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My professor mentioned that hydroxide ion is the strongest base when we only consider aqueous solutions. Then why don't the strongest bases outside of aqueous solution, like superbase, remain the strongest in water?

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If you add a superbase to water in small enough quantity that it still makes sense to think of water as the solvent, all (or essentially all) of your superbase will be converted to its conjugate acid by the reaction

$$\ce{B-}+\ce{H2O} \to \ce{HB} + \ce{OH-}$$

This will have a very large equilibrium constant (by the assumption that $\ce{B-}$ is a superbase) and will also be driven heavily to the right by the high concentration of water. If you add enough of your superbase, eventually you can have appreciable amounts of $\ce{B-}$ sticking around in the solution, but at this point it no longer really makes sense to call the solution "aqueous".

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A pH electrometer measures changes of [HO-] or [H3O+] ions (from that of neutral water) due to reaction of bases or acids with water. The reactions are expected due to solvent levelling (i.e. H2O). On the basic side, water levels to HO-, as a result of its own auto-ionisation process.

In another solvent, a given base, may exhibit a different ability for deprotonating the solvent molecules, which will to some extent be governed by that solvent's auto-ionisation process (which will differ from that of water). Relative to its behaviour in water, this may be expressed as an increase (stronger basicity) or decrease (weaker bacisity). Availability of the proton changes with solvent, and the resulting BH+ or (solvent)- may be stabilised by the system, or not.

pK's are solvent dependent. For example, in the solvent DMF, picric acid is stronger than HBr, but the reverse is true in water.

While a "super-acid" is anchored to a species having a Hammett acidity of -12 or lower, a "super-base" is not anchored to base strength, but is more of an acknowledgement that acidity changes with solvent. As defined, the notion of a superbase is misleading, since it is only a statement concerning structure (combine known bases to form a new base) or that such a species is a stronger base than in water (which it may, or, may not be, in varieties of solvents).

In short, there is nothing "super" about a given superbase, and one should not expect it to behave as a stronger base in general, although in some solvents it MAY be stronger, while in others, weaker.

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In this example we use the concentration of [H+] Ions solvated by H2O to form the Hydronium ion. Since [H+] also happens to be how we are defining the term acid in this example... The conjugate hydroxide Base [OH]- , the [H]+ acid, and the solvent [H2O] are in equilibrium. Because the [H+] in pure water should be 0, it has a pH of 7. The hydroxide ion is the most perfect species to attack and disassociate H+.

When you change the solvent to a non aqueous solution, H+ may not be present...if you’re dealing with a bronsted laury acid. In such cases it’s better to redefine acid and base in terms off a compounds ability to transfer a proton to another compound (acid). Hydrogen ions or hydroxide ions don’t have to be present to have strong non aqueous acids or bases. Like n-butyl-Li or antimony pentafloride.

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