As time has passed, and as the AP exam has been devastated in terms of its difficulty, I’ve decreasingly seen questions that pique my interest. Approximately once every decade the AP exam throws up something that propels me into deeper investigation. Now, don’t get me wrong, I’m not suggesting that the AP exam per se is ever stretching my mind in any way these days, but from time time it has been known to act as an inadvertent catalyst for some deeper thought. 2026, 5(b) did that.

Now, before we get into this let me make one thing quite clear. What follows in several subsequent paragraphs is of no relevance to 2026, 5(b)’s likely acceptable answer, but it offers some deeper background to what for me is likely to be a wholly unsatisfactory, “correct” answer.  Let’s start with that correct answer (or at least what I anticipate will be accepted as the correct answer).

To the 2026, 5(b) question,

In a molecule of CBrClF₂, the FCF bond angle is 106.8° and the BrCCl bond angle is 112.3°. Explain the difference in bond angles using principles of atomic structure and VSEPR theory. 

I expect/suspect (and we won’t know until official scoring standards are released) an absolutely acceptable answer in the context of AP Chemistry will be something like,

Cl and Br atoms have larger radii than F atoms, resulting in greater steric repulsion between the electron clouds of Cl and Br, and creating a larger bond angle for Br–C–Cl than F-C-F.

But while I was considering that potential answer, I started thinking about the influence of bond length, electronegativity and other things, and started to get dissatisfied. That research brought me to Bent’s rule, and in particular to this video.

I think the video is interesting and worth a watch – at least before it gets a little too involved for our purposes – but to make life easier I’ll summarize things below.

In a molecule such as the one in the AP question, i.e., one based upon AB₄ (or in this case AB₂CD), we would expect sp³ hybridization and the bonds to essentially be identical. However, Bent’s rule simply states that, “Atomic s character concentrates in orbitals directed toward electropositive substituents.” What that means is that when the electronegativities of the terminal atoms are no longer identical, a situation arises where the s and p character of the bonds that hold each atom to the central atom, start to vary from our original (sp³) prediction. The s and p character matters because the shapes of s and p orbitals mean that greater p character concentrates the electron density along the axes between atoms this reducing bond angles, whereas greater s character spreads electron density out, making for larger bond angles.

Apparently, for equivalent bonds (in this case the two, C-F bonds), one can apply a simplified form of something called the Colouson Directionality Theorem which says the following, Where x is the degree of p character in the bond.

For the C-F bonds we find that a bond angle of 106.8° gives us sp^3.464  and not sp³, i.e., more p character than one one expect, and hence a smaller bond angle than 109.5°. Unfortunately we don’t have enough information to do the same calulation for the C-Cl and C-Br bonds directly since the simplified Coulson Directionality Theorem won’t work when the bonds are not equivalent, but claude.ai solves my prompts to give C-Cl with bond character of sp^2.99 and C-Br with sp^2.33. Now, obviously I am out of my depth here, and claude may be working with (my) flawed inputs, BUT these results of greater s character in each of the other two bonds is entirely consistent with a larger bond angle which we know from the data to be true.

In attempting to understand this further I contacted Aaron Odum at Michigan State, the person responsible for the informative video. During our email exchange, Aaron writes,

In many cases the steric and electronic argument will point in the same direction

OK, no problem, but that does suggest that my instinct to be dissatisfied by the pure, simplified steric argument was right, since Aaron’s comment implies that sometimes the steric argument alone won’t get the job done. He goes on to say,

(VSEPR) is a very valuable theory that is often correct—just not for the reasons it thinks it is.

Anyway, there it is, 2026, 5(b) is deeper than you may think, and Bent’s rule is the real answer rather than simple steric factors. I should re-emphasize that Bent’s Rule and all of the associated calculations are obviously of no relevance to AP or the ultimate, accepted answer for this question, but it certainly got me thinking!