0.8 Energy and polarity of covalent chemical bonds  (Page 3/8)

Experimentally, it is indeed possible to observe H ₂ ⁺ . Even though it is far less common than H ₂ , it does exist. What does this mean in terms of chemical bonding? It means that H ₂ ⁺ does not spontaneously fall apart into an H atom and an H ⁺ ion. Instead, to break the bond we would have to do some work, or, in other words, add some energy. This amount of energy can be measured and is 269 kJ/mol. That is actually quite a lot of energy which must be added to pull an H atom and an H ⁺ ion apart, so a strong bond is formed when the two H ⁺ nuclei share a single electron. This might seem surprising, since our model of chemical bonding based on Lewis structures regards a chemical bond as a sharing of a pair of electrons. We’ll examine the importance of sharing two electrons instead of one in the next section.

But first, let’s ask why sharing an electron creates a bond. A better way to ask this question would be why is the energy of the electron lower when the electron is shared by two nuclei instead of being near to only one? We know that an electron and a proton attract each other via Coulomb’s law, and the closer the two are, the lower the energy. As such, if an electron can be attracted to two protons, it has a lower energy even if the two protons are not next to each other. This is illustrated in [link] b, which shows the attraction of the electron to both nuclei as well as the repulsion between the two nuclei. When the electron is near to two nuclei, it has a lower potential energy than when near to only one because its attraction to a second positively charged nucleus further lowers its energy.

We can rearrange the electron and the two nuclei, such that the electron is on the “outside” of the molecule ( [link] a). Here, it is close to one nucleus but not the other. In this case, the repulsion of the two nuclei is greater than the attraction of the electron to the distant nucleus. Just using Coulomb’s law, the energy of the electron in this position is slightly lower than when it is on one nucleus, but the repulsion of the nuclei is large.

From a comparison of the arrangements of the electron and the two nuclei, it appears that we get a lowering of energy when the electron is “between” the two nuclei and not otherwise. This suggests what “sharing an electron” means when forming a chemical bond. Since the shared electron has a lower energy, we would have to raise the electron’s energy to pull the two nuclei away from each other.

Now we know why a chemical bond is formed when two atoms share at least one electron. The energy of the electron is lower when shared in the molecule than it is in the separated atoms because it is attracted to both positive nuclei at the same time. To break the bond formed by sharing the electron, we must do work, which means we have to add energy to raise the energy of the electron to be able separate the atoms.

Attractions and repulsions in h ₂ ⁺

For now, we should make a note to ourselves that all of this discussion of electron energy includes only a discussion of potential energy. It also assumes that the electron is at some particular location where we can calculate its potential energy. This ignores the uncertainty principle of quantum mechanics, suggesting that the model is not physically accurate. Both of these issues need to be corrected, so we need a better understanding of the sharing of electrons in chemical bonds.