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The only answer which I found to this is that it's because strong acids and bases virtually completely dissociate, so the dissociation constants would be too large and hence aren't used. This doesn't really seem reasonable to me and I have a feeling there is another answer. Is there really another answer or is this the only answer?

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This is absolutely not true. $\mathrm{p}K_\mathrm{a}$ values are frequently quoted amoung organic chemists for very strong bases and sometimes even for very strong acids. For reference, check out the Evans $\mathrm{p}K_\mathrm{a}$ table and the values quoted therein.

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What you are answering yourself is quite correct. To elaborate, the pKa/b of a compound refers to its interaction with water. All strong, and especially magic or superstrong acids and bases react vigourously with water, and the disassociation constant stops being useful. While you can still use the constant in order to... rank two superacids by strength for example, this is hard to use for anything practical.

It also depends on the water. Example; HF is a weaker acid than HCl in water, but stronger than HCl in anhydrous acetic acid. To escape all these conundrums it is necessary to have a way of describing the acid and base potential without including interactions with water.

Instead, for acids and bases outside of this watery scope, you use other methods to calculate - like the Hammett Acidity Function which more directly attacks the parameter in question - the chemical potential of the proton.

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  • $\begingroup$ I consider this a generally wrong answer because it implies $\mathrm{p}K_\mathrm{a}$ values of strong acids/bases be generally not used (which is wrong). Also, I haven’t seen the Hammett Acidity Function being used outside of superacid researchers and lectures. $\endgroup$ – Jan Aug 22 '16 at 12:00
  • $\begingroup$ Fair enough, but it is clear from the question that Mathematician observed the use only for weak acids and bases. Just because you in your environment, or most people in their environment use pK's does not invalidate his question, and my answer. Truth is that the strength of strong acids and bases are not necessarily reflected by their pKa/b - or else HF would be a benign compound. Which it is not. $\endgroup$ – Stian Yttervik Aug 22 '16 at 12:13
  • $\begingroup$ Oh, it just means that there is more to the toxicity/aggressivity of $\ce{HF}$ than its ability to act like an acid. $\endgroup$ – Jan Aug 22 '16 at 12:17
  • $\begingroup$ @Jan I rather like that answer (it needs some polish though). You won't use pKa of HCl to calculate pH of its solution, will you? I would be pointless. Also in concentrated solutions pH stops being useful and H0 is needed. $\endgroup$ – Mithoron Aug 22 '16 at 14:26
  • $\begingroup$ @Mithoron Absolutely correct. I use the $\mathrm{p}K_\mathrm{a}$ of HCl to determine whether something will be fully protonated or not at concentraction $c$. I reverse the right to turn my downvote into an upvote once the required polish has been applied ;) $\endgroup$ – Jan Aug 22 '16 at 14:32

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