What exactly do you mean by “stable”?

Stability is a highly context-dependent concept, and so it often leads to confusion among students, and sometimes among professional chemists, too.

If I say that a certain molecule is “stable”, I might mean any of a number of things:

  1. It’s possible to make it, and it won’t spontaneously fall apart.
  2. It’s possible to isolate a pure sample of the substance.
  3. It won’t react with other things. This is often qualified, for example when we say that something is “stable in air”.

The trick is to pick up which one is meant from context. A recent example arose on a test question in my Chemistry 2000 class, where I asked, in a question on molecular orbital (MO) theory, if argon hydride, ArH, is a stable molecule. In this case, the “context” was in fact a lack of context: I simply asked about the stability of this molecule, without any mention of holding it (the isolable substance definition) or of bringing it into contact with anything else. Thus, I was relying on the first definition of stability. Unexpectedly, simple pen-and-paper MO theory predicts that ArH has a bond order of ½, and so is predicted to be stable, although clearly not by much. This ought to be quite a surprise to anyone who has studied chemistry since we normally think of noble gases like argon as being quite unreactive (stable in the third sense), and so unlikely to form compounds. And when we do get compounds of noble gases, they are usually compounds with very electronegative elements such as fluorine. Moreover, ArH would violate the octet rule. Students do run across non-octet compounds from time to time, but the octet rule is deeply ingrained from high school. Finally, ArH would be a radical, and students are often taught to think that radicals are “unstable”, in the sense that they are highly reactive.

As it turns out, the simple MO theory we learned in class is sort of right: excited states of argon hydride are stable enough to be studied spectroscopically—in fact the first such study was carried out at Canada’s National Research Council by JWC Johns1—but the ground electronic state is unstable in the first sense: it dissociates into H and Ar atoms. So our chemical instinct is right about this compound, too. Welcome to the nuances of chemistry.

For the sake of argument, suppose that ArH had a stable ground electronic state, as predicted by simple MO theory. It would fail to be stable in the second sense because the meeting of two ArH molecules would result in the energetically favorable reaction 2 ArH → 2 Ar + H2. And of course, ArH would react with a great many substances. In fact, we could think of this compound as a source of hydrogen atom radicals.

Before we move on from ArH, let’s talk about some of the reflexes that would have led us to predict it to be unstable. The fact that a material is normally unreactive doesn’t mean it won’t form a compound with something else under the right conditions. If I want to make ArH, I won’t try to react argon with hydrogen molecules because the atoms in H2 are held together by a strong bond, so it would be energetically unfavourable to swap that bond for an Ar-H bond. I will need a source of hydrogen atoms. If I do expose argon atoms to hydrogen atoms, the very reactive radical hydrogen atoms may well react with the normally unreactive argon, which is in fact what happens. But none of that is directly relevant to the question of the stability of the ArH molecule. If I ask about that, I just want to know if the thing will hold together assuming it has been made.

The octet rule is deeply embedded into the psyches of anyone who has studied chemistry. It is, indeed, an excellent rule of thumb in many, many cases, especially in organic chemistry. But students are soon exposed to non-octet compounds, so clearly the octet rule is not an absolute. And yet we often hear people talk about an octet as being a “stable electronic configuration”. There’s that word again! But what do people mean when they say that? The answer is, again, highly dependent on context. In s- and p-block atoms, an octet fills a shell, and so the next available atomic orbital is quite high in energy, and it will likely be energetically unfavourable to fill it. In molecules, the octet rule just happens to often result in electronic configurations with an excess of bonding over antibonding character, so they are stable in the first sense. And because eight is an even number, the resulting molecules often have all of their electrons paired, so they are less reactive than they might have been if they had an odd number of electrons. But you may recall that oxygen, on which more below, has two unpaired electrons, even though its Lewis structure satisfies the octet rule. We should always remember then that it’s the octet rule, and not the octet law. Arguing that something is especially stable because it has an octet is just not a very good explanation. Now having said that, the octet rule generally holds for compounds from the second period, largely because trying to add more electrons to these small atoms is energetically unfavourable. But even that is a contingent statement since it depends on where those electrons are coming from and whether they have anywhere else to go. Certainly, you can measure an electron affinity for many molecules with octet-rule structures.

As for the argument that radicals are “unstable” (which you will hear from time to time), it’s not true. Many radicals are very reactive. But a great many radicals are stable in the first and often in the second sense, too. This includes many of the nitrogen oxides, notably nitric oxide, which is stable enough to serve as a neurotransmitter, and can be stored in a gas cylinder, but is conversely reactive enough to be used as part of your body’s immune response. Again we see that stability and reactivity do not necessarily coincide, even though the word “stability” is sometimes used in the sense of “reactivity”.

Of course, ArH is an extreme, and NO is not a terribly familiar compound to most of us, even though our bodies make it. So let’s talk about a more mundane molecule. Oxygen has not one but two unpaired electrons. So despite its Lewis diagram, oxygen is a radical. Nevertheless, oxygen is certainly stable in the first and second senses. There are lots of oxygen molecules in the atmosphere, and they don’t just fall apart on their own. (They do fall apart if supplied with enough energy, for example in the form of an ultraviolet photon, but that is another question altogether.) You can store oxygen in a gas cylinder, so it is certainly isolable. But oxygen is highly reactive, in part because of its unpaired electrons, at least towards some substances and in some circumstances. It’s a fairly strong oxidizing agent for example. Many metals, if left standing in air, will become coated very quickly in a layer of their oxide. And if provided with a little heat, oxygen will react vigorously with many materials. We call these reactions of oxygen “fire”.

The very different meanings of “stable” mean that we have to think when we hear this word. Ideally, we would also banish the third meaning mentioned above in favour of more specific language, such as “reactive towards”. Conflating questions of stability and reactivity just makes it harder to think precisely about what we mean when we say that a molecule or substance is stable.

1J. W. C. Johns (1970) A spectrum of neutral argon hydride. J. Mol. Spectrosc. 36, 488–510.