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MARGINALIA

One Shocked Chemist

Molecular surprises are sometimes right in front of us, if only we’d do the math

Roald Hoffmann

A Gedankenexperiment

2011-03MargHoffmannFD.jpgClick to Enlarge ImageLet me tell you why I should have known it. The fourth figure (right) imagines a hypothetical formation of graphane from an array of benzenes. In the first step, the benzene molecules are deprived (on paper) of their aromaticity, their bonds localized into the cyclohexatrienes that August Kekulé (a principal founder of the theory of chemical structure in the mid-1800s) struggled with conceptually. How much might this “loss of resonance energy” or “loss of aromaticity” cost? (See the reference to the paper of Shaik and his coworkers for a clear discussion of different definitions of resonance energy.) One estimate is about 270 kilojoules per mole.

In the next step, the “dearomatized’ benzenes polymerize into a two-dimensional sheet. In the process six carbon-carbon sigma (σ) bonds (the strongest type of covalent bond) are formed, although there are effectively three per ring, because each new bond is shared by two benzene rings. Three double bonds in each cyclohexatriene are converted to single bonds.

What is the relevant energetics for the second step? The second (π) bond of any double bond is worth less than a single bond. This energy is not a number one can measure directly. One can get an estimate from the heat of reaction of three ethylenes (C2H4) to cyclohexane (C6H12), a process in which three π bonds are converted to three σ bonds. That heat is experimentally –282 kilojoules per mole. Another way to estimate the energy of breaking a π bond is to look at the energy of rotating the two CH2 groups in ethylene 90 degrees out-of-plane, and to compare that to the strength of a C-C σ bond. That would lead to a slightly larger estimate of –315 kilojoules per mole for three bonds.

The sum of the two heats for the processes is +270 –282 (or –315) = –12 (or –45) kilojoules per mole for C6H6. There are all kinds of assumptions being made here, and I’ve neglected the obvious entropy change in the process, favoring benzene. But the essence staring us in the face, what I should have seen but didn’t, is that graphane is more stable than benzene.

That conclusion is what the better calculations give too. The number varies with the quantum-mechanical method used; we get that all-chair graphane is about 90 kilojoules per mole of C6H6 more stable than benzene. I should mention that we were not the first to calculate that graphane is more stable than benzene. That was done by Jorge O. Sofo, Ajay S. Chaudhari and Greg D. Barber of the Pennsylvania State University. Perhaps I was the first to be surprised at the result, with the baggage of chemical experience weighing on me.





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