# How to calculate he equilibrium constant change for acid-base reactions in a different solvent?

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.

• Different solvent basically means different everything. The new constants can't be calculated easily. Nov 11, 2017 at 16:39
• 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.
– MaxW
Nov 11, 2017 at 17:01
• 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. Nov 11, 2017 at 18:23

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.

• 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? Nov 12, 2017 at 15:46
• @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.
– Jan
Nov 12, 2017 at 15:48