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So we know that $K_\mathrm w$ is $10^{-14}$. But what if I am working with non-aqueous systems? Suppose I were to add LDA to liquid ammonia, or dissolve HCl in concentrated sulfuric acid. How would I calculate the percentage of dissociation? I have some inkling of how to do this but I don't really see discussions online and want to make sure my procedure is correct. Furthermore, I don't know of what good keywords to find the self-dissociation constant of ammonia or sulfuric acid are and this is really frustrating.

To emphasize: I am looking for solutions for non-aqueous systems.

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    $\begingroup$ Different solvent basically means different everything. The new constants can't be calculated easily. $\endgroup$ – Ivan Neretin Nov 11 '17 at 16:39
  • $\begingroup$ To emphasize Ivan's point, there is no conversion formula for converting equilibrium constants in aqueous solutions to equilibrium constants in liquid ammonia. You need a whole different set of experimentally determined constants. $\endgroup$ – MaxW Nov 11 '17 at 17:01
  • $\begingroup$ I'm not exactly getting the point of question here. There's no problem with getting Kw of ammonia or H2SO4 but strength of acids and bases varies heavily depending on solvent. $\endgroup$ – Mithoron Nov 11 '17 at 18:23
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For all solvents that can dissociate into ions, a dissociation constant can indeed be measured. Expect them to be unpredictable in each direction.

Furthermore, the $\mathrm pK_\mathrm a$ values you know are typically those measured in water, although some organic chemists rely more heavily on the DMSO tables e.g. the one by Evans. Just a quick look at the first column shows you that there is no way you can predict the $\mathrm pK_\mathrm a$ value in one solvent from the one in a different solvent:

$$\begin{array}{lcc}\hline \text{compound} & \mathrm pK_\mathrm a(\ce{H2O}) & \mathrm pK_\mathrm a(\ce{DMSO}) \\ \hline \ce{HF} & 3.17 & 15\phantom{.0}\\ \ce{HCN} & 9.4\phantom{0} & 12.9\\ \hline\end{array}$$

While $\ce{HF}$ is the stronger acid in water, $\ce{HCN}$ is the stronger acid in $\ce{DMSO}$.

Couple this with a different dissociation constant means that you can calculate nothing ab initio.

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  • $\begingroup$ This probably should've been asked in chat, but still: do you know a good source besides Evans' DMSO table for $\mathrm{p}K_\mathrm{a}$ values in other solvents (primarily high-polar aprotic ones), where all the data would be accumulated together and citeable? $\endgroup$ – andselisk Nov 12 '17 at 15:46
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    $\begingroup$ @andselisk I only know Evans and the Bordwell data referenced therein. Both are only water and DMSO (Bordwell also a few gas phase values). Sorry I can’t be of help. $\endgroup$ – Jan Nov 12 '17 at 15:48

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