Why can acetic acid and ammonia neutralize each other without water as a solvent?

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Acetic acid and ammonia can neutralize each other without water because, according to the Brønsted–Lowry definition, an acid is simply a species with a tendency to lose a proton (H+) and a base is a species with a tendency to gain one. This definition is independent of the solvent, meaning acid–base reactions are fundamentally defined by the transfer of a proton from an acid to a base.1

The neutralization of acetic acid (CH3CO2H) by ammonia (NH3) involves a direct proton transfer:
CH3CO2H+NH3→CH3CO2−+NH4+

Because this equation describes a direct transfer of a proton from the acid to the base, it does not require water to proceed. Consequently, this reaction can occur in an inert solvent or even in the complete absence of any solvent. In this process, the acetic acid acts as the proton donor and the ammonia acts as the proton acceptor, forming the acetate ion and the ammonium ion, respectively.21