Binary pnictogen halides

Here’s a tricky (trick?) question from the final exam of MITx course Introduction to Solid State Chemistry:

Which compound has the higher boiling point, phosphorus trifluoride (PF₃) or phosphorus pentafluoride (PF₅)?

Naturally, you are supposed to figure this out from the first principles, or rather, from some principles taught in this course, not from Wikipedia (or “by googling”, as some put it).

(a)	(b)

The problem is, the “right” answer, PF₃, is actually, factually wrong. Even though this question cost only two points (of 150), a rather animated debate followed the exam.

Those who defended the “right” but factually wrong answer (a) were proposing that what the problem was testing our thinking rather than actual knowledge, and our thinking should have been along the lines of VSEPR model. VSEPR rules correctly predict PF₃ to be trigonal pyramidal and PF₅ to be trigonal bipyramidal. The dipole moment of a polar molecule PF₃ should make it less volatile than apolar PF₅. Those who chose the “wrong” but factually correct answer (b) were arguing that polarisability of larger PF₅ is higher than that of PF₃ and therefore the London dispersion forces in PF₅ would beat dipole-dipole interactions in PF₃. The (a) party were saying that making the answer you’d get by applying principles different to the one you’d get by “googling” is a good protection against cheating. The (b) party were retorting that this is a silly way of protection, that the question asked was what has the higher boiling point, not what could be expected to have the higher boiling point, and that expecting students to come up with the factually wrong answer is not exactly pedagogical.

Truth to be told, the methods of estimating boiling or melting points of materials were simply not a part of this course. The only thing one could do was to determine whether the molecule has a non-zero dipole moment. But there is no way to figure out which effect will be stronger, the increase in dispersion forces or dipole-dipole interactions.

One would think that the physical properties of such simple compounds as binary halides of Group 15 elements (pnictogens) are studied well and long ago. Not really. I tried to compile a table of dipole moments and melting/boiling points for pnictogen tri- and pentahalides, MX₃ and MX₅, using various resources [1—5]. As you can see, there are still many gaps.

Trihalide	μ (D)	mp (°C)	bp (°C)	Pentahalide	mp (°C)	bp (°C)
NF3	0.234	–207	–129	—
PF3	1.03	–151.5	–101.8	PF5	–93.7	–84.5
AsF3	2.59	–6.0	62.8	AsF5	–79.8	–52.8
SbF3	?	290	345	SbF5	8.3	141
BiF3	?	649	900	BiF5	154.4	230
NCl3	0.6	–40	71	—
PCl3	0.97	–93.6	76.1	PCl5	167	160s
AsCl3	2.15	–16.0	130.8	AsCl5	–50	?
SbCl3	2.75	73.4	223	SbCl5	4	140
BiCl3	4.6	233.5	441	BiCl5	?	?
NBr3	?	?	?	—
PBr3	?	–41.5	173.2	PBr5	<100d	106d
AsBr3	1.66	31	221	AsBr5	?	?
SbBr3	2.47	96	288	SbBr5	?	?
BiBr3	3.6	219	462	BiBr5	?	?
NI3	?	–20s	?	—
PI3	~0	61.1	227	PI5	41	?
AsI3	?	141	400	AsI5	?	?
SbI3	1.58	170.5	401	SbI5	79	401
BiI3	?	408.6	~542	BiI5	?	?

d, decomposition
s, sublimation

What, if any, trends can we see?

• The dipole moment of MX₃ grows larger down the group of the central atom M, e.g. μ(NF₃) < μ(PF₃) < μ(AsF₃), and grows smaller down the group of ligand atom X, e.g. μ(SbCl₃) > μ(SbBr₃) > μ(SbI₃).
• As the sizes of both central atom and ligands go up, so do the melting and boiling points.
• As dipole moments go up, so do the melting and boiling points.

Something curious happens, though, when one crosses the phosphorus—arsenic borderline. AsF₃ has a dipole moment of 2.59 debye. As expected, both mp and bp of AsF₃ are, respectively, higher than those of AsF₅. PF₃, however, has much lower moment of 1.03 D. Both mp and bp of PF₃ are, respectively, lower than those of PF₅. Similarly, mp of AsCl₃ is higher than mp of AsCl₅, whereas mp of PCl₃ is lower than mp of PCl₅. Similarly... but no, there are too many gaps in the table “down there”.

Which shows, by the way, that “googling” does not help if the data is not available. For the future, the course authors may consider asking a very similar question about a pair of compounds from “down there”. Thus the whole conflict between the (as yet unknown) “truth” and “expected answer” could be easily avoided.

Since the electronegativities decrease down the group for both M and L, the most polar M—L bond must be Bi—F bond and BiF₃ should have the largest dipole moment. Well I couldn’t find its value. But it is known that bismuth trifluoride has ionic structure, and has the highest melting (649 °C) and boiling (900 °C) points of all binary pnictogen halides. On the other side of the spectrum, we have extremely sensitive nitrogen triiodide. A feather tickle, a loud noise and, I suppose, any attempt to measure its dipole moment will set off an explosive decomposition (see the video below):

2 NI₃ → N₂ + 3 I₂

References

1. Earnshaw, A. and Greenwood, N. (1997) Chemistry of the Elements, 2^nd Edition. Butterworth-Heinemann, Oxford.
2. Nelson, R.D., Jr., Lide, D.R., Jr. and Maryott, A.A. (1967) Selected values of electric dipole moments for molecules in the gas phase. National Standard Reference Data Series — National Bureau of Standards 10, Washington, DC.
3. Cotton, S. (2001) Nitrogen triiodide. Molecule of the Month collection, University of Bristol.
4. WebElements
5. atomistry.com