van Arkel–Ketelaar allows for a more “definitive” classification of bonding type

February 28, 2024

One way or another I’ve spent the best part of four decades immersed in the world of secondary chemistry education. My experience is more diverse than most, and covers a lot of ground, but a large part of it has enabled me to do some detailed comparisons of post-16 chemistry courses, i.e., to compare and contrast A-level (UK), AP chemistry (US), and IB (international).

Most educators are likely to be acquainted with only one of those courses, and if IB hasn’t been your ‘thing’ it’s unlikely that you are not familiar with (if you’ve even heard of it at all) the van Arkel–Ketelaar triangle. If you’ve had relatively little experience with IB you’ll still understand the ideas behind the triangle, but you may not have seen those ideas presented in this manner.

So what is the vAK∆? Essentially it allows the classification of the type of bonding present between elements in various situations by considering electronegativity in two ways; differences and averages. Of course, strict classification has a rich history of conflict in chemistry, with attempts to force things into neat little boxes often causing nothing but arguments, but for now I’m going to put that to one side and assume that we can assign bonding types with some level of certainty.

The triangle has a rich history of development. Mark Leach gives a pretty comprehensive breakdown of its evolution, which has been ongoing for the majority of the 20th Century. For simplicity I want to concentrate on the version that appears in the latest IB Data Booklet for Chemistry (section 17, page 18) for first use in assessments in 2025.

van Arkel-Ketelaar triangle from IB Data Booklet

In AP there has been a tendency for some textbooks (and some teachers) to informally apply a simpler version of the triangle by using a sliding scale of electronegativity difference to distinguish between ionic and covalent bonding in compounds. Versions of the scale vary, but one such iteration appears in my UNIT 02 notes thus.

It’s important to note that such casual applications should always be interpreted very liberally, and that different versions of the scale will likely exhibit a significant degree of variation. In addition, several compounds will confound by acting quite differently to the prediction made by such a scale. All of those caveats suggest that any conclusions drawn from such a scale should always be treated with a large grain of salt. The difference between guidelines like that, and the van Arkel-Ketelaar triangle being printed in the IB data booklet, is profound. What this means for IB is that in the context of the exam there really are right and wrong ideas about what should be considered ionic or covalent. Of course such a “definition” may not necessarily hold up well in the real world, but (again), for the exam, there really are right and wrong answers when it comes to bond classification.

The distinction between what’s acceptable on the exam and what happens in the real world is very important, and sometimes lost on many folk in the US. In general, the idea of public, external exams being so important, and being so internally definitive goes against many of the principles behind the American attitude toward education, and sits poorly with some on this side of the pond. It confuses them. However, when one understands how exams work, things become clearer. Definitive answers absolutely are possible even if it is in the narrow context of the test.

As for the triangle itself it offers some significant advantages over the simplified “difference chart” that the AP audience might apply.

  • The average electronegativity allows the plotting of elements in the triangle, and for the classification of metals and non-metals
  • The inclusion of the metallic portion allows the inclusion of an extra type of bonding, and the consideration of alloys
  • Assuming appropriate data regarding electronegativity are given, the triangle allows for the classification of otherwise unfamiliar combinations of elements
  • It allows for a “definitive” classification, even if that classification is only really applicable in the context of the IB exam

Most questions in AP will not require such classification, rather they tend to concentrate more on linking observed physical properties such as melting point and conductivity to the type of bonding. Having said that, for my money, this is just another way that IB is superior to AP in terms of its content by allowing a “definitive” classification in an examination context.


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