pH 271 9.4 Coupled, Non-Equilibrium Reaction Systems 273 9.5 Energetics and Coupling 277 Appendix: Spectroscopy 283 Melanie Cooper and Michael Klymkowsky PREFACE TO THE READER Melanie Cooper and Michael Klymkowsky You might well ask, does the world really need another introductory chemistry textbook? The answer is, of course not—not if that book is just a variation on those currently available. Chemistry, and particularly introductory general chemistry, is simply not changing that much and people learn pretty much the same way they always did, at least if we restrict ourselves to the last few thousand years.1 On the other hand, there is compelling evidence that the way chemistry is commonly presented, both to the public and in college, is both off-putting and ineffective–a potent combination that leads to the widespread public misunderstanding of chemical principles. How many times do we hear about “natural remedies, without drugs or chemicals,” despite the fact that everything is composed of chemicals and the most toxic chemicals known are natural products.2 A growing body of research results on student understanding of chemistry indicates, pretty emphatically, that we need better ways to teach and assess students’ understanding of the fundamental ideas upon which chemistry is based. These are important ideas that students need to learn, and learn in a robust way that enables them to transfer their understanding to new situations rather than just remember what they were told. It would be even better if we could cultivate an appreciation for how science works and, in our most ambitious moments, light a spark of enthusiasm for the beauty, unity, and bizarre processes that make up the natural world. Our problem is how to approach the Socratic ideal in a practical and economically feasible manner. In this light, we should ‘fess up to where we stand on a number of important issues—we unambiguously accept the liberal ideals of the Enlightenment, namely that intellectual honesty and rigor, rational and logical discourse, and free and dispassionate analyses, together with compassion and empathy, something all too often forgotten by revolutionaries, are critical, both in the context of the scientific enterprise and more generally in making the world a better place for all of its inhabitants. Unfortunately, the ideals of the Enlightenment appear to have fallen somewhat out of favor, at least 1. Take a look at Pauling’s General Chemistry and tell us we are wrong. 2. http://www.the-scientist.com/?articles.view/articleNo/36919/title/Cancer-Causing-Herbal-Remedies/ x | PREFACE in some circles. While there is an apparent excess of passion, few appear to be willing to examine objectively or even consider both the positive and negative implications of their positions. Passionate advocacy devoid of rational analysis and the recognition that our understanding of the world is tentative and incomplete, and likely to remain that way for some time into the future, seems to encourage various forms of irrational, and often cruel and violent beliefs, many of which should be dismissed out of hand. So, back to the project at hand—how do we build a better chemistry book and course? We freely admit our inspirations. Books like Bill Bryson’s “A Short History of Nearly Everything” and Einstein and Infeld’s “The Evolution of Physics” present science in a logical and engaging manner; they are both interesting and stimulating to read. Unfortunately, this is quite different from the style found in most textbooks. So what is missing from the Bryson and Einstein and Infeld books that make them inappropriate for use as a college textbook? Most obviously, they do not concern themselves with determining whether their readers really–that is, accurately–understand and can apply the ideas presented. Therein lies the logic and impetus behind our book and its associated web-based and in-class materials. Our goal is to merge the inherently engaging aspects of chemistry with the active experiences and metacognitive reflections needed to rewire the student’s (that is, your) brain to really understand and accurately use chemical knowledge. While there have been many educational experiments over the last 100 years, we take our inspiration from Socrates (470–399 bce). Basically, our goal is to present concepts and skills in various ways, ask students to talk about and work with their understanding, and then ask questions about what students actually mean when they use specific words and ideas. Critical to the success of this approach is time: the time required to understand what students think before, during, and after reading the text and working with the applets and activities; the time required for students to recognize and talk about their assumptions; the time required to listen to them, to ask them what, exactly, they mean, and for them to explain, analyze, and where appropriate reconsider, their ideas. Because of the critical link between time and learning, we will not consider some of the topics often presented in standard textbooks and instead will concentrate on more foundational ideas. Does this mean that using this book and its associated materials will leave students unprepared in critical areas of chemistry? No, and we can demonstrate that is not the case. Rather, it leaves students able to work through many of these topics on their own and we will provide web resources to make this possible. We developed much of the material in this new curriculum using research on how people learn and our own work on how to improve understanding and problem solving in college-level science classes. In previous studies we have found that our methods, which include dramatic reorganization PREFACE | xi and reduction of materials covered, increase student interactions and activity and lead to equal or better performance on standardized exams, greater conceptual understanding, and improved problem- solving skills. By focusing the time and effort on the foundational ideas we expect that you will achieve a more robust and confident understanding of chemical principles, an understanding that should serve you well in subsequent chemistry and other science courses, not to mention “real life”! TO THE STUDENT Melanie Cooper and Michael Klymkowsky We designed this book to help you attain a confident, competent, and coherent understanding of basic chemistry, in particular of the chemistry associated with organisms and their origins. That said, this is not a chemistry for biologists or non-scientists book but rather an approach to the difficult and often counterintuitive ideas at the heart of chemistry, for an intelligent and engaged student who, often quite reasonably, finds these ideas unbelievable, arbitrary, or incoherent. Our goal is to assist you in developing an understanding of the foundations of chemistry, so that you can apply these ideas to a range of new situations. We are aware that many of you are not excited by the prospect of learning chemistry and we share your concerns—many of the ideas presented are difficult and often counterintuitive and past experiences with chemistry not have been optimal. At the same time, it is possible to approach chemistry from a more reasoned and rational direction, recognizing difficult ideas, why we are forced to accept them, and how we can apply them. Why is basic chemistry often perceived as boring? One reason maybe the way it is all too commonly presented: a laundry list of facts to remember and exercises to perform, often with little effort made to connect abstract and frankly weird concepts to your lifetime of day-to-day and quite real experiences. For example, it is certainly not obvious that matter is made of a small set of essentially indestructible objects–atoms–connected to one another in various ways; or how such combinations of atoms–molecules–can lead to complex processes like life and dreams. Where did this strange idea come from? How is it that we come to appreciate and accept the reality of things as abstract as atoms and molecules, or that a tree is composed primarily of gas, carbon dioxide, and water molecules, rearranged? Is it even possible for the average person to really accept, understand and learn to work with, such bizarre abstractions? We think we are reasonably average people not withstanding our excessive amounts of formal education and our obsessive efforts to understand what may seem to be insignificant, weird, and occasionally trivial problems. We think that while scientific understanding is not easy, it can be made more engaging by recognizing explicitly which ideas are odd and what types of observations and logic led or forced scientists to accept them. Throughout our journey we will consider what makes sense from our day-to-day experiences, how that differs from the current models of chemical systems, and what types of observations resolve the TO THE STUDENT | xiii apparent contradictions between the two. We encourage you to take your own ideas seriously and consider when they do and do not make scientific sense. This is not an easy task, but it is the only way to understand scientific ideas, rather than simply memorizing words and formulae. Why think about chemistry from a biological perspective? The answer is simple really. Biological systems, whether cells, organisms, or ecosystems, are the most complicated examples of chemical systems. They rely on chemical reactions and the chemical properties of atoms and molecules to produce truly amazing behaviors. They are the end products of evolutionary processes that have been going on form more that 3.5 billion years; processes based on random variations that are captured and turned into information through natural selection. Molecular analyses strongly support the rather amazing conclusion—namely that all organisms currently living on earth are related and descended from a common ancestor through unbroken lineages. The underlying unity of life, and its chemical basis, is only one of many amazing, bizarre, and counterintuitive ideas we will encounter. To help you grapple with these ideas we will use various interactive materials that will help you test and strengthen your understanding. Where you feel lost, try to articulate what, exactly, you find confusing and why. You can start a socratic dialog with yourself, and then bring it to your instructor and fellow students. That is the best way to learn, or so claims Socrates. A note on footnotes: The authors have an inordinate fondness for footnotes. We do not expect you, the student, to read them or the follow the links within them, but they enable us to indulge our interests in various topics. Please be careful to avoid getting lost in them–that may well be a mistake. INTRODUCTION TO THE COURSE Melanie Cooper and Michael Klymkowsky (as opposed to the book) This text is intended to provide an in-depth introduction to the key ideas in chemistry. We have designed the book to show how these ideas are developed from simple to complex systems and how they relate to each other. We consider three ideas central to an understanding of chemistry: the structure of matter, the properties of matter, and the energy changes involved in the reorganization of matter; all are connected by the interactions or forces that cause matter to interact. We aim to provide compelling reasons why you will find yourself wanting to learn chemistry and to illustrate what you will be able to do with this knowledge once you have learned it. We hope that you will find the book both readable and engaging, but keep in mind, it is not intended to contain everything that will be learned in this course. It is purposely not cluttered with boxes, asides, and long descriptions about how to solve problems or learn other skills such as learning how to construct a scientific explanation, or developing a model. This is not because these aspects of chemistry are unimportant – quite the contrary – but rather that there is little evidence that reading a book will lead to effective mastery of such skills. Instead, you will work with activities within the class. We have designed these to be interactive and to support and expand on the text. In some cases these ancillary materials introduce ideas that are not, perhaps, as engaging to read about even though they are important to master. These ancillary CLUE materials include: 1. A set of class presentations and activity materials; 2. A set of YouTube videos showing how to do various skills and solve different types of problems; and 3. A set of online activities using the beSocratic system that can be done in class, in recitation, or for homework. Much like the “questions to answer, questions to ponder, and questions for later” sections of the book, these ancillary activities require you to actively construct answers rather than choose from a list of responses. This is a deliberate focus of the CLUE curriculum because we have compelling evidence 2 | INTRODUCTION that drawing, writing, and constructing answers help students learn more deeply. These materials are also available as worksheets that can be done off-line. Materials integral to the CLUE curriculum but that are not covered exhaustively in the text are: 1. Common chemistry calculations, illustrated by YouTube videos, including: ◦ Stoichiometry; ◦ Energy, frequency, and wavelength conversions; ◦ Mass energy conversions; ◦ Thermochemistry, including specific heat, bond energy and entropy, enthalpy, and Gibbs energy; ◦ Equilibrium calculations, pH and Ka; ◦ Reaction rates and rate law determinations; and ◦ Buffers and linked chemical reaction energy changes. 2. Common skills, including: ◦ Electron configurations, particularly to determine the number of valence electrons; ◦ Drawing Lewis structures; ◦ VESPR; ◦ Assigning oxidation numbers; and ◦ Using curved arrows to predict the outcome of simple reactions. 1. ATOMS Melanie Cooper and Michael Klymkowsky If, in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generation of creatures, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis (or the atomic fact, or whatever you wish to call it) that all things are made of atoms—little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling on being squeezed into one another. In that one sentence, you will see, there is an enormous amount of information about the world, if just a little imagination and thinking are applied. – Nobel Laureate Richard Feynman, 1963 Most of us are quite familiar with the core principle of atomic theory—the idea that matter is composed of atoms—because we have been told that this is so since childhood. But how many of us really, and we mean really believe it, use it in our day-to-day life, understand its implications, or know the reasons why it is assumed to be true? It seems so completely and totally impossible and improbable because we do not experience atoms directly and it is easy to go through life quite successfully, at least for the vast majority of us, without having to take atoms seriously. The average person’s brain is simply not wired to believe in the reality of things like atoms in a concrete and day-to-day way. Yet 4 | CHAPTER 1: ATOMS most scientists, and certainly most chemists, would agree that Feynman’s deceptively simple statement contains the essence of chemistry. Atomic theory is also critical for understanding a significant number of the underlying concepts of biology and physics, not to mention geology, astronomy, ecology, and engineering. How can one sentence contain so much information? Can we really explain such a vast and diverse set of scientific observations with so little to go on? In the next two chapters we will expand on Feynman’s sentence to see just what you can do with a little imagination and thinking. At the same time, it is worth remembering that the fact that atoms are so unreal from the perspective of our day-to-day experience means that the atomic theory poses a serious barrier to understanding modern chemistry. This is a barrier that can only be dealt with if you recognize it explicitly and try to address and adjust to it. You will be rewiring your brain in order to take atoms, and their implications, seriously. We are aware that this is not an easy task. It takes effort, and much of this effort will involve self-reflection, problem- solving, and question-answering. In an important sense, you do not have to believe in atoms, but you do have to understand them. 1.1 What Do You Think You Know About Atoms? You almost certainly have heard about atoms and it is very likely you have been taught about them. If asked you might profess to believe in their reality. You might accept that matter, in all its forms, is made up of atoms — particles that are the smallest entities that retain the identity of an element (we will discuss elements in much greater detail in the next few chapters.) It is very likely that you have been taught that atoms are made up of even smaller particles: positively charged protons, uncharged neutrons, and negatively charged electrons. You may even have heard, and perhaps even believe, that protons and neutrons can be further subdivided into quarks and gluons, while electrons are indivisible. Equally difficult to appreciate is that all atoms are organized in a very similar way, with a very tiny, but relatively heavy, positively charged nucleus surrounded by the much lighter, negatively charged electrons. Part of the difficulty in really understanding atoms is the fact that the forces holding the atomic nucleus together, the so-called strong and weak forces, operate at such infinitesimal distances that we do not experience them directly. This is in contrast to electromagnetism and gravity, which we experience directly because they act over longer, macroscopic or visible distances. A second problem is associated with the fact that to experience the world we need to use energy; at the atomic scale the CHAPTER 1: ATOMS | 5 energy used to observe the system also perturbs it. This is the basis of the Heisenberg uncertainty principle, which you may have encountered or at least heard of before, and to which we will return. Finally, objects at the atomic and subatomic scales behave differently from the macroscopic objects with which we typically interact. A particle of light, a photon, an electron, a proton, or a neutron each behaves as both a particle and a wave. In terms of physics, these are neither particles nor waves; they are quantum mechanical particles. Luckily, the weirder behaviors of atomic and subatomic entities can often, but not always, be ignored in chemical and biological systems. We will touch on these topics as necessary. Current theory holds that each atom contains a very, very small, but very dense nucleus, which contains protons and neutrons and is surrounded by electrons. These electrons are very light, relatively, but the space occupied by moving electrons accounts for the vast majority of the volume of an atom. Because the number of positively charged protons and negatively charged electrons are equal and the size of the charges are the same but opposite, atoms are electrically neutral when taken as a whole; that is, each positively-charged proton is counterbalanced by a negatively-charged electron. Often the definition of an atom contains some language about how atoms are the smallest particle identifiable as that element. What do we mean by that? For example, can an atom have chemical properties? And how can ensembles of the same particles, that is protons, electrons, and neutrons, have different properties? This is the mystery of the atom and understanding it is the foundation of chemistry. In this first chapter, we hope to lead you to a basic understanding of atomic structure and inter-atomic interactions. Subsequent chapters will extend and deepen this understanding. Questions Questions to Ponder If you had to explain to a non-scientist why it is that scientists accept the idea that all material things are composed of atoms what evidence would you use? Does the ability of science to explain so much about the world influence your view about the reality of supernatural forces? 6 | CHAPTER 1: ATOMS 1.2 Atomic Realities and Scientific Theories We assume that you have lots of ideas about atoms but did you ever stop to think how we came to accept this information as reasonable or what the reality of atoms implies about how the world we perceive behaves? Atoms are incredibly and unimaginably small. A gold atom with its full complement –9 of electrons is less than a nanometer (1 x 10 meters) in diameter and its nucleus, which contains 79 –14 protons and generally around 116 neutrons, has a radius of ~1.5 x 10 meters. While these sizes are actually unimaginable, there are a number of web-based activities that can help you come to terms with the scales of atoms.1 There is no way you could see an atom with your eye or with a light microscope, although there are now techniques that allow us to view computer representations of individual atoms using various types of electron and force-probe microscopes. The smallest particle of matter that you can see with your naked eye contains more atoms than there are people in the world. Every cell in your body contains a huge number of atoms. Obviously, whatever we know about atoms is based on indirect evidence; we do not directly experience atoms. The full story of how we know what we know about the existence and structure of atoms is fascinating, complex, and perhaps fortunately for you, too long to go into in detail. What we do want to do is to consider a number of key points that illustrate how our ideas of atoms arose and have changed over time. We will present the evidence that has made accepting the atomic theory unavoidable if you want to explain and manipulate chemical reactions and the behavior of matter. Atomic theory is an example of a scientific theory that began as speculation and, through the constraints provided by careful observation, experimentation, and logical consistency, evolved over time into a detailed set of ideas that make accurate predictions and are able to explain an increasing number of diverse, and often previously unknown, phenomena. As scientists made new observations, atomic theory was adapted to accommodate and organize these observations. A key feature of scientific ideas, as opposed to other types of ideas, is not whether they are right or wrong but whether they are logically coherent and make unambiguous, observable, and generally quantitative predictions. They tell us what to look for and predict what we will find if we look at or measure it. When we look, we may find the world acts as predicted or that something different occurs. If the world is different from what our scientific ideas suggest then we assume we are missing something important: either our ideas need altering or perhaps we are not looking at the world in 1. Scale of the universe: http://htwins.net/scale2/ CHAPTER 1: ATOMS | 7 the right way. As we will see, the types of observations and experimental evidence about matter have become increasingly accurate, complex, and often abstract, that is, not part of our immediate experience. Some of these observations can be quite difficult to understand, because matter behaves quite differently on the atomic and sub-atomic scale than it does in the normal, macroscopic world. It is the macroscopic world that evolutionary processes have adapted us to understand, or at least cope with, and with which we are familiar. Yet, if we are to be scientific, we have to go where the data lead us. If we obtain results that are not consistent with our intuitions and current theories, we have to revise those theories rather than ignore the data. However, scientists tend to be conservative when it comes to revising well-established theories because new data can sometimes be misleading. This is one reason there is so much emphasis placed on reproducibility. A single report, no matter how careful it appears, can be wrong or misinterpreted and the ability of other scientists to reproduce the observation or experiment is key to its acceptance. This is why there are no miracles in science. Even so, the meaning of an observation is not always obvious or unambiguous; more often than not an observation that at first appears to be revolutionary turns out to have a simple and even boring explanation. Truly revolutionary observations are few and far between. This is one reason that the Carl Sagan (1934-1996) quote, “Extraordinary claims require extraordinary evidence” is so often quoted by scientists. In most cases where revolutionary data is reported, subsequent studies reveal that the results were due to poor experimental design, sloppiness, or some irrelevant factor. The fact that we do not all have cold fusion energy plants driving perpetual motion refrigerators in our homes is evidence that adopting a skeptical approach that waits for experimental confirmation is wise. A common misconception about scientific theories is that they are simply ideas that someone came up with on the spur of the moment. In everyday use, the word theory may well mean an idea or even a guess, a hypothesis, or a working assumption, but in science the word theory is reserved for explanations that encompass and explain a broad range of observations. More than just an explanation, a theory must be well tested and make clear predictions relating to new observations or experiments. For example, the theory of evolution predicted that the fossil record would show evidence for animals that share many of the features of modern humans. This was a prediction made before any such fossils were found; many fossils of human-like organisms have since been and continue to be discovered. Based on these discoveries, and on comparative analyses of the structure of organisms, it is possible to propose plausible family trees, known as phylogenies, connecting different types of organisms. Modern molecular genetics methods, particularly genome (DNA) sequencing, have confirmed these predictions and produced strong experimental support for the current view that all organisms now 8 | CHAPTER 1: ATOMS living on Earth are part of the same family–that is, they share a common ancestor that lived billions of years ago. The theory of evolution also predicts that the older the rocks, the more different the fossilized organisms found will be from modern organisms. In rocks dated to ~410 million years ago, we find fossils of various types of fish but not the fish that exist today. We do not find evidence of humans from that period; there are, in fact, no mammals, no reptiles, no insects, and no birds. A scientific theory is also said to be falsifiable, which doesn’t mean that it is false but rather that it may be proven false by experimentation or observation. For example, it would be difficult to reconcile the current theory of evolution with the discovery of fossil rabbits from rocks older than 300 million years. Similarly, the atomic theory would require some serious revision if someone discovered an element that did not fit into the periodic table; the laws of thermodynamics would have to be reconsidered if someone developed a successful perpetual motion machine. A theory that can be too easily adapted to any new evidence has no real scientific value. A second foundational premise of science is that all theories are restricted to natural phenomena; that is, phenomena that can be observed and measured, either directly or indirectly. Explanations that invoke the supernatural or the totally subjective are by definition not scientific, because there is no imaginable experiment that could be done that might provide evidence one way or another for their validity. In an important sense, it does not matter whether these supernatural explanations are true or not; they remain unscientific. Imagine an instrument that could detect the presence of angels. If such an instrument could be built, angels could be studied scientifically; their numbers and movements could be tracked and their structure and behaviors analyzed; it might even be possible to predict or control their behavior. Thus, they would cease to be supernatural and would become just another part of the natural world. Given these admitted arbitrary limitations on science as a discipline and an enterprise, it is rather surprising how well science works in explaining (and enabling us to manipulate) the world around us. At the same time, science has essentially nothing to say about the meaning of the world around us, although it is often difficult not to speculate on meaning based on current scientific ideas. Given that all theories are tentative, and may be revised or abandoned, perhaps it is wise not to use scientific ideas to decide what is good or bad, in any moral sense. As we will see, the history of atomic theory is rife with examples of one theory being found to be inadequate, at which point it must be revised, extended, and occasionally totally replaced by a newer theory that provides testable explanations for both old and new experimental evidence. This does not mean that the original theory was necessarily completely false but rather that it was unable to fully capture the observable universe or to accurately predict newer observations. Older theories are CHAPTER 1: ATOMS | 9 generally subsumed as newer ones emerge; in fact, the newer theory must explain everything explained by the older one and more. Questions Questions to Answer: Scientific Questions and Theories: How would you decide whether a particular question was answerable scientifically? How would you decide whether an answer to a question was scientific? What is the difference between a scientific and a non-scientific question? Provide an example of each. Questions to Ponder What things have atoms in them? Air, gold, cells, heat, light? How do you know atoms exist? 1.3 Some History of Atomic Theory Modern atomic theories have their roots in the thinking of ancient peoples, in particular ancient Greek philosophers who lived over 2500 years ago. At that time the cultural, economic, and intellectual climate in Ancient Greece permitted a huge surge of philosophical and scientific development, the so- called Greek miracle. While most people of that time believed that the world was ruled by a cohort of semi-rational gods a series of philosophers, beginning with Thales of Miletus (died 546 bce),2 were intent on developing rational and non-supernatural explanations for observable phenomena such as what we are made of and where we came from. As we know now, they could not possibly have 2. http://www.iep.utm.edu/t/thales.htm 10 | CHAPTER 1: ATOMS understood the underlying nature of matter because they lacked the tools to observe and experiment at the atomic scale. However, this does not mean that their ideas were simple idle speculation. The ideas they produced, although not scientific as we understand the term today, contained remarkable insights – some of which appear to be true. This era gave birth to a new way to approach and explore natural phenomena in order to gain understanding of their complexity and diversity in terms of natural explanations. It is worth considering that such a rational approach did not necessarily have to be productive; it could be that the world is really a totally irrational, erratic, and non-mechanistic place, constantly manipulated by supernatural forces; but given that science can not address these kinds of ideas, let us just leave them to fantasy authors. The assumption that the world is ruled solely by natural forces has been remarkably productive; that is, consistent with the way the world appears to behave when we look at it dispassionately. The ancient Greeks developed complex ideas about the nature of the universe and the matter from which it was composed, some of which were accepted for a long time. However, in response to more careful observation and experimental analysis, these ideas were eventually superseded by more evidence-based theories. In large part this involved a process by which people took old ideas seriously, and tried to explain and manipulate the world based on them. When their observations and manipulations failed to produce the expected or desired outcomes, such as turning base metals into gold, curing diseases, or evading death altogether, they were more or less forced to revise their ideas, often abandoning older ideas for newer ideas that seemed to work. The development of atomic theories is intertwined with ideas about the fundamental nature of matter, not to mention the origin of the universe and its evolution. Most Greek philosophers thought that matter was composed of some set of basic elements, for example, the familiar earth, air, fire, and water. Some philosophers proposed the presence of a fifth element, known as quintessence or aether.3 These clearly inadequate ideas persist today as part of astrology and the signs of the Zodiac—a poor tribute to some very serious thinkers. The original elements, that is, earth, air, fire, and water, were thought to be composed of tiny indestructible particles, called atoms by Leucippus and Democritus (who lived around 460 bce).4 The atoms of different elements were assumed to be of different sizes and shapes, and their shapes directly 3. Of course if you know your movies, you know that the “Fifth Element” is love. 4. http://plato.stanford.edu/entries/democritus/ CHAPTER 1: ATOMS | 11 gave rise to the properties of the particular element. For example, the atoms of earth were thought to be cubic; their close packing made earth solid and difficult to move. The idea that the structure of atoms determines the observable properties of the material is one that we will return to, in a somewhat different form, time and again. Although the particulars were not correct, the basic idea turns out to be sound. In addition to their shapes, atoms were also thought to be in constant motion, based on watching the movement of dust motes in sunlight, with nothing, or a void, between them.5 Many centuries later Einstein’s analysis of this type of motion, known as Brownian motion, provided strong experimental support for the physical reality of molecules, larger structures composed of atoms, and the relationship between molecular movement, temperature, and energy, which we will consider later on in this chapter. All in all the combined notions of the Greek philosophers provided a self-consistent and satisfactory basis for an explanation of the behavior of matter, as far as they could tell. The trap here is one that is very easy to fall into, namely that a satisfying explanation for a phenomenon is not necessarily true. Even if it seems to be self-consistent, useful, or comforting, an explanation is not scientific unless it makes testable, quantitative predictions. For example, it was thought that different materials were made up of different proportions of the four ancient elements. Bones were made of water, earth, and fire in the proportions 1:1:2, whereas flesh was composed of these elements in a ratio of 2:1:1.6 While these ideas are now considered strange, they contain a foreshadowing of the “law of multiple proportions”, which would come some 2300 years later and which we will deal with later in this chapter. Some philosophers even thought that the soul was composed of atoms or that atoms themselves had a form of consciousness, two ideas that seem quite foreign to (most of) us today. Such ideas about atoms and elements provided logical and rational, that is, non-supernatural explanations for many of the properties of matter. But the Greeks were not the only ancient people to come up with explanations for the nature of matter and its behavior. In fact, it is thought that the root of the words alchemy and chemistry is the ancient Greek word Khem, the Greek name for Egypt, where alchemy and chemistry are thought to have originated.7 Similar theories were being developed in India 5. First description of Brownian motion - Epicurus 6. A History of Greek Philosophy by William Keith Chambers Guthrie. p. 212. 7. http://www.chm.bris.ac.uk/webprojects2002/crabb/history.html and http://en.wikipedia.org/wiki/ Chemistry_(etymology) 12 | CHAPTER 1: ATOMS at about the same time, although it is the Greek ideas about atoms that were preserved and used by the people who eventually developed our modern atomic theories. With the passage of time ancient ideas about atoms and matter were kept alive by historians and chroniclers, in particular scholars in the Arab world. During the European Dark Ages and into medieval times, there were a few scattered revivals of ideas about atoms, but it was not until the Renaissance that the cultural and intellectual climate once again allowed the relatively free flowering of ideas. This included speculation on the nature of matter, atoms, and life. Experimental studies based on these ideas led to their revision and the eventual appearance of science, as we now know it. It is also worth remembering that this relative explosion of new ideas was occasionally and sometimes vigorously opposed by religious institutions, leading to torture, confinement, and executions.8 Questions: Questions to Answer: What properties ascribed by the Greeks to atoms do we still consider to be valid? Questions to Ponder: If earth had atoms that were cubic, what shape would you ascribe to the elements air, water, and fire? Questions for Later If atoms are in constant motion, what do you think keeps them moving? 8. An important event was the rediscovery by Poggio of Lucretius’s “On the Nature of Things,” a poem centered on the atomic nature of the universe (see The Swerve by Stephen Greenblatt). One reason Giordano Bruno was burnt at the stake was the fact that he took these ideas seriously. CHAPTER 1: ATOMS | 13 1.4 Identifying and Isolating Elements The Greek notion of atoms and elements survived for many centuries and it was eventually fleshed out with the addition of a few more elements, mostly through the efforts of the alchemists. Some elements such as gold were discovered much earlier – mainly because they exist as elements rather than compounds. By the late eighteenth century, the idea of an element as a substance that cannot be broken down into more fundamental substances had begun to be accepted. In 1789 Antoine Lavoisier (1743–1794) produced a list of 33 elements. His list did not include earth, air, fire, and water, but it did contain light and heat, along with a number of modern elements including cobalt, mercury, zinc, and copper. It had already been established that oxygen and hydrogen were elements, while water was not. The stage was set for a rapid growth in our knowledge about the underlying structure of matter. We now know of 91 naturally occurring elements, and quite a number of unnatural, that is, human-made ones which are not found in nature because they unstable. These human-made elements are heavier in atomic terms than the naturally occurring elements and are typically generated by smashing atoms of natural elements into one another; they break down, or decay, rapidly into atoms of other elements. As examples of how science can remove some of the mystery from the universe: our understanding of atoms and elements means that no new natural, light elements are theoretically possible. We know of all the light elements that can possibly exist anywhere in the universe, a pretty amazing fact. Similarly, our current understanding of the theory of general relativity and the laws of thermodynamics make faster-than-light travel and perpetual motion machines impossible, although it does not stop people from speculating about them. The first modern chemical isolation of an element is attributed to the alchemist Hennig Brand (c. 1630–c. 1710).9 He isolated phosphorus from urine while in pursuit of the philosopher’s stone.10 While this may seem like an odd thing to do, people have done much stranger things in pursuit of gold or cures for diseases like syphilis. Imagine his surprise when, after boiling off all the water from 9. http://elements.vanderkrogt.net/elem/p.html 10. The Philosopher’s stone was thought to be able to turn base (common) metals into gold, and perhaps even be the key to everlasting life. It was the ultimate goal of the alchemists. Interestingly the first Harry Potter book was titled Harry Potter and the Philosopher’s Stone in England but was re-titled in America, because the publishers thought that American children would not be interested in a book with this title, perhaps due a failure to appreciate the importance of philosophy. 14 | CHAPTER 1: ATOMS the urine, the residue burst into flames and gave off a gas that, when condensed, produced a solid that glowed green in the dark. It was for this reason that he named it phosphorus, from the Greek for light- bearer. Similarly, mercury was originally isolated by roasting the mineral cinnabar. Despite being quite toxic, mercury was used as a treatment for syphilis prior to the discovery of effective antibiotics. Questions Questions to Answer Given what you know, how would you explain the difference between an atom and an element? What differentiates one element from another? What is the difference between an atom and a molecule? What is the difference between an element and a compound? Questions to Ponder What types of evidence might be used to prove you had isolated a new element? When can unproven/unsubstantiated assumptions be scientific? Under what conditions are such assumptions useful? Why do you think gold was recognized as an element earlier than many others? 1.5 Evidence for Atoms It is important to note that from the time that the first ideas of atoms arose, and for thousands of years thereafter, there was not one shred of evidence for the particulate nature of matter or the physical existence of atoms. The idea of atoms was purely a product of imagination, and while there was vigorous debate about the nature of matter, this debate could not be settled scientifically until there was objective empirical evidence one way or another. CHAPTER 1: ATOMS | 15 So the question arises, how did scientists in the nineteenth century eventually produce clear evidence for the existence of atoms? We have already said atoms are much too small to be seen by any direct method. So what would lead scientists to the unavoidable conclusion that matter is composed of discrete atoms? It is often the case that a huge intuitive leap must be made to explain the results of scientific observations. For example, the story about Isaac Newton (1643–1727) and the falling apple captures this truism, namely the remarkable assumption that the movement of Earth around the Sun, the trajectory of a cannon ball, and the falling of an apple to Earth are all due to a common underlying factor, the force of gravity, which acts at a distance and obeys an inverse square relationship, 1/r2 where r is the distance between two objects. This seems like a pretty weird and rather over-blown speculation; how does this “action at a distance” between two objects work? Yet, followed scientifically, it appeared to be very powerful and remarkably accurate. The point is that Newton was able to make sense of the data, something that is in no way trivial. It requires a capacity for deep, original, and complex thought. That said, it was not until Albert Einstein (1874-1955) proposed his general theory of relativity in 1915 that there was a coherent, mechanistic explanation for gravitational forces. The first scientific theory of atomic structure was proposed by John Dalton (1766–1844), a self- taught Quaker11 living in Manchester, England.12 In 1805 Dalton published his atomic theory to explain the observed law of multiple, or definite, proportions, which stated briefly is “when elements combine, they do so in the ratio of small whole numbers”, we will return to this idea later on, in much greater detail.13 Rather surprisingly, Dalton never really explained what led him to propose his atomic theory, although he certainly used it to explain existing rules about how different elements combine. Among these rules was the observation that the total matter present in a system does not change during a chemical reaction, although a reaction might lead to a change from a solid to a gas or vice versa. Dalton’s atomic theory (1805) had a number of important components: Elements are composed of small indivisible, indestructible particles called atoms. All atoms of an element are identical and have the same mass and properties. 11. Religious dissenters, that is, non-Anglicans, were not allowed access to English universities at that time. 12. An extraordinary number of discoveries related to the structure of the atom were made by scientists in or from Manchester. There must be something in the air there. It is, of course, completely fortuitous that one of the authors was also born and bred in Manchester! 13. https://en.wikipedia.org/wiki/Law_of_multiple_proportions 16 | CHAPTER 1: ATOMS Atoms of a given element are different from atoms of other elements. Compounds are formed by combinations of atoms of two or more elements. Chemical reactions are due to the rearrangements of atoms, and atoms (matter) are neither created nor destroyed during a reaction. Based on these tenets he was able to explain many of the observations that had been made, by himself and others, about how matter behaves and reacts. More modern atomic theories have made some modifications, for example to include the existence of atomic isotopes, that is, atoms with different numbers of neutrons, but the same number of protons and electrons, and the conversion of energy into matter and vice versa, but Dalton’s core ideas remain valid. Questions Questions to Answer In what ways is Dalton’s atomic theory different from the ideas of the Greek philosophers? Which tenets of Dalton’s theory still hold up today? Design an experiment to investigate whether there is a change in mass when water changes phase. What data would you collect? How would you analyze it? Questions to Ponder How did Dalton conclude that there were no half-atoms? Which parts of Dalton’s theory were unfounded speculation and which parts were based on direct observation? CHAPTER 1: ATOMS | 17 1.6 The Divisible Atom The opposite of a correct statement is a false statement. But the opposite of a profound truth may well be another profound truth. Neils Bohr (1865–1962) Dalton’s theory of atoms as indivisible, indestructible, objects of different sizes, weights, and perhaps shapes, depending on the element, held up for almost 100 years, although there was considerable dissent about whether atoms really existed, particularly among philosophers. By 1900 the atomic theory was almost universally accepted by chemists. More evidence began to accumulate, more elements were discovered, and it even became possible to calculate the number of atoms in a particular sample. The first step, along this direction, was made by Amedeo Avogadro (1776–1856). In 1811 he proposed that, under conditions of equal temperature and pressure, equal volumes of gases contained equal numbers of particles (molecules) and that the densities of the gases, that is their weight divided by their volume, were proportional to the weight of the individual molecules. This was expanded on by the Austrian high school teacher Josef Loschmidt (1821–1895) who, in 1865, combined Avogadro’s conclusion with the assumption that atoms and molecules move very much as elastic objects, think billiard balls. This enabled him to calculate the force a molecule would exert when traveling at a particular speed, something difficult to measure, and relate that to the pressure, something easily measured. In fact, this assumption enabled physicists to deduce that the temperature of a gas is related to the average kinetic energy of the molecules within it, a concept we will return to shortly. Probing the Substructure of Atoms The initial Greek assumption was that atoms were indivisible, essentially unchangeable from their initial creation. However, gradually evidence began to accumulate that atoms were neither indivisible nor indestructible. Evidence for the existence of particles smaller than atoms had been building up for some time, although it was not recognized as such. For example, the well-recognized phenomenon of static electricity had been known since the ancient Greeks. The name electricity comes from the Latin electricus, meaning amber-like. Rubbing amber with fur generates static electricity—the same type of spark that jumps from your finger to a doorknob or another person under dry conditions. In the late 1700s Luigi Galvani (1737–1798) discovered that animals can produce and respond to electricity, perhaps the most dramatic example being the electric eels and rays that stun their prey through electrical shocks. The discovery of bioelectricity was exploited in many novels and movies, beginning 18 | CHAPTER 1: ATOMS with Mary Shelly’s (1797–1851) novel Frankenstein and continuing through Mel Brook’s (b. 1926) comedy film, Young Frankenstein. Galvani discovered that a dead frog’s leg would twitch in response to exposure to static electricity; it appeared to come back to life, just like Frankenstein’s monster. He assumed, correctly it turns out, that electrical activity was involved in the normal movement of animals. He thought that a specific form of electricity, bioelectricity, was carried in the fluid within the muscles and was a unique product of biological systems, a type of life-specific force. We now recognize that a number of biological phenomena, such as muscle contraction and brain activity, are initiated by changes in electric fields (across membranes) and that the underlying physicochemical principles are similar to those taking place in non-biological systems. The excitement about electricity and its possible uses prompted Alessandro Volta (1745–1827) to develop the first modern battery, now known as a voltaic pile. He alternated sheets of two different metals, such as zinc and copper, with discs soaked in salt water (brine). It produced the first steady electrical current that, when applied to frog muscles, caused them to contract. Such observations indicated that biological systems can both generate and respond to electrical currents, suggesting that bioelectricity was no different than any other form of electricity. What neither Volta nor Galvani knew was the nature of electricity. What was it, exactly, and how did it flow from place to place? What was in the spark that jumped from finger to metal doorknob, or from Benjamin Franklin’s (1705–1790) kite string to his finger? What was this “electrical fluid” made of? Progress in the understanding of the nature and behavior of electricity continued throughout the 19th century and the power of electricity was harnessed to produce dramatic changes in the way people lived and worked, powering factories, lighting houses and streets, and so on. Yet there was no deep of understanding as to the physical nature of electricity. It was known that electric charge came in two forms, positive and negative, and that these charges were conserved; that is, they could not be created or destroyed, ideas first proposed by Franklin. The electrical (charged) nature of matter was well established, but not where those charges came from or what they were. CHAPTER 1: ATOMS | 19 A key step to understanding electricity involved unraveling the idea of the indivisible atom and involved a series of experiments by J. J. Thompson (1856–1940), another Mancunian.14 Although the idea of electricity was now well appreciated, Thompson and other scientists wanted to study it in a more controlled manner. They used what were, and are now, known as cathode ray tubes (CRTs). Once common in televisions, these have now been replaced by various flat screen devices. CRTs are glass tubes with wires embedded in them; these wires are connected to metal discs. The inside of the tube is coated with a chemical that glows (fluoresces) in response to electricity. They generally have ports in the walls that can be connected to a vacuum pump, so that most of the air within the tube can be removed, typically the ports are then sealed. When connected to a source of electricity, such as a voltaic pile, the fluorescent material at one end of the tube glows. In a series of experiments (1897) Thomson was able to show that: Rays emerged from one disc (the cathode) and moved to the other (the anode). “Cathode” rays were deflected by electrical fields in a direction that indicated that they were negatively charged. The rays could also be deflected by magnetic fields.15 The rays carried the electrical charge; that is, if the ray was bent, for example by a magnetic field, the charge went with it. The metal that the cathode was made of did not affect the behavior of the ray; so whatever the composition of the ray, it appeared to be independent of the element that it came from. In all of these experiments, it needs to be stressed that “positive” and “negative” are meant to indicate opposite and are assigned by convention. That means that we could decide tomorrow that positive was negative, and negative positive, and nothing would change, as long as we were consistent. From these experiments, Thompson concluded that “cathode” rays were carried by discrete charged particles, he called them corpuscles, and he assigned these particles a negative charge. But the truly stunning conclusion he reached was that these particles must come from within the atoms of the metal cathode. Because the type of metal did not affect the nature or behavior of the cathode rays, he assumed that these particles were not newly created but must pre-exist within the atoms of the cathode. Moreover, he 14. That is, a person from Manchester, England. 15. This works because the electrons are spinning. 20 | CHAPTER 1: ATOMS hypothesized that identical particles must be present in all atoms, not just in the atoms of one particular metal. Do you see how he jumps from experimental results using a few metals to all elements and all atoms? Of course, we now know these particles as electrons but it is difficult to imagine what a huge impact this new theory had on scientists at the time. Since electrons can be produced by all chemical elements, we must conclude that they enter the constitution of all atoms. We have thus taken our first step in understanding the structure of the atom. —J. J. Thomson, The Atomic Theory, 191416 The discovery of the electron made the old idea of an atom as a little indestructible billiard ball-like objects obsolete and necessitated a new model. It is an example of a paradigm shift17—a fundamental change in scientific thinking driven by new evidence. Thompson’s first version of this new model became known as the plum pudding model.18 His basic idea was that the atom is a ball of positively charged, but apparently amorphous, matter with electrons studded here and there, like the raisins in a pudding. Because it contained equal numbers of positive and negative charges, the overall structure was electrically neutral. Subsequent work by Thompson and Robert A. Millikan (1868–1953) established that all electrons are identical, each with the same, very small mass and negative charge. The mass of an electron is less than 1/1000th of the mass of a hydrogen atom. Thompson’s proposed plum pudding model of the atom spurred much experimental and theoretical work and led to a remarkable number of subsequent discoveries. For example, it was soon recognized that the β particles emitted by some radioactive minerals and elements, were, in fact, electrons. Other studies found that the number of electrons present in the atoms of a particular element was roughly proportional to half the element’s atomic weight, although why this should be the case was unclear. However, as more and more data began to accumulate, the plum pudding model had to be abandoned because it just could not explain what was being observed. The key experiment that led 16. http://www.aip.org/history/electron/jjsound.htm 17. A term made popular (although often misunderstood) by T. S. Kuhn, The Structure of Scientific Revolutions, 1st. ed., Chicago: Univ. of Chicago Pr., 1962 18. This can be a little confusing to those not familiar with plum pudding – a “delicious” English delicacy composed of dried fruit (raisins) in a spongy base, usually prepared by boiling for several days and often served with rum sauce. CHAPTER 1: ATOMS | 21 to a new model of the atom was carried out in 1908 by Ernest Rutherford (1871–1937). As you may have already guessed, he was working at the University of Manchester. In this experiment, he examined how alpha (α) particles, which he knew to be positively charged particles made of the element helium without it’s electrons, behaved when they were fired at a very thin sheet of metal, such as gold or platinum. In the experiment a narrow parallel beam of α particles was directed at a thin sheet of gold foil and the angles at which the deflected particles scattered were detected. The observed result was completely unexpected. Instead of passing straight through the thin sheet of foil, he found that a few particles were deflected, some of them at large angles. Rutherford wrote, “It is as if I had fired a cannon ball at a piece of tissue paper, and it bounced right back.” Here again, we see a particular aspect of the scientific enterprise, namely that even though only a few alpha particles bounced back, we still need to explain how this could possibly occur. We could not just say, “Only a few particles were bounced so it doesn’t matter”; we have to provide a plausible scenario to explain the observation. Often it is paying attention to, and taking seriously, the unexpected result that leads to the most profound discoveries. Based on these experimental results Rutherford reasoned that the positively charged α particles were being repelled by positive parts of the atom. Because only a very small percentage of alpha particles were deflected, only a very small region of each atom could be positively charged. That is, the positive charge in an atom could not be spread out more or less uniformly, as the plum pudding model assumed; instead it must be concentrated in a very small region. This implied that most of the atom is empty (remember the void of the ancient Greeks?) or occupied by something that poses little or no resistance to the passage of the α particles. What it left unexplained was why positively charged particles (which we now know as protons) concentrated in such a small volume, did not repel one another – the answer to which had to wait to discovery of the strong nuclear force (see below). Again we see a scientist making a huge intuitive leap from the experimental observation to a hypothesis that was consistent with that evidence and that makes specific predictions that can be confirmed or falsified by further experiment and observation. Rutherford’s model, which became known as the planetary model, postulated a very, very small nucleus where all of the positive charge and nearly all of the mass of the atom was located; this nucleus was encircled by electrons. In 1920 Rutherford went on to identify the unit of positive charge and called it the proton. In 1932 James Chadwick (1891–1974)(who co- incidentally studied at the University of Manchester) identified a second component of the nucleus, the neutron. Neutrons are heavy, like protons. In fact they are slightly heavier than protons, but have no charge. The identity of the element depends on the number of protons, however the number of neutrons may be different in different atoms of the same element. For example an atom of carbon 22 | CHAPTER 1: ATOMS always has six protons, but it can have different numbers of neutrons. Most carbon atoms have six neutrons (C-12), but some have seven (C-13) and some have eight (C-14). Questions Questions for Later If atoms are mostly empty space, why can’t we walk through walls? What is radiation? How does an atom change when it emits an alpha particle? Or a beta particle/ electron? Questions to Ponder If the original discoverers of electricity had decided that electrons have a positive charge, would that have made a difference in our understanding of electricity? Why do you think electrons were the first sub-atomic particles to be discovered? How exactly did Rutherford detect alpha particles? Can you think of an alternative model of the atom based on Rutherford’s observations? How would the experiment change if he had used electrons or neutrons? 1.7 Interactions Between Atoms and Molecules At this point we have arrived at a relatively simple model of the atom. Do not to worry, we will move to more complex and realistic models in the next chapter. In this simple model the atom has a very small but heavy nucleus that contains both protons and neutrons. As we talk about biology now and again, take care not to confuse the nucleus of an atom with the nucleus of a cell; they are completely different – besides the fact that they are of very different sizes. For example, there is no barrier round the nucleus CHAPTER 1: ATOMS | 23 of an atom—an atomic nucleus is a clump of protons and neutrons. Surrounding the atomic nucleus are electrons, in the same number as there are protons. The atom has no net electrical charge since the number of electrons is equal to the number of protons. Where the electrons actually are in an atom, however, is a trickier question to answer, because of quantum mechanical considerations, specifically the Heisenberg uncertainty principle, which we will return to in the next chapter. For now we are going to assume the electrons are outside the nucleus and moving. We can think of them as if they were a cloud of electron density rather than particles whizzing around (don’t worry we will provide evidence for this model soon). This simple model captures important features and enables us to begin to consider how atoms interact with one another to form molecules and how those molecules can be rearranged—real chemistry! There are four fundamental forces that we know about at the moment: gravity, the electromagnetic force, the strong nuclear force, and the weak nuclear force. For now we can largely ignore the strong nuclear force that is involved in holding the nucleus together:.it is an attractive force between neutrons and protons and is the strongest of all known forces in the universe, ~137 times stronger than the -15 electromagnetic force. The strong nuclear force, acts at very short ranges, ~10 m, or about the diameter of the nucleus. The other force involved in nuclear behavior, the weak force, plays a role in -18 nuclear stability, specifically the stability of neutrons, but it has an even shorter range of action (10 m). Because the nucleus is much smaller than the atom itself we can (and will) ignore the weak and strong nuclear forces when we consider chemical interactions. The force we are probably most familiar -37 with is gravity, which is the weakest force, more than 10 times weaker than the electromagnetic force, and we can ignore it from the perspective of chemistry, although it does have relevance for the biology of dinosaurs, elephants, whales, and astronauts. The electromagnetic force is responsible for almost all the phenomena that we encounter in our everyday lives. While we remain grounded on the Earth because of the gravitational interaction between our body and the Earth, the fact that we don’t fall through to the center of the earth is entirely due to electromagnetic interactions. One obvious feature of the world that we experience is that it is full of solid things—things that get in each other’s way. If atoms and molecules did not interact with one another, one might expect to be able to walk through walls, given that atoms are mostly empty space, but clearly this is not the case. Similarly, your own body would not hold together if your atoms, and the molecules they form, failed to interact. As we will see, all atoms and molecules attract one another—a fact that follows directly from what we know about the structure of atoms and molecules. 24 | CHAPTER 1: ATOMS Questions Questions to Ponder What would a modern diagram of an atom look like and what could it be used to explain? Why don’t the protons within a nucleus repel one another? Why don’t the electrons and protons attract each other and end up in the nucleus? How the electrons within an atom interact? Questions for Later Can an atom have chemical and/or physical properties; if so, what are they? What are chemical and physical properties? Can you give some examples? What distinguishes one element from another? Interactions Between Atoms: A Range of Effects The attractions and repulsions between charged particles and magnets are both manifestations of the electromagnetic force. Our model of the interactions between atoms will involve only electric forces; that is, interactions between electrically charged particles, electrons and protons. In order to understand this we need to recall from physics that when charged particles come close to each other they interact. You probably recall that “like charges repel and unlike charges attract”, and that this interaction, which is known as a Coulombic interaction, depends on the sizes and signs of the charges, and is inversely proportional to the square of the distance between them (this interaction can be modeled by the equation: (Coulomb’s Law), CHAPTER 1: ATOMS | 25 where q1 and q2 are the charges on the particles and r is the distance between them. That is: there is a force of attraction (or repulsion if the two charges are of the same sign) that operates between any two charged particles. This mathematical description of the electromagnetic interaction is similar to the interaction due to gravity. That is, for a gravitational interaction there must be at least two particles (e.g. you and the Earth) and the force of the attraction depends on both masses, and is inversely proportional to the square of the distance between them:. The difference between the two forces are: a) gravitational interactions are much weaker than electromagnetic interactions and b) gravity is solely an attractive interaction while electromagnetic interactions can be either attractive or repulsive. Now, let us consider how atoms interact with one another. Taken as a whole, atoms are electrically neutral, but they are composed of discrete electrically charged particles. Moreover, their electrons behave as moving objects.19 When averaged over time the probability of finding an electron is spread uniformly around an atom, the atom is neutral. At any one instant, however, there is a non-zero probability that the electrons are more on one side of the atom than the other. This results in momentary fluctuations in the charge density around the atom and leads to a momentary charge build up; for a instant one side of the atom is slightly positive (δ+) and the other side is slightly negative (δ–). This produces what is known as an instantaneous and transient electrical dipole – that is a charge separation. As one distorted atom nears another atom it affects the second atom’s electron density distribution and leads to what is known as an “induced dipole”. So, for example, if the slightly positive end of the atom is located next to another atom, it will attract the electron(s) in the other atom. This 6 results in an overall attraction between the atoms that varies as 1/r – where r is the distance between the atoms. Note that this is different than the attraction between fully charged species, the Coulombic attraction, which varies as 1/r2. What does that mean in practical terms? Well, most importantly it 19. Yes we did tell you to think of electrons as a cloud - because this is a helpful model - but electrons are both particles and “clouds” as we will discuss later, in fact in some instances they appear to be quite close to perfect spheres in shape, In fact “The experiment, which spanned more than a decade, suggests that the electron differs from being perfectly round by less than 0.000000000000000000000000001 cm. This means that if the electron was magnified to the size of the solar system, it would still appear spherical to within the width of a human hair. (Hudson et al "Improved measurement of the shape of the electron" DOI: 10.1038/nature10104). 26 | CHAPTER 1: ATOMS means that the effects of the interaction will be felt only when the two atoms are quite close to one another. As two atoms approach, they will be increasingly attracted to one another. But this attraction has its limit – when the atoms get close enough, the interactions between the negatively charged electrons (and positively charged nuclei) of each atom increase very rapidly, which leads to an overall repulsion,which will stop the two atoms approaching so closely. A similar effect was in also seen in Rutherford’s experiment. Recall that he accelerated positively charged alpha particles toward a sheet of gold atoms. As an alpha particle approaches a gold atom’s nucleus, the positively (+2) charged alpha particle and the gold atom’s positively (+79) nucleus begin to repel each other. If no other factors were involved, the repulsive force would approach infinity as the distance between the nuclei (r) approached 0. (You should be able to explain why.) But infinite forces are not something that happens in the macroscopic, atomic, or subatomic worlds, if only because the total energy in the universe is not infinite. As the distance between the alpha particle and gold nucleus approaches zero, the repulsive interaction grows strong enough to slow the incoming alpha particle and then push it away from the target particle. If the target particle is heavy compared to the incoming particle, as it was in Rutherford’s experiments, the target, composed of gold atoms that weigh about 50 times as much as the alpha particle, will not move much while the incoming alpha particle will be reflected away. But, if the target and incoming particle are of similar mass, then both will be affected by the interaction and both will move. Interestingly, if the incoming particle had enough initial energy -15 to get close enough (within ~10 m) to the target nucleus, then the strong nuclear force of attraction would come into play and start to stabilize the system. The result would be the fusion of the two nuclei and the creation of a different element, a process that occurs only in very high-energy systems such as the center of stars or during a stellar explosion, a supernova. We return to this idea in Chapter 3. Questions Questions to Answer How does the discovery that atoms have parts alter Dalton’s atomic theory? CHAPTER 1: ATOMS | 27 What would the distribution of alpha particles, relative to the incident beam, look like if the positive nucleus took up the whole atom (sort of like the plum pudding)? What if it took up 50% of the atom? What does the distribution of alpha particles actually look like (recall that 1 in every 8000 particles were deflected)? Forces and Energy: an overview. We would like to take some time to help you think about the interactions (forces) between atoms and molecules, and how these interactions lead to energy changes. These energy changes are responsible for the formation of molecules, their reorganization through chemical reactions, and the macroscopic properties of chemical substances (i.e. everything). While you may have learned about forces and energy in your physics classes, most likely these concepts were not explicitly related to how things behave at the atomic-molecular level. We are going to begin with a discussion of the interactions and energy changes that result from the force of gravity, because these ideas are almost certainly something you are familiar with, certainly more familiar with than electromagnetic interactions – but the purpose of this section is to help you make the connections between what you already know (at the macroscopic level), and how these ideas are transferred to the molecular level, including similarities and differences. For example, Newton’s Laws of Motion describe how objects behave when they come into contact, say when a baseball comes in contact with a bat. But often objects interact with one another at a distance. After the ball is hit, its movements are determined primarily by its gravitational interactions with all other objects in the Universe, although because of the nature of the gravitational interaction, by far the most important interaction is between the ball and the Earth (see below). A force is an interaction between objects that causes a pull (attraction) or a push (repulsion) between those objects. When such an interaction occurs, there is a change in energy of the objects. As noted above, there are four fundamental forces: gravitational, electromagnetic, the strong and the weak nuclear forces. We will have more to say about the electromagnetic force that is relevant for understanding chemical interactions, that is how atoms and molecules behave. Many of the phenomena you are familiar with are based on electromagnetic forces. For example, electromagnetic forces stop the ball from going through the bat – or you from falling down to the center of the Earth. 28 | CHAPTER 1: ATOMS Now let us consider what happens when you throw a ball straight up into the air. You apply a force to the ball (through the action of your muscles), and once it leaves your hand the only force acting on the ball is gravity (we are, of course, ignoring friction due to interactions with the molecules in the air). The ball, initially at rest, starts moving upward. Over time, you observe the velocity of the ball changes, as the ball slows, stops and falls back to earth. So what forces cause these changes? The answer is the force of gravity, which is a function of the masses of the ball and the Earth, which do not change over time, and the distance (r) between the Earth and the ball, which does. This gravitational force F, can be modeled by an equation that shows it is proportional to the product of the masses of the ball (M1) and the Earth (M2) divided by the square of the distance between the objects (r).20 In gravitational interactions, the force decreases as the distance between the objects increases (the 2 decrease is proportional to 1/r ), which means the further away you get from the Earth the smaller is the attractive force between you and the Earth. If you get far enough away, and you are moving away from the Earth, the interaction will not be enough to keep you attracted to the Earth and you will continue to move away forever. Of course, why objects with mass attract each other is a subject for physics – beyond the scope of this course.21 What we can say is that the force is mediated by a gravitational field. Any object with mass will interact with other objects with mass through this field. The field can also be said to transfer energy through space between two (or more) objects. That is, the interaction leads to an energy change in the system of interacting objects. In chemistry we are concerned with both the forces that cause interactions and the energy changes that result. How do forces influence energy? If we take our macroscopic example of your throwing a ball upwards, we know that you transfer some energy to the ball. Of course this begs the question “what do we mean by energy?” and unfortunately we do not have an easy answer, in fact Richard Feynman once famously said “in physics we have no idea of what energy is”. Physicists might say energy is the capacity to do work, and then define work as force times distance, which does not really get us anywhere, especially in chemistry where the notion of work is often not helpful. What we can say is 20. See http://www.youtube.com/watch?v=p_o4aY7xkXg for an excellent explanation of this phenomenon. 21. That said, we recommend the discription given in Einstein and Infeld’s Evolution of Physics: https://archive.org/ details/evolutionofphysi033254mbp CHAPTER 1: ATOMS | 29 that any changes are accompanied by energy changes, and that we can calculate or measure these energy changes.22 You may be familiar with what are often referred to as “forms of energy”, such as mechanical, or elastic, or chemical, but at the most basic level all forms of energy we will be concerned with can be described either as kinetic energy, potential energy, or electromagnetic energy (e.g. light). Kinetic 2 energy is often called the energy of motion (KE = ½ mv , where m is the mass and v the velocity of the object), and potential energy the energy of position, or stored energy (it is calculated in various ways as we will see). Changes between kinetic and potential forms of energy involve forces. The ball that you throw straight up and then comes down has changing amounts of kinetic energy (it changes as the velocity of the ball changes) and potential energy (which changes as the distance between the Earth and the ball changes.) As the ball rises, you can observe that the velocity of the ball decreases, and therefore the KE decreases. At the same time the PE increases since the distance between the Earth and ball is increasing. On the way down the opposite is true, the ball starts moving faster – the KE increases and the PE decreases. Recall the principle of the conservation of energy; after the ball leaves your hand, no energy is added or taken away as the ball is traveling, if one form of energy increases, the other must decrease. Another important point about energy is that it is a property of a system, rather than of an object. Although it may be tempting to consider that a ball in motion has a certain amount of kinetic energy it is important to remember the frame of reference from which you are considering the ball. Certainly the ball’s velocity is related to the KE, but that velocity depends upon where you are viewing the ball from. Usually (almost always) we consider the velocity from the point of view of an observer who is stationary, but if we changed the system we were considering, and viewed the ball while we were also moving, then the velocity of the ball would be different. This may seem quite an abstract point, but it is an important one. Similarly it is quite tempting to say that the ball has potential energy, but in fact this is also not entirely accurate. It is more accurate – and more useful – to say that the system of the ball and the Earth has potential energy – again we are taking a systems perspective here. Unlike kinetic energy, the potential energy in a system also depends on the force that is acting on it, and that force is a function of the position of the objects that are interacting within the gravitational field. For example, 22. The trouble with chemical energy: why understanding bond energies requires an interdisciplinary systems approach. CBE Life Sci. Education,12:306-12. 30 | CHAPTER 1: ATOMS a “frictionless” object traveling through a space free of fields (gravitational or otherwise) at a constant velocity has a constant kinetic energy, but no potential energy. Potential energy (often called stored energy) or the energy of position, raises the question – where is the energy “stored”? A useful way to think about this is that for the example of the ball and the Earth, this energy is stored in the gravitational field. In this way we can accommodate the idea that the PE depends on the distance between the two interacting objects. It will also allow us to generate a more overarching concept of potential energy that will be useful in chemistry, as we extend these ideas to interactions of atoms and molecules. You might ask why then is it OK to say an object has kinetic energy (as long as you specify the frame of reference), and the difference here is that any object in motion can have energy associated with it (for example, you, an atom or a car), but potential energy must be associated with objects that are interacting via a field, be it gravitational or electromagnetic. That said, fields are everywhere – there is no place in the universe where there are no fields (although they can be balanced, leaving the net force zero). What is important here is that i) you understand that objects interact, ii) that these interactions cause a change in energy of the system, and iii) that the interacting forces depend on the distance between the interacting objects (as well as other factors, such as mass, which are constant). The electromagnetic force: While gravitational interactions are, for all intents and purposes, irrelevant in chemistry (except to hold the beaker down on the lab bench!) they do provide a familiar example of the relationship between the kinetic and potential energies of a system that we can use to explore the electromagnetic interactions that are responsible for the behavior of atoms and molecules. There are some important similarities between gravitational and electromagnetic interactions; both act at a distance, both are mediated by fields, and both display the same relationship between force and distance. There are also important differences. In the context of chemistry, electromagnetic interactions are much stronger and while gravity is always attractive, electromagnetic interactions can be either attractive or repulsive.23 All electrically charged objects interact via electromagnetic forces. As we have already seen (and will to return to again) atoms and molecules are made up of charged particles (electrons and protons) and 23. Magnetic, like electrical force can also be attractive or repulsive. Most of us have played with magnets and felt the force of attraction between a north and south pole of a set of magnets, which gets stronger as the magnets get closer together, and the repulsion between two north poles which also gets stronger as the magnets get closer together. CHAPTER 1: ATOMS | 31 these produce unequal charge distributions that lead to the same kinds of interactions. The strength of these interactions between charged particles can be modeled using an equation, Coulomb’s Law. You will note that its form is similar to Newton’s Law of Gravitation. Instead of the masses of the two interacting objects, however, the electromagnetic force depends on the charges on the two particles (q1 and q2). The electromagnetic force typically acts over much shorter distances than gravitation, but is much stronger. It is the force that affects interactions of atoms and molecules. As with the gravitational force as the charged particles get closer together, the interaction (whether attractive or repulsive) gets stronger. Just like gravity, the interaction between charged particles is mediated by a field, which transfers energy between interacting objects. We can identify (and calculate) the types of energy changes that are occurring as the particles interact. For example two oppositely charged particles are attracted to each other. As they approach one another, the force of attraction becomes stronger, the particles will move faster – and their kinetic energies increase. Given the fact that energy is conserved, the potential energy of the system of particles must decrease to a similar extent.24 If, on the other hand the two charges are of the same sign, then the force between them is repulsive. So if two particles of the same charge are moving toward each other, this repulsive force will decrease their velocity (and kinetic energy), and increase their potential energy. As the distance between the particles decreases, the repulsion will eventually lead to the two particles moving away from one another. Of course you may have noticed that there is a little problem with the equations that describe both gravitation and electromagnetic forces. If the forces change as r decreases, what happens as the distance between the interacting objects approaches zero? If we were to rely on the equations we have used so far, as r approaches 0, the force (whether repulsive or attractive) would approach infinity. Clearly something is wrong here since infinite forces are not possible (do you know why?). The ball is stopped by the surface of the Earth – it does not plummet to the center of the Earth, and charged particles do not merge into each other (or fly away at infinite speed). What is it that we are missing? Well, the problem lies in the idea that these equations are really dealing with idealized situations such as point charges or masses, rather than taking into account the fact that matter is made up of atoms, molecules and ions. When two atoms, or two molecules (or two particles made up of atoms or molecules) approach each other, they will eventually get close enough that the repulsions between like charges will become stronger than the attractive forces between unlike charges. As we will see, when two 24. A point we have not considered is why the atoms or molecules stop moving toward each other, which will return to shortly. 32 | CHAPTER 1: ATOMS macroscopic objects appear to touch, they do not really – what stops them is the electron-electron repulsions of the atoms on the surface of the objects.25 We will revisit all these ideas as we discuss how atoms and molecules interact at the atomic-molecular level, and how electrons behave (quantum mechanically). Interacting Atoms: Forces, Energy Conservation and Conversion Let us step back, collect our thoughts, and reflect on the physics of the situation. First, remember that the total matter and energy of an isolated system are conserved; that is the first law of thermodynamics. As we mentioned above, while energy and matter can, under special circumstances, be interconverted, typically they remain distinct. That means in most systems the total amount of matter is conserved and the total amount of energy is conserved, and that these are separate. So let us consider the situation of atoms or molecules in a gas. These atoms and molecules are moving randomly in a container, colliding with one another and the container’s walls. We can think of the atoms/molecules as a population. Population thinking is useful for a number of phenomena, ranging from radioactive decay to biological evolution. For the population of atoms/molecules as a whole, there is an average speed and this average speed is a function of the temperature of the system.26 25. http://www.youtube.com/watch?v=BksyMWSygnc 26. Remember speed is a directionless value, while velocity involves both speed and direction. CHAPTER 1: ATOMS | 33 If we were to look closely at the population of molecules, however, we would find that some molecules are moving very fast and some are moving very slowly; there is a distribution of speeds and velocities (speed + direction). As two atoms/molecules approach each other they will feel the force of attraction caused by the electron density distortions, these are known as London dispersion forces, which we will abbreviate as LDFs. The effects of these LDFs depend on the strength of the interaction (that is the magnitude of the charges and the distance between them) and on the kinetic energies of the atoms and molecules. LDF are one of a number of intermolecular forces (IMFs), which we will consider later. LDFs are the basis of van der Waals interactions in biological systems. To simplify things we are going to imagine a very simple system: assume for the moment that there are just two isolated atoms, atom1 and atom2. The atoms are at rest with respect to one another, but close enough that the LDF-based attractive interactions between them are significant. For this to occur 6 they have to be quite close, since such attractive interactions decreases rapidly, as 1/r where r is the distance between the two atoms. At this point, the system, which we will define as the two atoms, has a certain amount of energy. The exact amount does not matter, but as long as these two atoms remain isolated, and do not interact with anything else, the energy will remain constant. So what does all this have to do with atoms approaching one another? We can use the same kinds of reasoning to understand the changes in energy that occur as the atoms approach each other. Initially, the system will have a certain amount of energy (kinetic + potential). If the atoms are close enough to feel th

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