Sodium Trichloride

Chemical bonding is at the heart of an introductory course in chemistry. Often, this topic is divided into three categories: ionic, covalent, and metallic bonding. Ionic bonding is often covered first as the introductory segue into chemical bonds; I’ve eschewed this approach for a more generalized introduction to “attractive forces between particles”. However, I do quickly get to ionic bonding, as there are many concepts to be illustrated!

We begin with the interaction between two separated ions, Na(+) and Cl(-). The attractive impetus between the ions is calculated using Coulomb’s Law. At some point, the ions can’t get any closer due to the Pauli Exclusion Principle. We can calculate the “strength” of the bond at the optimal distance between the two ions. We conclude that the ionic bond is stable because this stabilizing “bond energy” exceeds the cost of electron transfer from a sodium to a chlorine atom (primarily due to the first ionization energy of sodium).

But NaCl experienced macroscopically is a solid. Now we may introduce the structures of cubic solids and packing considerations. The larger chloride ions are positioned according to a face-centered cube while the “holes” are where the smaller sodium ions reside. We then consider the favorable formation of NaCl from its elements, sodium metal (solid) and molecular chlorine gas. Energies are calculated. We set up what is known as a Born-Haber cycle, and we can extract a quantity known as the lattice energy. The lattice energy is not equal to the simple bond energy we calculated from two ions; in G-Chem the N-body interactions are hand-waved, while in Inorganic, we can estimate the Madelung constant.

Now that we’re working with standard energies under standard conditions, we can start to ask interesting questions. In G-Chem, I show students a table of (calculated) lattice energies, and we reason our way through how to qualitatively extrapolate these values to ionic compounds not captured in the simple table. At this point I attempt to convince the students that Na(2+) and Cl(2-) should be a better representation for sodium chloride because the lattice energy stabilization should be much greater. After probing the variables, students eventually make an appropriate counterargument. We then discuss the analogous MgS followed by other interesting and more complex cases.

My students at this point can make an argument as to why Na₂Cl or NaCl₂ should not be stable (at least under standard conditions). I try to impress on them that the argument needs to be made based on energy and packing considerations and not on the “happy atoms” story they may have imbibed in secondary school. But I didn't push it further. What about sodium trichloride, NaCl₃?

We know that NaCl₃ and Na₃Cl exist at high pressures, along with a range of other stoichiometries from an interesting study in Science (2013, vol. 342, pp. 1502-1505), studied computationally and then synthesized. There’s even a cool picture of the cubic unit cell of NaCl₃ in a New Atlas article highlighting the study. We computational chemists are not just designers, we’re also artists! (We have to rely on our experimental colleagues for the actual craft of making these compounds.) A more recent article (Chem. Phys. Lett., 2017, vol. 672, pp. 97-98) calculates the lattice energies of these unusual compounds. I could set up a Born-Haber cycle problem for my students, who can dutifully calculate.

I find that the strongest students – usually the ones who had good chemistry preparation in secondary school – upon encountering a problem-to-solve quickly jump to calculating instead of spending a bit more time thinking. Why might NaCl₃ exist? Are there ways to think about it chemically? Could there be an Na(+)Cl(-) lattice with four equivalents of molecular Cl₂ somehow stuffed into the face-centered-cubic unit cell? How might the unit cell change? If we’ve covered drawing more complex Lewis structures by this juncture, could we consider the trichloride anion and have an ionic lattice with Na(+) and Cl₃(-)? (Drawing the Lewis structure of I₃(-) is a standard example my students tackle in G-Chem.)

As interesting as I’m finding this example to ponder, it’s utility to further concepts in G-Chem is limited. I might use it as an extra credit exercise or something to occupy the advanced students. However, it could work well for Inorganic, which I haven’t taught in a while so I’m not sure how I would choose to rejigger the syllabus to include this sort of investigation. Since I use my blog as a memory-offload, I’ve recorded my quick thoughts here – and maybe I’ll return to this example (hopefully) in the near future.