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Why is acid called proton donor?

On the internet, I found:

Acids are substances that can donate $\ce{H+}$ ions to bases. Since a hydrogen atom is a proton and one electron, technically an $\ce{H+}$ ion is just a proton. So an acid is a 'proton donor.'

However, my teacher said that it is not fully correct. If this is the case, then what's the correct definition of an acid?

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    $\begingroup$ All H+ donors are acids but not all acids are H+ donors. To explain why other substances which didn't donate H+ ion were acids, we needed to revise our definitions of acids. We have three most common definitions of acids-Arrhenius, Bronsted-Lowry and Lewis acids. You can read about them anywhere. $\endgroup$ – Arishta Feb 16 '17 at 3:06
  • $\begingroup$ Related: chemistry.stackexchange.com/questions/6751 $\endgroup$ – Klaus-Dieter Warzecha Feb 16 '17 at 8:12
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Your teacher said that this is not completely correct as there are (at least) three common definitions for acids and bases (Wiki has a good article for this https://en.wikipedia.org/wiki/Acids_and_Bases):

  1. Arrhenius: In water, acids under this definition protonate the water and form Hydronium (H3O+). Bases in this definition deprotonate the water.
  2. Brønsted–Lowry: This is your proton donor definition. Acids in this definition donate protons to bases.
  3. Lewis: In this definition acids are electron pair acceptors and bases are electron pair donors.

The relationship between these definitions is that as chemistry evolved we ran into more chemicals (acids and bases) with similar reactivities that the previous definitions didn't quite encompass and so chemists broadened the definitions. So, as you go down the list above you will find more and more chemicals that match your new definition of acid or base.

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    $\begingroup$ No, you’re misciting Arrhenius’ definitions. An Arrhenius acid is a substance that dissociates in water to give $\ce{H+}$ and an Arrhenius base is a substance that dissociates in water to give $\ce{OH-}$. Ammonia, for example, deprotonates water but does not dissociate to give $\ce{OH-}$ and thus is not an Arrhenius base. $\endgroup$ – Jan Mar 21 '17 at 23:24
  • $\begingroup$ Jan I'm afraid that I cannot agree. In Arrhenius's 1887 paper (I have only read an English translation) "On the Dissociation of Substances Dissolved in Water" he expressly calls out Ammonia as a base and talks about it as an "active molecule" i.e. for every molecule of ammonia in solution two ions are produced (in very dilute solutions). So, what he seemed to care about was the production of either Hydroxide or Hydronium as the definition of acid or base in solution. $\endgroup$ – Rampallian Mar 22 '17 at 14:58
  • $\begingroup$ Which Arrhenius paper are you referring to? I found one with a matching title (Z. phys. chem. 1887, 1, 631–648. DOI: 10.1515/zpch-1887-0164.) where he does call ammonia a base but not an active molecule. (Having read the German original.) $\endgroup$ – Jan Mar 26 '17 at 20:41
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Acids have different definitions according to different concepts. Acid is a proton donor according to brønsted lowry concept. According to Lewis concept, acids are electron pair acceptors. Now there are some acids like Boric acid which doesn't donate hydrogen by itself but still its an acid. The reason being it accepts electron pair from OH- and hence obeys Lewis definition. So all acids cannot be explained through brønsted lowry or Arrhenius concept. Here are the three definition of acids:

Arrhenius acids are those which when added to water, increases the concentration of H+ ions in the water.

The Brønsted-Lowry definition is the most widely used definition; unless otherwise specified, acid-base reactions are assumed to involve the transfer of a proton (H+) from an acid to a base.

Lewis acids is a species that accepts a pair of electrons from another species; in other words, it is an electron pair acceptor.

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