What is the $K_\mathrm{a}$ of $\ce{OH^-}$ and $K_\mathrm{b}$ of $\ce{H_3O^+}$? Have these constants been determined?
Answer
For $\ce{O^2-}$, the $\mathrm{p}K_\mathrm{b}$ is approximately $-22$, so the $\mathrm{p}K_\mathrm{a}$ of hydroxide is about $36$.
sources: http://www.newworldencyclopedia.org/entry/Oxide and https://www.chem.tamu.edu/rgroup/hughbanks/courses/462/lecturenotes/class6-2.pdf
For hydronium, the reference Fred Senese cited
Protonated hydronium dication...
suggests that at acidities of Hammet acidity function $H_o = -25$ to $-28$, protonated hydronium can be present.
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