From the molecular to the macroscopic:

Up to now we have been concerned mainly with isolated atoms, an extremely abstract topic. We will now move on to consider the macroscopic behavior of atoms, that is: the behaviors of very (very) large numbers of atoms that form the materials that we observe with our own eyes, that we can touch, feel, and smell. Before we do that it is important to understand and be explicit about what properties atoms, molecules and their aggregates can and cannot exhibit.

When atoms interact with one another to form molecules or larger structures, the molecules have different properties than their component atoms - they display what are often referred to as “emergent” properties, where the whole is more than (or different from) the sum of its parts.

In a similar way groups of atoms/molecules have different properties from isolated atoms/molecules. For example, while groups of atoms/molecules exist in solid, liquid or gaseous states, and often have distinct colors and other properties, isolated atoms/molecules do not – there are no solid or liquid isolated atoms, they do not have a color or a boiling point. So the obvious question is, how many atoms/molecules need to aggregate before they display these emergent properties, before they have a color, before they have a melting point, boiling point, heat capacity, and other properties that isolated atoms don’t?

The answer is not completely simple (as you are probably slowly coming to expect): as we add more and more atoms/molecules together, their properties change, but not all at once. You have probably heard about nanoscience and nanotechnologies; they have been the focus of a great deal of research and economic interest in the past decade or so. Nanoparticles are generally classified as being between 1 to 100 nm in diameter (a nanometer is one billionth of a meter or 1 x 10^-9 m); they often have properties that are different from those of bulk (macroscopic) materials. Nanomaterials can be thought of as a bridge between the atomic/molecular and macroscopic. Assuming that they are pure, macroscopic materials have predictable properties and it doesn’t really matter where you obtain the material.

But just knowing the equations (often the only thing learned in many introductory chemistry courses) is not sufficient to understand chemistry and the behavior of atoms and molecules. Much of the information implied by even the simplest chemical equations can easily be missed – or misunderstood – if the reader does not also have a mental picture of what the diagram or equation represents, how a molecule is organized (and its shape), and how it is reorganized during a particular reaction.

We will be trying to help you get these broader pictures, which should help make the diagrams and equations used here make sense. That said, it is always important to try and explicitly identify what you are assuming when you approach a particular chemical system, that way you can go back and check whether your assumptions are correct.

Where do atoms come from?

“We are stardust, we are golden, We are billion year old carbon.” Woodstock - Joni Mitchell

“Sometimes I’ve believed as many as six impossible things before breakfast” - Alice in Wonderland, Lewis Carroll.

Did you ever stop to ask yourself where the atoms in your body came from? Common answers might be food, water, air, but these are not the “ultimate” answers, since we then need to ask, “where did those atoms come from?” Where did the atoms in the Earth come from? There are really two general possibilities: either that the atoms that make up the Earth (and the rest of the universe) are eternal or that they were generated/created by some process. How do we decide which is which? What is the evidence favoring one model over the other? The answers come not from chemistry, but from astrophysics.

Since we are thinking scientifically, what kinds of evidence can we look for to decide whether atoms (or the Universe) are eternal or recently created? Clearly, the evidence must be observable in the here and now, and can be used to formulate logical ideas that make clear and unambiguous predictions. As we will see, we will be called upon once again to believe many apparently unbelievable things. The current organizing theory in astrophysics and cosmology, known as the Big Bang Theory, holds that the universe is approximately 13,730,000,000 ± 120,000,000 years ago years old (an unimaginable time) and that the sun and earth are approximately 5,000,000,000 years old, while the universe as a whole is approximately 156 billion light-years in diameter.

The Big Bang Theory was put forward in a response to the observation that galaxies in the universe appear to be moving away from one another. Since the galaxies that are further away from us are moving more rapidly away than those that are closer, it appears that space itself is expanding (now there is a seriously weird idea). Based on this observation, we can carry out a “thought experiment”. What happens if we run time backwards? Taken to its logical conclusion, the universe would shrink until, at some point, all of the universe would be in a single place, a single point – which would be unimaginably dense. Based on a range of astronomical measurements, this “singularity” existed approximately 13.73 x 10⁹ years ago – that is: the universe is about 13.73 billion years old. The Big Bang Theory tells us nothing about what happened before 13.73 x 10⁹ years ago, and while there is no shortage of ideas, nothing scientific can be said about it, since it is theoretically unobservable (or at least that is what we have been led to believe, but we are not astrophysicists!)

Thinking about atomic origins

The current model of the Big Bang begins with a rapid expansion of the universe, a process known as inflation. As you might well imagine, there is some debate over exactly what was going on during the first 0.000000000001 second (a picosecond or 1x 10^-12 second) after the universe’s origin. Surprisingly, there is a remarkable level of agreement on what has happened afterward. This is because there is lots of observable evidence that makes it relatively easy to compare hypotheses, to accept some and rule out others. Over time, the temperature (local energy levels) of the universe dropped to those that are reachable in modern particle accelerators, so we have actual experimental evidence of how matter behaves under these conditions. At 1 picosecond after the Big Bang, there were no atoms, no protons, or neutrons, the temperature was simply too high. There were only the elementary particles (photons, quarks, leptons - electrons are leptons) – that is, particles that have no substructure.

By the time the Universe was a 0.000001 second old (a microsecond or 1 x 10^-6 second), the temperature had dropped sufficiently to allow quarks and gluons to form stable structures, and protons and neutrons appeared. A few minutes later the temperature dropped to about 1,000,000,000 K (1 x10⁹ K) – low enough for some protons and neutrons to stick together and stay together without flying apart again. That is, the kinetic energy of the particles colliding with them was less than the forces (the weak and strong nuclear forces) holding the protons, neutrons, and nuclei together. At this point the density of particles in the universe was about that of our air.

By the time the Universe was a few minutes old it contained mostly hydrogen (^-1H¹ = one proton, no neutrons), deuterium (²H¹ = one proton and one neutron), some Helium (³He², and ⁴He² = two protons and either one or two neutrons, respectively), and a little Li (⁷Li³ = three protons and four neutrons) nuclei - all formed by nuclear fusion reactions such as: ¹p⁺+ ¹n⁰→ ²H⁺ + gamma radiation and ²H⁺ + ²H⁺ → ³He²⁺ + ¹n⁰. These fusion reactions take place in a temperature range where the nuclei have enough kinetic energy to overcome the electrostatic repulsion associated with the positively charged protons, but less that needed to disrupt the nuclei once formed. After a few minutes the temperature of the Universe fell below 10,000,000 (10⁷) K. At these temperatures, the kinetic energy of protons and nuclei was no longer sufficient to overcome the electrostatic repulsion between their positive charges. The end result was that there was a short “window” of time following the big bang when a certain small set of nuclei (e.g. 1H+, 2H+, 3He²⁺, ⁴He²⁺, and ⁷Li³⁺) could be formed. After approximately 400,000 years, the temperature of the universe had dropped sufficiently for electrons to begin to associate in a stable manner with these nuclei, and the first atoms (as opposed to bare nuclei) were formed. This early universe was made up of mostly (> 95%) hydrogen atoms with a small percentage each of deuterium, helium and lithium – chemically not very interesting (Isotope tutorial).

The primary evidence upon which these conclusions are based comes in the form of the cosmic microwave background radiation (CMBR), which is the faint glow of radiation that permeates the Universe. The CMBR is almost perfectly uniform, that is no matter where you look in the sky, the intensity of the CMBR is (essentially) the same. To explain the CMBR, it is assumed that the unimaginably hot and dense early universe consisted almost entirely of a plasma of hydrogen nuclei that produced vast amounts of electromagnetic radiation – the early universe glowed. The CMBR is what is left of this radiation – it is a relic of that early universe. As the universe expanded it cooled, but those photons continued to whiz around. Since they have to fill a much larger universe they, as individuals, have less energy now (although the total energy remains the same!) The current background temperature of the universe is approximately 2.27 K, which corresponds to a radiation wavelength of 1.9 mm – radiation in the microwave region – hence the name cosmic microwave background.

After a billion years or so, things began to heat up again, literally (albeit locally). As in any randomly generated object, the matter in the universe was not distributed in a perfectly uniform manner, and as time passed this unevenness became more pronounced as the atoms began to be gravitationally attracted to each other. The more massive the initial aggregates – the more matter was attracted to them. As the clumps of (primarily) hydrogen became denser, the atoms banged into each other and these systems, proto-stars, began to heat up. At the same time gravity (due to the overall mass of the system) was able to condense the matter into an even smaller volume, pull it together, and draw in more (mostly) hydrogen. As this matter condensed, its temperature increased (gravitational potential energy was converted into kinetic energy). At a temperature of around 10,000,000 (10⁷) K, the atoms (which because of the higher temperature had lost their electrons again) began to undergo nuclear fusion. At this point we would probably call such an aggregate of matter a “star”. This process of hydrogen fusion produced a range of new types of nuclei. Hydrogen fusion (or hydrogen burning as it is sometimes called) is exemplified by reactions such as the formation of helium nuclei: 4 ¹H⁺ → ⁴He²⁺ + ²e⁺ + energy. When four protons are fused together they produce one helium-4 nucleus, containing two protons and two neutrons, plus two positrons (e+ - the antiparticle of the electron), and a great deal of energy. As the number of particles decreases (4 ¹H⁺ into 1 ⁴He²⁺), the volume decreases. Gravity will produce an increase in the density of the star (fewer particles in a smaller volume). The star’s core, where fusion is occurring, gets smaller and smaller. The core does not (usually) collapse totally into a black hole, because the particles have a huge amount of kinetic energy, which keeps them in motion and moving (on average) away from one another.

As the star’s inner temperatures reached ~108 K there is enough kinetic energy available to drive other “fusion” reactions. For example, three helium nuclei could fuse to form a carbon nuclei: 3 ⁴He²⁺ → ¹²C⁶⁺ + (lots of) energy (note again, the result is fewer atoms). If the star was massive enough, a further collapse of its core would increase temperatures so that carbon nuclei could fuse, leading to a wide range of new types of nuclei, including those of elements up to iron (⁵⁶Fe²⁶⁺) and nickel (⁵⁸Ni²⁸⁺) as well as many of the most common elements found in living systems, such as nitrogen (N⁷), oxygen (O⁸), sodium (Na¹¹), magnesium (Mg¹²), phosphorus (P¹⁵), sulfur (S¹⁶), chlorine (Cl¹⁷), potassium (K¹⁹), calcium (Ca²⁰), manganese (Mn²⁵), cobalt (Co²⁷), copper (Cu²⁹), and zinc (Zn³⁰).

In some instances these nuclear reactions caused rapid and catastrophic contraction of the star’s core, followed by a vast explosion – a supernova. Supernovae can be observed today, often by amateur astronomers (in part because seeing one is a matter of luck.) They are characterized by a sudden burst of electromagnetic radiation, as the supernova expels most of its matter into interstellar dust clouds. The huge energies involved in such stellar explosions are required to produce the naturally occurring elements heavier than iron and nickel, up to and including Uranium (Ur⁸²⁺). The material from a supernova is ejected out into the interstellar regions, only to reform into new stars (and planets) and so begin the process all over. So the song is correct, many of the atoms in our bodies were produced by nuclear fusion reactions in the cores of stars which, at one point or another, must have blown up – we are literally stardust (except for the hydrogen formed before there were stars)!

Looking at stars

At this point you may still be unclear as to how do we know all this. How can we know about processes and events that took place billions of years ago? Part of the answer lies in the fact that all the processes involved in the formation of new elements are still occurring today in the centers of stars. Our own sun is an example of a fairly typical star; it is composed of about 74% (by mass, 92% by volume) hydrogen, 24% helium, and trace amounts of heavier elements. There are many other stars (billions) just like it. How do we know? Because we can look at the light emitted by the sun, analysis of the emission spectra of that light (or the light emitted from any other celestial object) enables us to deduce which elements are present. Similarly, we can deduce which elements and molecules are present in the clouds between stars by looking at which wavelengths of light are absorbed! Remember that emission/absorption spectra are a result of the interaction between the atoms of a particular element and electromagnetic radiation (light). They are a “fingerprint” of that element (or molecule). The spectrum of a star reveals which elements are present. No matter where an element is found in the Universe it appears to have the same spectroscopic properties.

Astrophysicists have concluded that our sun (Sol) is a third generation star - that is, the material in it has already been through two cycles of condensation and explosive distribution. This conclusion is based on the fact that the sun contains materials (heavy elements) that it could not have formed itself, and so must have been generated previously within larger and/or exploding stars. Various types of data indicate that the sun and its planetary system was formed by the rapid collapse of a molecular (mostly hydrogen) cloud, about 4.59 billion years ago. It is possible that this collapse was triggered by a shock wave from a nearby supernova. In response to gravitational attraction and the conservation of angular momentum led to the condensation of the gas; most (>98%) became the sun, while the rest formed a flattened disc, known as a planetary nebulae. The planets were formed from this disc, with the small rocky/metallic planets closer to the sun, gas giants further out, and remnants of the dust cloud distributed in the Oort cloud. As we will see, living systems as we know them depend upon elements produced by second and third generation stars. This process of planet formation appears to be relatively common, and more and more planetary systems are being discovered every year.

Stars have a “life cycle” from birth to death; our sun is currently about half way through this life cycle. There is not enough matter in the sun for it to become a supernova, so when most of its hydrogen has undergone fusion, about 5 billion years from now, the sun’s core will collapse and helium fusion will begin. This will lead to the formation of heavier elements. At this point, the sun’s outer layer is predicted to expand and the sun will be transformed into a “red giant.” Its radius will grow to be larger than the earth’s current orbit (that will be it for life on earth, although human are likely to become extinct much sooner than that.)

Eventually the sun will lose its outer layers of gas (they may become a part of other stars elsewhere in the galaxy), and the remaining core will shrink, grow hotter and hotter, and eventually form a white dwarf star. Over (a very long) time, the Sun will cool down, stop emitting light, and fade away.

3.1 Elements & Bonding
3.2 Interactions
3.3 Carbon
3.4 Metals

Question to answer:

• Do isolated atoms or molecules have properties that we can directly observe in the “real world” (do they have melting points, or boiling points, are they colored?)
• What properties to atoms have?
• Do isolated atoms/molecules exist in a state - (solid liquid, gas)?
• Where do the atoms in your body come from? (go back as far as you can)
  Is the number of atoms in the universe constant?
• How does the size of the universe influence the density of particles?
• How many protons, neutrons and electrons does ⁴He have? How about ⁴He²⁺?
• How old are the atoms in your body?
• Generate a graph that estimates the number of atoms in the universe as a function of time (beginning with the big bang, up to the present day)
• Draw another graph to illustrate the number of elements in the universe as a function of time. Explain your reasoning behind both graphs.
  

Questions for later:

• Can an atom of one element change into an atom of another element?
• What is temperature?