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The Arrhenius definition and the Brønsted-Lowry definition are very similar and most “acids” we typically work with are both Brønsted-Lowry and Arrhenius acids.
The Arrhenius model is built around water. An Arrhenius acid increases the concentration of ##H^+## in the solution, while an Arrhenius base increases the concentration of ##OH^-## in the solution.
The Brønsted-Lowry definition is built around the direct exchange of protons. A Brønsted-Lowry acid donates a proton to a Brønsted-Lowry base. No consideration is given to the solution that the chemicals are in.
Technically if you crystallize HCl and NaOH, smash them into powders and mix them, they are still Brønsted-Lowry (since they’re exchanging protons to create water and salt) but are not because they are not in aqueous solution.
The Arrhenius model was made first, which is why it’s more limited. Of course the third definition, , is even more broad and applies to things that don’t even have protons to donate.
Detailed with good pictures can be found here: http://leah4sci.com/arrhenius-bronsted-lowry-and-lewis-acids-and-bases-in-organic-chemistry/.
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