Saturday 16 February 2008

Valency: sticking atoms together

To recap my last Long Post, everything in the world is made up of atoms. These (nearly) indivisible units combine in different ways to make different things. These things are called "compounds". What do they look like? How do they work? That's what I'll try to explain in this post.

Atoms and bonds

It's actually pretty easy to say what elements a compound is composed of, in what proportion. Any volume of water, for example, contains twice as many hydrogen atoms as oxygen atoms. That gives us its chemical formula (or more specifically its empirical formula), H2O. Likewise, big bad carbon dioxide is CO2.

As it happens, the chemical formulas here also describe a single molecule of that substance. Pictures of molecules are pretty commonplace. They usually show a bunch of atoms represented by coloured balls, linked together by sticks which represent "chemical bonds", whatever those are. The number of bonds an atom will form is specific to that atom, and decides what sort of structures it can form. Here's an oxygen atom (red), and some hydrogen atoms (white), and there's only a couple of ways I can stick them together:

So, if we had a cloud of carbon dioxide, and we zoomed in far enough, eventually we'd see individual molecules, and closer still, we'd see that each molecule is made up of a carbon atom and two oxygen atoms stuck together. There's a different way of building things up, though. Salt, for example, has the chemical formula NaCl, usually we don't get a single unit "NaCl" - instead we get a big collection of Na (sodium) and Cl (chlorine) stuck together in a ratio of one-to-one, like Na800Cl800.

What decides how many bonds an atom can make? One of the best pictures for this - which works on many different conceptual levels - is valence bonding.

Valence bonding

There are around 100 different elements to choose from in making molecules. The selection box is called the Periodic Table. Here's the "main group":

They're arranged in order of the weight of individual atoms from the top left to the bottom right. Oddly, we have a cycle in the elements (or "periodicity", hence the name of the table), where if you start at a particular atom and go along eight steps, we have something similar. Dmitri Mendeleev spotted this when he was creating this table, which is why the main group table has eight columns, which we call chemical groups. Mendeleev had to leave gaps and suppose there were missing, unknown elements with properties similar to their neighbours above and below to keep the pattern going. This was a great intuition - although the reason for the cycle wasn't understood at the time - and it worked remarkably well.

Starting from the top right, we have helium, He. This is really chemically inert - an atom of helium doesn't do much, preferring to sit around on its own. Going down one (eight atoms heavier) an atom of Neon (Ne) is also inert, but it's a bit heavier. Then there's Ar, Argon, which is heavier again, and so on. These are called the noble gases, or inert gases. They're the last column, so that's group eight (VIII).

This is interesting, but because these elements don't really do anything, it doesn't give us any insight into chemistry, so let's go along to group four (IV). Here we have carbon, silicon, and germanium. Carbon can form methane, CH4. Silicon can form silane, SiH4. Germanium can form germane, GeH4. We could reasonably suggest that carbon and its relatives can stick to any four other atoms. We would say they all have a valency of four.

This idea, called valence bond theory, was an early breakthrough in chemistry. By comparing different compounds, we can come up with the valencies of the different elements. It increases from a valency of 1, in group I, to a valency of 4 in group IV. Then it declines again, from a valency of 3 in group V to a valency of 0 in group VIII. By satisfying these valencies, we can stick atoms together to make compounds. Oxygen has a valency 2, so you need two of them to satisfy carbon's valency of 4 and make CO2. You may notice that this means there are two bonds going between the carbon and each oxygen. These "double bonds" really exist, and are much stronger than single bonds.

Shared electrons and where valency comes from

If you're an inquisitive sort, you'll be wondering where this valency thing comes from, and why it's associated with this number eight. To think about that, we have to look at the structure of the atom. From a chemist's point of view, there's a tiny little, heavy indestructible lump called a nucleus with a particular positive electrical charge, +1 for example. Around this nucleus in a very big, very loose cloud are light particles called electrons, each of which has a charge of -1. Opposites attract, so the +1 charge of our hypothetical atom can attract and hold 1 electron.

Let's start with some of the oddities of the main group, the first two elements. An atom with a +1 nucleus and 1 electron is called hydrogen. If you want to give the nucleus a bigger charge, you have to stick some more stuff in there, so the next atom, with a +2 nucleus and 2 electrons, is heavier. It's called helium. As it happens, if an atom only has two electrons, they're very happy together and the atom doesn't need to do anything else to be stable. This is a "closed shell"

Atoms want to have closed shells where possible, so a hydrogen atom is on the lookout for one electron. It can get to this by sharing an electron with another hydrogen atom. They then each have two electrons, and the molecule as a whole has a closed shell. Having one electron to share gives hydrogen its valency of 1:

Pairing up valence electrons by sharing like this is called covalent bonding.

Let's go up to lithium, +3 with 3 electrons around it. The first two form an s-shell on their own, leaving one electron to form an s-shell of its own. We call this the "core", and those two electrons are core electrons. We're left with one electron to deal with, giving the molecule a valency of 1. For this reason, we call this electron a "valence" electron.

As it happens, lithium's really bad at holding onto this odd electron. In fact, everything in its group is pretty easy to take an electron from, if another atom really wants it. This is fine, though - by taking that electron away, it gets down to the same closed shell as helium. By giving up this electron, though, lithium winds up only two electrons for its +3 nucleus. That's a +1 charge left. As it has a charge, we call it an ion. Whatever snagged lithium's electron has picked up an extra electron, so it now has a charge of -1 (it is also an ion). Opposite charges attract, so the two ions will stick together:

Reaching a closed shell by giving up electrons like this is an exampe of an ionic bond. Bonds can really be in between the two situations - the shared electrons can be a bit off-centre rather than in the middle (we'd call this a polarised covalent bond) or way off centre (completely ionic). Either way, you can only get one negatively-charged ion with each positively charged ion, so that's valence 1.

So, atoms like to pair up their electrons, and they particularly like to get to a closed shell by doing this. If you get a closed shell, the valence count "resets", at least when we look at going from helium to lithium. This is an interesting diversion, but the original question is: why this cycle every 8 atoms? We're getting there.

Boron is in group III, which is +5 with 5 electrons. The first two electrons form a closed, s-shell core as in lithium. That leaves us with 3 valence electrons. It can then use those to pair The same holds for carbon - group IV, 6 electrons, 2 in the core and 4 valence. So it can share those 4 to form 4 bonds, like we saw earlier.

Now, when you get up to nitrogen, group V (+7, 7 electrons) you might reasonably assume that because it has 5 valence electrons (remember, 2 electrons go into a core) it will be able to form 5 bonds by pairing those up. You'd be wrong, though! Actually, the closed shell for the main-group elements (except hydrogen and helium) has eight electrons, basically a 2-electron s-shell plus an extra 6-electron thing called a p-shell. Nitrogen has 5 valence electrons already, so it only needs 3 more and it's in business. So, it pairs up 3 of its valence electrons with electrons from other atoms. The other 2 electrons pair up on their own:

Nitrogen has 5 valence electrons and only has a valency of 3. So, that explains why the valence starts going back down when we get past carbon. The need to form a closed shell starts to take over, and atoms start pairing their own electrons off with each other. We can see the same thing with oxygen, which has 8 electrons, a valency of 6, and only forms 2 bonds with hydrogen atoms to form water:

Next up is fluorine. It has 9 electrons, of which 7 are valence. Fluorine only needs 1 electron to reach the closed shell, then. That means it's actually pretty tenacious when it comes to grabbing electrons. In fact it's just the sort of thing which will steal an electron from lithium as mentioned before:

Last, but not least, we have neon. It has 10 electrons, of which 8 are valence. That's the closed shell, right? It doesn't have any need for more electrons, so it hardly interacts with other things at all. And once we have a closed shell of 8 electrons, we have to start building up electrons around it again, using everything underneath as a core. So, that's where this cycle of 8 comes from. Elements with a similar number of valence electrons have the same sort of needs with regards to grabbing other atoms' valence electrons.

Summing up

Most of this post has been about satisfying atoms' need to link to other things, without discussing what sort of structures it makes. I've tried to keep it fairly simple, to get across this idea that an atom of a particular element can only stick to a specific number of other atoms, determined by this property we call valency. This comes from the number of electrons on the outside of an atom, and the need to pair those electrons up and/or form a closed shell around the atom. There are two "characters" a bond can have - it can be about sharing electrons (covalent), or transferring them completely (ionic), although often bonds can be found which lie in between.

Next, I'll be writing about how molecules stick together to form larger structures. Eventually, the limitations of valence bond theory will become apparent, but it's a good starting point. Now that I've addressed this, I'll get on to how molecules stick to each other, and I should be in a position to explain what my supervisor's paper is about.

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