0.9 Energy and polarity of covalent chemical bonds  (Page 4/8)

Observation 2: the simplest molecule, h ₂

The hydrogen molecule is familiar to us from our early efforts to determine molecular formulae. Avogadro was the first person to suggest that hydrogen gas consists of diatomic molecules, H ₂ , instead of individual hydrogen atoms. This was a perplexing idea for the chemists of the early nineteenth century. Why would identical H atoms be attracted to each other? Of course, they did not know anything about the structure of these atoms, including that each atom contains a positive nucleus and an electron. From our work on H ₂ ⁺ , we now have a clue as to what holds the two H atoms together. It must be electron sharing.

What observation can we make about the bonding in H ₂ ? Clearly, it is a stable molecule. Although H ₂ molecules are highly reactive, they do not spontaneously fall apart into H atoms except under very extreme circumstances. Experimental data tell us that the bond energy of H ₂ is 436 kJ/mol. This is even more energy than is required to break the bond in H ₂ ⁺ , nearly twice as much in fact. Remember that to break the bond in H ₂ ⁺ we must raise the energy of the shared electron. Perhaps, in H ₂ , we have to raise the energy of the two electrons, costing us about twice the energy. This seems to be a good starting point for understanding the strong bond in H ₂ .

But there are some troubling questions about this simple picture. This model would suggest that sharing more than two electrons should give an even greater bond energy. But this is only true for some molecules, and it is certainly not true for H ₂ . There is something significant about sharing a pair of electrons, rather than one or three. In addition, the strength of the bond (436 kJ/mol) is actually less than double the strength of the bond with one shared electron (269 kJ/mol). There must be another factor at work. And finally, there are the questions we ended with in the last section: what about kinetic energy? And what about the uncertainty principle, which states that an electron is not actually localized?

Let’s work our way backwards through these questions. We know from our study of quantum mechanics that the motion of an electron is described by an “orbital” which provides the probability for where the electron might be found. We can’t actually know where an electron is, but we can look at its probability distribution. This is true for electrons in molecules just like it is in atoms. We just need to observe what an orbital looks like for an electron that is shared by two nuclei.

Such a “molecular orbital” for the electron in H ₂ ⁺ is shown in [link] . We’ve seen images like this when we discussed atomic orbitals. Remember that this image of a cloud gives us a probability: where there are many dots, the probability is high. The electron can be found near either nucleus but can also be found with high probability in the area between the two nuclei. This seems encouraging when thinking about the energy of the electron in the molecule as we discussed in the previous section. When the electron is in the region between the two nuclei, the potential energy of the electron is lower.