All high school and college chemistry students must memorize the difference between Arrhenius, Bronsted-Lowry, and Lewis acids and bases. This article provides the definition of each, plus a brief description and (potentially useful) mnemonic device to help memorize the differences in the theories of acids.
An Arrhenius acid is a compound that adds hydrogen ions (H+) to a solution, while an Arrhenius base adds hydroxide ions (OH-) to a solution. For example, in the reaction:
HBr(g) + H2O(l) ----> Br-(aq) + H2O(l) + H+
HBr is an Arrhenius acid. Note that it is more proper to write:
HBr(g) + H2O(l) ----> Br-(aq) + H3O+(aq)
We do this because some of the hydrogen ions will combine with the water to produce hydronium (H30+). Also note that we don't need to write water in the products, for it is implied that water exists in an aqueous solution.
An example of an Arrhenius base in NaOH. Notice how it dissociates to add a hydroxide ion to the reaction:
NaOH(s) ----> Na+(aq) + OH-(aq)
A Bronsted-Lowry acid is identical to an Arrhenius acid for it donates a proton or hydrogen ion nucleus, which is really the same thing. A Bronsted-Lowry base is a proton acceptor. For example:
H20(l) + NH3(g) <----> NH4+(aq) + OH-(aq)
Ammonia (NH3) is a Bronsted-Lowry base.
Lewis acids are defined as electron pair acceptors, while a Lewis base is an electron pair donor. This concept may be difficult to visualize without electron dot diagrams, so when looking for Lewis acids and bases, be sure to draw out your dot diagrams. If you see a pair of non-bonded electrons on one molecule and another molecule without a full octet (such as boron compounds), you may have a Lewis acid and base. For example, NH3, with its extra pair of non-bonded electrons is a Lewis base while BCl3 is a Lewis acid for there are only six electrons orbiting boron, so it can accept the extra pair of electrons to complete its octet.
If you having trouble remembering the difference between the theories of acids, try coming up with your own mnemonic device. It doesn't matter if they seem silly, for example, you can remember Arrhenius by thinking "AH! ACID!". The "A" in "AH" stands for Arrhenius, while the "H" stands for hydrogen, for Arrhenius was only concerned with hydrogen ions in solutions. You can think "Lewis 'Lectrons", for Lewis was concerned with the movement of electrons.