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Is ammonia a nucleophile and hydrogen the electrophile in the Brønsted-Lowry acid-base reaction of acietic acid with ammonia?

I say that ammonia is the nucleophile because I drew a curved arrow from the lone pair on the ammonia to the ionizable hydrogen on acetic acid, and I drew a curved arrow from the bonding pair in the hydroxyl group to the oxygen in the hydroxyl group. It seems that ammonia is the nucleophile because it is attacking the hydrogen proton (a bare proton) and that hydrogen is the electrophile because it likes the lone pair on ammonia.

So if the above is right, this would make ammonia a Lewis base and the hydrogen proton a Lewis acid? Or do we say the entire acetic acid molecule is a Lewis acid?

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In my opinion your statements are both right, this is the IUPAC definition:

lewis acid: A molecular entity (and the corresponding chemical species ) that is an electron-pair acceptor and therefore able to react with a Lewis base to form a Lewis adduct, by sharing the electron pair furnished by the Lewis base.

You can see that the author say molecular entity (atom, molecule, ion, ion pair, radical, radical ion, complex, conformer etc., identifiable as a separately distinguishable entity) and the corresponding chemical species ( a boarded concept, that in this case I interpret as the combination of different molecular entity) so I think that the exegesis of this definition is that either the acetic acid and the hydron can be call lewis acid. And in fact is what usually all the chemists used.

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