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Question

Why is the Bronsted-Lowry definition of acids and bases more encompassing than the Arrhenius definition?

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The Brnsted-Lowry definition, being less specific, is more encompassing than the Arrhenius definition.
Here's what I mean.
The Brnsted-Lowry definition says that:
An acid donates a proton (H+) No further qualification is involved.A base accepts a proton(H+)No further qualification is involved.The Arrhenius definition says that:
An acid donates a proton (H+)with the qualification that it occurs upon dissociation and the proton is donated to water.A base donates an OHwith the qualification that it occurs upon dissociation and the OHis donated to water.As a result of the more specific nature of the Arrhenius definition, it is confined to only aqueous solutions. With Arrhenius bases, it is additionally specific in that a OH must be donated to solution... while protons aren't really considered.
One example of a Brnsted-Lowry base that is NOT an Arrhenius base is sodium ethoxid
We should notice that it can accept a proton (by donating electrons), just like the Brnsted-Lowry base definition requires, but it does not donate an OH to water; it can't, because we aren't even using water as the solvent!
Thus, sodium ethoxide in ethanol is not an Arrhenius base; though, it IS a Lewis base since its oxygen donates two valence electrons to get its proton.

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