Chemistry, life, the universe and everything - Chapter 1

Chapter 1: Atoms – knowledge statements and learning goals

In 1963, Nobel Laureate Richard Feynman (1918-1988), one of the most accomplished and influential scientists of the 20th century, wrote:

“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.” (Feynman 1963)

Most of us are quite familiar with the idea that matter is composed of atoms, we have been told that this is so since childhood. But how many of us really (and we mean really) believe it, or know the reasons that it is assumed to be true? It seems so completely and totally impossible (and improbable) - we do not experience atoms directly, and it is easy to go through life, quite successfully for the vast majority of us, without having to take atoms seriously.

It seems so completely and totally impossible (and improbable) - we do not experience atoms directly, and it is easy to go through life, quite successfully for the vast majority of us, without having to take atoms seriously.

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 hypothesis 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 all that they imply, 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.

What do you think you know about atoms:

You almost certainly have heard about atoms, and 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 entity that retains 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 in to 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 associated with the fact that the forces holding the atomic nucleus together, the so called strong and weak forces, operate at such small 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) distances. A second problem is associated with the fact that to experience the world we need to use energy, at the atomic scale the 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 which we will come back to). Finally, objects at the atomic and subatomic scales behave differently from the macroscopic objects we are used to interacting with. A particle of light (a photon), an electron, a proton, or a neutron behaves as both a particle and a wave; in terms of physics, these are neither particles or 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 atoms consist of a very (very) small, but very dense nucleus that contains protons and neutrons, which is surrounded by electrons, which are very light, relatively. 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 have the same chemical properties of an element, but what do we mean by chemical properties? Can an atom have chemical properties? And how can ensembles of the same particles (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 will (hopefully) lead you to a basic understanding of atomic structure and inter-atomic interactions. Subsequent chapters will extend and deepen this understanding.

Question to ponder:

Is it obvious that the material world is composed of atoms?
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 to explain so much about the world scientifically influence your view about the reality of supernatural forces?

Atomic Realities

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 (unimaginably) small. A gold atom with its full complement of electrons, is less than a nanometer (1 x 10–9 m) in diameter and its nucleus, which contains 79 protons and generally around 116 neutrons, has a radius of ~1.5 x 10–14 meters (m)[optional link]. 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 (and for that matter cells) is based on indirect evidence, that is, not from direct observation with the naked eye, or through our other senses.

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 complete detail here. This is partially because much of it is considered physics - although in fact where physics ends and chemistry begins is rather arbitrary. 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 made accurate predictions and was able to explain an increasing number of diverse, and often previously unknown, phenomena. As new observations were made and became well established, atomic theory was adapted to accommodate and organize them. A key feature of scientific, 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 what we will find if we measure it. When we look, we may find the world to be as predicted (confirmation of the ideas) or something different. 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 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 it can be quite difficult to understand, since matter behaves quite differently on the atomic and sub-atomic (microscopic) 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 leads 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 in 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; the ability of other scientists to reproduce the observation/experiment is key to its acceptance (this is why there are no “miracles” in science.) Even then, the meaning of an observation is not always obvious or unambiguous; more often than not a "revolutionary observation" has a prosaic, that is simple, unrevolutionary, and often boring explanation. Truly revolutionary observations are few and far between (and one might argue, getting rarer as we approach an increasingly complete scientific understanding of the world in which we live.[optional link]) This is one reason that the oft quoted statement by Carl Sagan is oft quoted: "Extraordinary claims require extraordinary evidence." In many cases where revolutionary data is reported, subsequent studies often find that results are due to poor experimental design, sloppiness, or irrelevant factors - the fact that we all do not have cold fusion energy plants driving perpetual motion refrigerators in our homes is evidence of that.

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 hypothesis or working assumption, but in science the word theory should be (but often isn't) reserved for explanations that encompass and explain a broad range of observations. More than just an explanation, however, a theory must be well tested and make clear predictions relating to new observations or experiments. For example, the theory of evolution predicts that when one looks at the fossil record one will find evidence for animals that share many of the features of modern humans. This is a prediction made before any such fossils were found; in fact, many fossils of human-like organisms have, and continue to be discovered. Based on these discoveries, and comparative analyses of the structure of organisms (a field known as cladistics), it is possible to propose plausible "family trees" (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 currently living on the earth are part of the same family, that is they share a common ancestor, an ancestor that lived billions of years ago. The theory of evolution also predicts the older the rocks, the more different will the fossilized organisms found be from modern organisms. In rocks dated to be 410 million years old, we find fossils of various types of fish, but not fish that exist today; we do not find evidence of humans, 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 ago. Similarly, the atomic theory would require some serious revision if an element were discovered that did not "fit" into the periodic table; the laws of thermodynamics would have to be reconsidered if a successful perpetual motion machine were to be developed. A "theory" that can be 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, since 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 (in the deepest sense) 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 - 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 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 theories. 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, right or wrong (morally).

As we will see the history of atomic theory is rife with examples of one theory being found to be inadequate, upon which it is revised, extended and occasionally totally replaced by a newer theory that provide testable explanations for both old and new experimental evidence. This does not mean that the original theory was completely false – but rather that it was unable to fully capture the observable universe or to accurately predict newer observations. Older theories are generally subsumed as newer ones emerge - in fact, the newer theory must explain the failings of the older one.

Question to answer:

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 for ponder:

What things have atoms in them? (air?, gold? cells? heat? light?)
How do you know atoms exist?

Atoms: Invisible and Indivisible - some history:

Modern atomic theories have their roots in the thinking of ancient peoples, in particular with Greek philosophers who lived over 2500 (0.0025 x 106) years ago. At this 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 still believed the world was ruled by a cohort of semi-rational gods, a series of philosophers, beginning with Thales of Miletus (died 546 BCE)[optional link], were intent on developing rational and non-supernatural explanations for observable phenomena (such as what we are made of and where we came from), rather than relying on unfathomable and apparently irrational acts of the gods. While they could not possibly (as we know now) hope to understand the true underlying nature of matter, since they lacked the tools to observe and experiment at the atomic scale - this does not mean that their ideas were simple idle speculation. The ideas produced, while not scientific as we understand the term today, had within them remarkable insights, some of which appear to be true (or rather an accurate description for how the world appears to be organized.) This era gave birth to a new way to approach and explore natural phenomena, 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 since science can’t address these kinds of ideas let’s just leave them to fantasy authors. The fact is that the assumption that the world is ruled solely by naturalistic forces has been remarkably productive.

The ancient Greeks developed complex ideas about the nature of the universe (and the matter from which it was composed) that were accepted for a long time. However, in response to more careful observation and experimental analysis, these ideas were eventually superseded by more rigorous 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 ideas that "worked".

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 of the 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”. These clearly inadequate ideas remain today as part of astrology and the signs of the Zodiac – a not particularly fitting 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)[optional link]. The atoms of different elements where assumed to be of different sizes and shapes, and their shapes directly 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” difficult to move and solid. 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, and while 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)[First description of Brownian motion - Epicurus], and that there was nothing or a “void” between them. 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).

Question to answer:

What properties ascribed by the Greeks to atoms do we still consider to be valid?
If “earth” had atoms that were cubic, what shape would you ascribe to the elements “air’ “water”, and “fire”?

Questions for 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?

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 - or better put, all that they needed to know for their day to day purposes. The trap here is one that is very easy to fall into. That is: a satisfying explanation for a phenomenon does not necessarily mean that it is true. An explanation, even if it seems to be self-consistent and useful or comforting, 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.[from A History of Greek philosophy By William Keith Chambers Guthrie. p212.] 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. While these ideas are now considered preposterous (if not just silly), they contain a foreshadowing of the Law of Constant Proportions (which would come some 2300 years later and which we will deal with later in this chapter).

Such ideas about atoms and elements provided logical and rational (non-supernatural) explanations for many of the properties of matter. But Greeks weren’t 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, their name for Egypt, where alchemy/chemistry are thought to have originated.[optional link] Similar theories were being developed in India 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 Arabic 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 and atoms. Experimental studies based upon 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 [Think Giordano Bruno and Galileo].

Identifying (and isolating) elements

The Greek notion of atoms and elements survived for many centuries, and it was eventually fleshed out with a few more elements, mostly through the efforts of the alchemists. Some elements such as gold were discovered much earlier. By the late eighteenth century, the idea of an element as a substance that cannot be broken down into more fundamental substances was beginning to be accepted. In 1789 Antoine Lavoisier (1743 – 1794) produced a list of 33 elements; missing from this list were 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. That oxygen and hydrogen were elements, while water was not, had been established. 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 man-made ones. As we will see, these man-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; typically they are unstable and rapidly "decay" 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 “light” elements are theoretically possible, we know 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 doesn’t 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)[link]; he isolated phosphorus from urine while in pursuit of the Philosopher’s stone. 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 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; while mercury is quite toxic, it was used as a treatment of syphilis prior to the discovery of effective antibiotics.

Question to answer:

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 for ponder:

What types of evidence might be used to conclude that you had isolated a new element?
What types of elements would be difficult to identify?
When can unproven/unsubstantiated assumptions be scientific?
Under what conditions are such assumptions useful?

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 iota 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 evidence one way or another.
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? In fact, often 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 the earth around the sun, the movement of the moon around the earth, and the falling of an apple to earth are all due to a common 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 assumption; how does this “action at a distance” work? Yet, followed scientifically it appears to be quite 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 proposed his general theory of relativity (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 Quaker [religious dissenters, that is non-Anglicans, were not allowed access to English universities at that time. ] living in Manchester, England38. In 1805 Dalton published his atomic theory to explain the observed law of multiple proportions. 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 (or Laws) was the observation that the total matter present in a system did not change when a chemical reaction occurred, although a reaction might lead to a change from a solid to a gas or vice versa. Inspection of his laboratory notebooks suggests that he first began to develop this atomic theory as he was experimenting on the nature of different gases and their solubility in water. In 1803 he wrote:

"Why does not water admit its bulk of every kind of gas alike? This question I have duly considered, and though I am not able to satisfy myself completely I am nearly persuaded that the circumstance depends on the weight and number of the ultimate particles of the several gases. (emphasis added)" [link].

This was the first indication that he was thinking about gases in terms of particles (atoms/molecules, that is combinations of atoms). In case you missed this extraordinary deduction (and it is very easy to do), Dalton made the leap to the idea of atoms with different weights from his observations that different gases dissolved in water in different amounts and the law of multiple proportions.

Dalton’s atomic theory (1805) had a number of important points:

Elements are composed of small indivisible, indestructible particles called atoms
All atoms of an element are identical and have the same mass and properties
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, atoms (matter) are neither created nor destroyed during a reaction.

Based upon these tenets he was able to explain many of the observations that had been made up to that time, 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.

The law of multiple proportions

The law of multiple proportions is an empirical law, that is a law based on observation rather than theoretical logic. It states that when two elements (for example carbon and oxygen) combine to form more than one type of compound, such as carbon monoxide and carbon dioxide, the ratio of the mass of oxygen in carbon monoxide is always in some whole number to the mass of oxygen in carbon dioxide.

Mass O in carbon monoxide / Mass carbon monoxide = an integer x Mass O in carbon dioxide / Mass carbon dioxide

This law makes complete sense in terms of atomic theory which assumes that each molecule is composed of a whole (positive integer) number of atoms, and each atom of a particular element is identical to every other atom of that element, that is, an atom of oxygen in carbon monoxide is the same as an atom of oxygen in carbon dioxide, or an atom of oxygen in any other imaginable molecule. Atoms cannot be divided into parts, that is, there is no such thing as a half or a quarter atom; they also do not have a memory of where they have been. An atom of oxygen that was once in the brain of a dinosaur behaves no differently than an atom of oxygen that has been in the oceans for the last 300 million years. The atomic formula for carbon monoxide is CO and the formula for carbon dioxide is CO2. You wouldn’t dream (we hope) of writing carbon dioxide as C0.5O or water (H2O) as HO0.5. Such formulae would make no sense in modern atomic theory.

Connecting the real world and the molecular world

One problem chemists have is that we deal with things that happen at a scale that we cannot see (and is very difficult to imagine). As a result we have to develop a number of skills and tools to connect the molecular world with the world we can see. For example: a large part of the later sections of the book is taken up with developing ways to help you visualize molecular level structures and events. But, while thinking about the molecular level is important, it is also necessary to be able to connect those molecular changes with what we can see and measure in the world we live in. For example we might visualize a chemical reaction as a molecule of one reactant interacting with another molecule to give a product. We generally write reactions down in the form of equations, for example:
2H2(g) + O2(g) → 2 H2O(g)

This equation can mean many things - the simplest being that two molecules of hydrogen react with one molecule of oxygen, resulting in two molecules of water. However in the world that we live in we can not measure out materials in terms of atoms or molecules, we have to use mass or volume. In order to relate such measurements to the reaction equation, we need a way to translate between the number of molecules and mass. The unit used for this purpose is the mole. The mole is simply a number, 6.022 x 1023. It is a big number to be sure – but just a number. So why this number? The reason is that it enables us to convert directly between the mass of atoms and molecules, measured in atomic mass units (amu), and the mass of the element or compound in grams.
One atom of carbon-12 is defined as having a mass of exactly 12 amu, so 1 mole of carbon-12 has a mass of 12 grams and 12 grams of carbon-12 contains 6.022 x 1023 carbon atoms.

All the other elements have masses that are defined relative to this mass. So for example, the equation above could mean all these things:

Once you know this relationship and the atomic mass of all the atoms in your reaction, you can calculate the mass in grams of every reactant or product from a given mass or reactant (or product). In the accompanying workbook there are a number of activities that will allow you to work through some of these kinds of calculations.

A note on the conservation of matter:

A key component of Dalton's atomic theory was the assumption of the conservation of matter, that is that matter can not be created nor destroyed, but can change between different states. The most common example is the transformation of water from ice (solid) to liquid to vapor (gas). People are often confused about the conservation of matter, one because it is not completely obvious that when a cube of ice evaporates matter is not, in fact, lost. This is something that requires careful experimental observations to confirm - it is certainly not self-evident. Another factor which may contribute to confusion is that in the modern world, most people have been exposed to Einstein's famous equation
e (energy) = m (mass, which is a measure the amount of matter) x c 2 (the speed of light, squared). Based on this equation, you might reasonably assume that matter and energy are freely interconvertable, but the conditions under which matter converts into energy or energy into matter are not so common, and when they occur in the “normal world” they involve extremely small mass changes. When plants absorb light, they do not convert it into matter, but use the energy to rearrange atoms and molecules, a topic we will return to later. All living organisms use some kind of energy to make changes, but energy is not directly converted into matter. In fact it is the interconversion of matter into energy that is ultimately responsible for the light given off by the sun and the energy released by nuclear power plants (and atomic bombs). In Dalton's day, the possibility of the interconversion of matter and energy was not known, and from our perspective as chemists is not something we need to consider. But so that we do not confuse you further, energy and matter are forms of the same basic stuff and the total amount of energy + matter in the universe is a constant (or so it appears to modern astrophysicists).

Question 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 for ponder:

How did Dalton conclude that there were no half-atoms?
Which parts of Dalton's theory were unfounded speculation and which parts based on direct observation?

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 (a wacky bunch, if ever there was one). 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 upon 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 inelastic 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 that can actually be 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 or 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 1700’s Luigi Galvani (1737 – 1798) discovered that animals can produce and respond to electricity, a fact exploited in many novels and movies, beginning with Mary Shelly's (1797 – 1851) Frankenstein and continuing through Mel Brook's (b. 1926) Young Frankenstein. Galvani discovered that a dead frog’s leg would twitch following 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 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 dependent upon electrical processes, and that the underlying physicochemical principles are the same as those taking place in non-biological systems.

The excitement about electricity and its possible uses prompted Alessandro Volta (1745 –1827) to develop the first 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 bioelectricity could be generated non-biologically, that it 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 door knob, or from Benjamin Franklin's (1705 – 1790) kite string to his finger? What was this electrical “fluid” made of?

Question to ponder:

What if the original discoverers of electricity had decided that electrons have a positive charge, would that have made a difference in our understanding of the way matter behaves or electricity?

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, etc. Yet there was no real 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 that charge came from or ”what it was”.

A key step that began to unravel the idea of an indivisible atom was made by J. J. Thompson (1856 – 1940), another Mancunian40. While 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 are being 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 tubes are 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) Thompson was able to show that:

”Rays” emerged from one disc (the cathode) and moved to the other (the anode).
These rays could be deflected by electrical fields in a direction that would indicate they were negatively charged.
The rays could also be deflected by magnetic fields.[This works because the electrons are spinning. ]
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 the cathode rays were carried by charged discrete particles (he called them corpuscles) and he assigned these particles a "negative" charge. But the truly stunning conclusion that he reached was that these particles must come from within the atoms of the metal cathode. Since 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 and moreover, that identical particles were present in all atoms – not just the atoms of one particular metal. Do you see how he jumps from experimental results using a few metals to all elements, 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. Thompson. The Atomic Theory, Oxford, Clarendon Press. 1914.[link]

The discovery of the electron made the old idea of an atom as a little indestructible billiard ball-like object obsolete, and necessitated a new model. It is an example of a paradigm shift [A term made popular (although often misunderstood) by T. S. Kuhn, The Structure of Scientific Revolutions, 1st. ed., Chicago: Univ. of Chicago Pr., 1962]– 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 44. 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 the pudding); since 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 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 (beta) 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.

As more and more data began to accumulate, the plum pudding model had to be abandoned, it just could not explain what was being observed. The key experiment that led to a new model of the atom was carried out in 1908 by Ernest Rutherford (1871–1937) working, as you may have already guessed, at the University of Manchester. In this experiment, he examined how α (alpha) particles, which he knew to be positively charged nuclei of the element helium, 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 these 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 α particles bounced back, we still need to explain how this could possibly occur. We couldn't just say, "only a few particles were bounced and 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. Since only a very small percentage of α 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 they 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 posed little or no resistance to the passage of the α particles. Again we see a scientist making a huge intuitive leap from the experimental evidence to a hypothesis that is 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 call 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. Neutrons are not completely stable, however, and can decay into a proton, an electron, and another particle, called an anti-neutrino. Both the electron (a β-particle) and the anti-neutrino are expelled from the nucleus while the proton remains. Changing a neutron into a proton changes the identity of the element.

Question to answer:

How does the discovery that atoms have parts alter Dalton's atomic theory?
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%?
What does the distribution of alpha particles actually look like (recall that 1 in every 8000 particles were deflected)

Questions for ponder:

Why do you think electrons were the first sub-atomic particles to be discovered?
How exactly did Rutherford detect these alpha particles?
Can you think of an alternative model based on Rutherford's observations?
How would the experiment change if he had used electrons or neutrons?

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 β-particle/electron?

Interactions between atoms and molecules.

At this point, we have arrived at a relatively simple model of the atom (not to worry, we will move to more complex and realistic models in the next chapter). This model has a very small, but heavy nucleus that contains both protons and neutrons. Since 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 being of very different sizes - for example, there is no barrier round the nucleus of an atom, an atomic nucleus is a clump of protons and neutrons. Surrounding the atomic nucleus are electrons, the same number as there are protons. The atom has no net electrical charge.

Where the electrons actually are, however, is a trickier question to answer, because of quantum mechanical considerations, specifically the Heisenberg uncertainty principal (which we will return to in the next chapter). For now let’s just 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. This simple model captures important features that enables us to begin to consider how atoms interact with one another to form molecules and how those molecules can be rearranged – real chemistry! One thing we can ignore (for now) are the interactions involved in holding the nucleus together. There is an attractive force between neutrons and protons, known as the strong nuclear force, that holds these particles together in the nucleus. This is the strongest of all known forces in the universe, approximately 137 times stronger than the electrostatic force, but it acts only at very short ranges, approximately 10-15 m, or about the diameter of the nucleus. The other force involved in nuclear behavior, the "weak force", plays a role in nuclear stability, specifically the stability of neutrons, but it has an even shorter range of action (10-18 m). Since the nucleus is much smaller than the atom itself, we can (and will) ignore the weak and strong forces when we consider chemical interactions. The only other force that appears to exist in the universe is gravity, but it is so weak (more than 10-37 times weaker than the electrostatic force), that we can ignore it from the perspective of chemistry (although it does have relevance for the biology of dinosaurs, elephants, whales, and astronauts).

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. Moreover, there is a relationship between temperature and the form things take - consider water. At various temperatures water can be a solid (ice), a liquid, or a gas (water vapor). More unfamiliar substances, such as helium, carbon dioxide, methane, and propane display similar behaviors, changing from a gas to a liquid or solid as the temperature drops. Understanding why, and under what conditions these transitions occur, and why different substances change their "phase" under different conditions will lead us to a clearer understanding of how atoms and molecules interact with one another. If atoms and molecules did not interact with one another, one might expect to be able to walk through walls (since atoms are mostly empty space), but clearly this is not the case. Similarly, you 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).

Question to ponder:

Why don’t the protons within a nucleus repel one another?
Why don’t the electron and protons come together within the nucleus?
Why don’t atoms collapse?
Do the electrons within an atom repel each other?

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? How do the atoms of different elements differ?

Interactions between atoms – a range of effects:

Our model of the interactions between atoms will involve (initially) only electrostatic interactions - that is interactions between electrically charged particles, electrons and protons. Let us consider how atoms interact with one another. Taken as a whole, atoms are electrically neutral, but they are composed of electrically charged particles. Moreover, their electrons behave as moving objects [Yes we did tell you to think of electrons as a cloud - because this is a helpful model - but electrons are particles, in fact 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).]. While the probability of finding an electron is spread uniformly around an atom when averaged over time; at any one instant there is a probability that the electrons are more on one side of the atom than the other. This leads to momentary fluctuations in the charge density around the atom and leads to a slight charge build up, with one side of the atom being slightly positive and one side being slightly negative. This produces what is known as an instantaneous and transient electrical dipole - a separation of charge. As one atomic dipole nears another atom it will affect the electron density distribution, 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 results in an overall attraction between the atoms that varies as 1/r6 (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 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. This attraction has its limit, however - when the atoms get close enough the repulsive effects between the negatively charged electrons and the positively charged nuclei increases very rapidly (look back at the opening quote from Feynman).

The repulsive interactions between nuclei are easier to imagine, since they behave more like billiard balls rather than clouds, but bear in mind that the electron clouds also repel each other if they get too close.

Reflect back to Rutherford's experiment (please!) He accelerated positively charged α particles, toward a sheet of gold atoms. As an α particle approaches a gold atom's nucleus, the positively (+2) charged α particle and the gold atom’s positively (+79) nucleus begin to repel each other. If no other factors were involved the force of repulsion 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 real or the atomic/subatomic world, if only because the total energy in the universe is not infinite. As the distance between the α particle and gold nucleus approaches zero, the repulsive interaction grows strong enough to slow the incoming α 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 (gold atoms - which weigh about 50 times as much as the α particle) will not move much, while the incoming α particle will be reflected away. But, f 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 to get close enough (within about 10-15 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 will return to this idea in chapter 3.

Interacting atoms: energy conservation and conversion:

Let us step back, collect our thoughts and reflect upon 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/molecules are moving randomly in a container, and 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 [remember speed is a directionless value, while velocity involves both speed and direction], and this average speed is a function of the temperature of the system. If we were to look closely at the population of molecules, however, we would find that some molecules are moving very fast and some 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 LDF). The effects of these LDF’s depends upon their strength and on the atoms/molecules’ kinetic energies. The type of attraction between atoms and molecules that involves LDF is known as a van der Waals interaction (there are various types of van der Waals interactions which we will get to later). To simplify things (as physicists are wont to do), let us consider a very specific situation. If we assume that there are two isolated atoms, atom1 and atom2; the atoms are at rest with respect to one another, but close enough so that the LDFs between them are significant. For this to occur they have to be quite close, because LDFs, which result from the movement of electrons, fall off as 1/r6 where r is the distance between the two atoms. In response to the attractive LDF’s, the atoms begin to move toward each other – potential energy associated with the atoms initial state is converted into kinetic energy (EK = ½mv2). If there was no attraction, the potential energy of the system would be zero.

So what happens as they approach each other? The LDF grows stronger and more and more potential energy is converted into kinetic energy (the atoms move faster). [Imagine, as an analogy that the two atoms are balls rolling down opposite sides of a hill towards a valley, their potential energy falls as they move down - but their kinetic energy rises and they speed up.] This continues until the atoms get close enough, at which point the repulsive interactions between the electrons becomes stronger (and if they approach even more closely the repulsive interactions between the positively charged nuclei also come into play).

As the atoms begin to slow down, their kinetic energy is converted back into potential energy. They will eventually stop and then be repelled from one another - potential energy will be converted back into kinetic energy. As they move away, however, repulsion will be replaced by attraction, and they will slow - their kinetic energy will be converted back into potential energy. With no other factors acting within the system, the two atoms will oscillate forever.

Question to answer:

What is potential energy? Can you provide an example?
What is kinetic energy? Can you provide an example?
At the atomic level – what do you think potential energy is?
At the atomic level – what do you think kinetic energy is?
Why does raising the temperature affect the speed of a gas molecule?

Questions for ponder:

What is energy?

Questions for later:

When we talk about potential energy of a system, what does system mean? Helium liquifies at around 4K, what makes the helium atoms stick together? (why don’t they turn into a gas?)
Consider two atoms separated by 1 spatial unit versus 4 spatial units - how much weaker is the interaction between the more distant atoms? How does that compared to the behavior of simple charges (rather than atoms)

Here we have a core principle that we will return to time and again - a stabilizing interaction always lowers the potential energy of the system, and conversely, a destabilizing interaction always raises the energy of the system. In an isolated system with only two atoms, this oscillation would continue forever because there is no way to change the energy of the system. This situation doesn’t occur in “real life” because two-atom systems do not occur. For example even in a gas, where the atoms are far apart, there are typically large numbers of atoms that have a range of speeds (and kinetic energies), present in a system . These atoms frequently collide and transfer energy. Therefore, when two atoms collide and start to oscillate, some of the energy may be transferred to other particles by collisions. If this happens a stable interaction can form between the two particles and make them stick together. If more particles approach, they can also become attracted, and if their extra energy is transferred by collisions, the particles can form a bigger and bigger “clump”.

As we discussed earlier, London dispersion forces arise due to the fluctuations of electron density around nuclei, and are a feature common to all atoms; all atoms/molecules attract one another in this manner. The distance between atoms/molecules where this attraction is greatest is known as the van der Waals radius of the atom/molecule – if atoms/molecules move closer to one another than their van der Waals radii, they repel one another. The van der Waals radius of an atom is characteristic for each type of atom/element. As mentioned earlier, it is only under conditions of extreme temperature and pressure that the nuclei of the two atoms can fuse together to form a new type of atom; such a nuclear/atomic fusion event results in the interconversion of matter into energy.

Interactions between helium atoms and hydrogen molecules:

Now lets take a look at a couple of real systems. For simplicity, we begin by considering interactions between the simplest atoms hydrogen (H), and helium (He), and the simplest molecule - molecular hydrogen (H2). Hydrogen atoms have 1 proton and 1 electron, Helium atoms have 2 protons and 2 neutrons in the nucleus, and 2 electrons in their electron clouds. We will consider more complicated atoms and molecules after we discuss atomic structure in greater detail in the next chapter. One advantage of focusing on molecular hydrogen and helium is that it also allows us to introduce, compare and briefly consider (we will do much more considering later on) both van der Waals interactions and covalent bonds.

When two atoms of helium approach each other LDFs come into play and a van der Waals interaction develops. In the case of He, the interaction potential energy drop is quite small (that is: the stabilization due to the interaction) and it does not take much energy to knock the two atoms apart. This energy is supplied by collisions with other He atoms. Helium melts at ~1K (−272.2 ºC) and boils at ~4K (−268.93ºC), only a few degrees above absolute zero 0K (−273.15 ºC). Meaning that at all temperatures above ~4K, there is enough kinetic energy in the atoms of the system to disrupt the van der Waals interactions between He atoms. The lack of stable interaction at these “higher” temperatures means that helium atoms do not stick together above 4K; helium is a gas at temperatures above 4K.

Now let us contrast the behavior of helium with that of hydrogen (H). As two hydrogen atoms approach one another, they form a much more stable interaction (about 1000 times stronger than the He-He van der Waals interactions. In an H-H interaction, the atoms are held together by the attraction of each nucleus for both electrons. This leads to a potential energy minimum for the two interacting hydrogen atoms that is much deeper than that for He-He. Because of its radically different stability, the H-H system gets a new name, it is known as molecular hydrogen or H2, and the interaction between the H atoms is known as a covalent bond. In order to separate the hydrogen molecule back into two atoms, that is, to break the covalent bond between them, we have to supply energy. 51 This energy can take several forms: energy delivered by molecular collisions with surrounding molecules or electromagnetic energy due to the absorption of light ?are some of the ways covalent bonds can be broken, and we will return to them later.

Each H can form only a single covalent bond, leading to the formation of H-H molecules. These H-H molecules are themselves attracted to one another through LDFs, leading to van der Waals interactions. We can compare energy associated with the H-H covalent bond and the H2 – H2 van der Waals interaction.

To break a H-H covalent bond, you will need to heat the system to around 5000K. On the other hand, to break the van der Waals interactions between H2 molecules, the system temperature only needs to rise to ~20K, above this temperature H2 is a gas; the interactions between individual H2 molecules are not strong enough to resist the kinetic energy of colliding molecules. Now you may ask yourself, why does H2 boil at a higher temperature than He? Good question! The answer is addressed by the web activity on interactions. It turns out that the strengths of these types of interactions depend upon several factors, including shape of the molecule, surface area, and number of electrons. For example, the greater the surface areas shared between interacting atoms or molecules the greater the London dispersion forces experienced and the stronger the resulting van der Waals interaction. Another factors is the ability of the electron cloud to become charged, a property known as polarizability. Polarizability is related to the “floppiness” of the electron cloud, and as a rough guide, the further away from the nucleus the electrons are - the more polarizable (moveable or floppy) the electron cloud becomes. We will return to this and related topics later on. As we will see, larger molecules with more complex geometries, such as biological macromolecules - proteins and nucleic acids – can interact through more surface area and polarizable regions, leading to correspondingly stronger van der Waals interactions.

Question to answer:

Can you draw a picture (with about 20 helium atoms, represented as circles) of what solid Helium would look like if you could see it?
How would that differ from a representation of liquid helium, or gaseous helium?

Questions for ponder:

How do the properties of solids liquids and gases differ?

At this point, you are probably (or should be) asking yourself some serious questions, such as, why don’t helium atoms form covalent bonds with one another? Why does a hydrogen atom form only one covalent bond? What happens when other kinds of atoms interact? To understand the answers to these questions, we need to consider how the structure of atoms differs between the different elements, which is the subject of the next chapter.

12-Apr-2012