No Special K – treating the six Ks as one

January 15, 2024

The annual student struggle with acid-base chemistry usually revolves around questions that deal with weak acids and bases. If you pause to think about that for a moment, the difficulties are actually coalesce around equilibrium and not so much around acid-base chemistry per se. This means that much of the pain of UNIT 8 – and there’s plenty – can be pre-empted in UNIT 7, before we even get to the traditionally tortuous struggles with buffers and the like.

In my opinion, the key to reducing some of the pain-points here is to emphasize that the six Ks (Kc, Kp, Ksp, Ka, Kb, and Kw) encountered in the course are, for all intents and purposes, not “special”, but rather are EXACTLY the same as one another. Hammering this over and over and over again is central to success, and it almost makes UNIT 8 largely part of UNIT 7. When I first start teaching UNIT 7, I formally declare that we will dealing with six equilibrium constants that are identical to one another, just applied to slightly different situations; three of them happen to be in what we call UNIT 7, and three happen to be in UNIT 8, but the distinction in terms of UNITS is somewhat artificial.

So what are the points of similarity that do not change no matter what follows the K, and that you can focus on when adopting this approach?

  • All are constructed in the same manner, i.e., are no more than some function of the products (concentration or pressure) raised to their stoichiometric coefficients and multiplied together in the numerator, with the same applied to reactants in the denominator at the single equilibrium position
  • Each omits the same things, i.e., pure solids and pure liquids
  • Q, the reaction quotient applies to each in exactly the same way, meaning that predicting shifts is also handled in the same way each time
  • Each are temperature dependent
  • Each are considered unitless for AP purposes
  • Each can have ICE tables applied in exactly the same way
  • Each can have both huge and tiny values considered in a similar manner

Prior to 2014, there seemed to be a greater willingness among teachers to adopt this ‘universal K’ approach. I put this down to the certainty surrounding FRQ #1 on the legacy exam. On that exam, question number #1 on the free response portion was dedicated to some kind of equilibrium problem. Starting in the late 1970s, and with the exception of only a couple of years in ’96 and ’97 (when the old NIE question was shifted to #1), the AP exam featured a K problem as Q1 all the way through to the final year of the legacy exam in 2013. In fact, even on the new exam in 2014 and 2015, question #1 still had a small equilibrium element to it, and it wasn’t until 2016 that we saw a complete break from K on the opening question. A small summary of what was asked over a period of 11 years in the 00s is shown below.

The pattern made for some fairly simple guesses as to what would (or perhaps more easily what wouldn’t) be the topic of that question in any given year (you’ll note that on the operational exam there was never a time when the specifics of K were repeated for any year in the 00s). This predictability seemed to encourage the idea of treating acid and base in a manner that was more closely tied to Kc.

Treating the complexity of buffers as purely equilibrium problems offers an alternative approach too, and also has some advantages as I write more extensively about here.

So next time you start UNIT 7 think ahead. Perhaps even introduce the idea of Ka, Kb and Kw while you’re still delivering that UNIT, and maybe, just maybe, things will get better in the following weeks amongst the weeds of buffers and the like.

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