What if?

Serious scientific answers to absurd hypothetical questions – this is the premise to “what if?” authored by Randall Munroe, creator of xkcd comics. A colleague once remarked that he could probably teach an entire course using xkcd comics. This book, in particular, is a good source of quantitative reasoning Fermi problems – ones that are absurd, of course, otherwise where’s the fun? I’m having a blast reading through the humorous explanations accompanied by xkcd illustrations.

My favorite question in the book that Randall attempts to answer is “How quickly would the oceans drain if a circular portal of 10 meters in radius leading into space were created at the bottom of Challenger Deep, the deepest spot in the ocean? How would the Earth change as the water was being drained?” (submitted by Ted M.) First, Randall locates the other end of the portal far away from Earth; otherwise “the ocean would just fall back down into the atmosphere [while wreaking] all kinds of havoc with our climate”. The more interesting part is his drawings of the world map showing the landmasses and the sea as the ocean levels drop. A 50-meter drop doesn’t show that much change (at least on a global scale). A 250-meter drop though starts to show up some strange features. A bunch of islands start to appear and Indonesia is a big blob. New Zealand grows dramatically at the 1-km mark. What’s interesting is that after about 3-km, most of the major sea bodies would be disconnected and the draining would stop. You get the following picture below. (I’ve skipped the intermediate pictures, which you can find in the book or possibly on the web by searching for “Drain the Oceans”.)

As a chemist who ponders the origin of life, I thought about my “what if?” question. Here it goes: What if the elements in the Li-Ne Line (pun intended) of the Periodic Table disappeared?” Since the molecules of life are mainly built of carbon, hydrogen, oxygen and nitrogen (abbrievated as CHON), what would happen if the entire row Li, Be, B, C, N, O, F, Ne did not exist? (Maybe there was some absurd mechanism that caused all their isotopes to be unstable.)

This of course begs the question as to why life makes use of C, N, O in particular. So let’s try and get a handle on this. (Disclaimer: I have no good xkcd-style comics to accompany my explanations because I’m simply too lazy.) Let’s first consider the elemental abundances in our solar system (see Wikipedia figure below). Note that the vertical axis is a log plot, i.e., each unit is an order of magnitude (e.g. 6 on a log plot is 10 times larger than 5.)

While H and He are the most abundant, you can see a fair amount of C, N, O. Hence it is perhaps not surprising that most of the molecules you come across are “organic” molecules that contain CHON. Actually there’s probably a slightly higher diversity of CHO compounds, partly due to the lower abundance of N. There’s a second reason – the triple covalent bond that holds the two N atoms in N₂ is very strong. One of the most important biological innovations was to “fix” nitrogen by breaking this strong bond and converting it to compounds such as ammonia (NH₃). There is an interesting biochemical evolution story here but I’m going to pass over it.

Let’s take a closer look at the bond energies of other such covalent bonds. A typical table (search “Bond Energy” on Google images) is the one shown below.

As you can see most of the bonds shown are single bonds (one line between the atoms) and there are not many multiple bonds shown. Of the multiple bonds shown, they involve C, N, O in at least one of the partners. There’s a reason for this. Atoms that are smaller in size can get closer to each other to form that second (or third) bond. For example, the double bonds C=C, N=N, O=O have strengths of 620, 420 and 495 kJ/mol respectively. They are also quite a bit stronger than their single bonds C–C, N–N, O–O with strengths of 345, 160 and 145 respectively. (The N–N and O–O single bonds are anomalously weak for reasons I won’t get into.) On the other hand, you don’t see the analogous Si=Si, P=P, S=S bonds listed. That’s because they are just a tad stronger than their single bonds, and therefore if you’ve got a lot of hydrogen hanging around (it being the most abundant element), it’s energetically much more favorable to have single bonds all around (the Si–H, P–H, S–H bonds are decently strong too).

The molecules of life have a large variety of single and double bonds giving rise to a large diversity of structures. The strong C=O bond, in particular, is quite prevalent. It’s part of the reason why burning “organic molecules” as fuels provide energy when carbon dioxide and water are formed. Such molecular diversity cannot be found among Si, P and S (which I shall now refer to as SiPS).

There is another problem with silicon. Even though it can form four bonds just like carbon, it does not form compounds that are more stable than pure silicon and pure hydrogen. On the other hand, many hydrocarbons are more stable than pure carbon and pure hydrogen. For example, methane (CH₄) has a “heat of formation” of –75 kJ/mol, i.e., it is more stable compared to graphite and molecular hydrogen by 75 kJ/mol as indicated by the negative sign. Silane (CH₄) on the other hand is +34 kJ/mol less stable than its pure elements in their standard states. Silane is quite reactive because Si–O and O–H bonds are much stronger; silane is quite susceptible to oxidation.

Phosphine (PH₃) is only marginally less stable than its elements (+5.5 kJ/mol) but it is susceptible to oxidation for similar reasons. Phosphorus is also much less abundant as seen in the earlier chart. It is only when you get to H₂S and HCl that you get relatively better stability than the elements but it’s difficult to form a diversity of structures with S and Cl. Therefore, at least in our current atmosphere with plenty of oxygen, SiPS compounds will tend not to form. In fact, it is only when silicon and chlorine combine do you get compounds that are somewhat analogous to the hydrocarbons. For example, SiCl₄, Si₂Cl₆ and Si₃Cl₈ are relatively stable. There was even a nice report in 2011 on forming Si₅Cl₁₂ analogous to neopentane, C₅H₁₂^.

But if there was no oxygen, perhaps you can get SiPS compounds to hang around. There would still be the problem of not being able to form as large a molecular diversity because of the relative strengths of SiPS with hydrogen compared to bonds just within SiPS. I would expect molecules with single bonds to form, but there probably won’t be any double bonds.

As a computational chemist, I could calculate a suite of SiPS molecules and actually come up with a scenario of what sorts of molecules one might expect to observe if the Li-Ne Line indeed disappeared. This isn’t the sort of project that will attract grant funding, although it might be publishable if pitched properly to a journal that might be interested in such speculation and not deem it too absurd. I haven’t burned any computer time on the project although I can outline the steps that I would take. Maybe one day I’ll have a student who is a fan of xkcd, knocking on my door and who thinks it would be fun to do something so absurd without any potential “real world” payoff. Or when I have a chunk of free time and I don’t mind burning some computer time. It might just get a kick out of it.