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A LEWIS acid is simply a molecule or ion that can accept an electron pair, while a Lewis base is something that can donate an electron pair. Lewis merely extended the definition of acids and bases beyond the simple Bronsted definition of acid as a proton (H+) donor and base as a proton acceptor. If you think about an example of a Bronsted acid, like HF, he looks at this and says that the HF molecule is an acid because it can donate a proton, and F- is a base because it can accept a proton. By Lewis's definition the F- is still a Lewis acid because it can donate a lone-pair to form a bond with the H+, but the H+ (not HF) is the Lewis acid because it can accept a lone pair to form a bond. So at this point the differences in the definition may seem only like semantics, but there are cases where molecules can be classified as Lewis acids but don't fit the conventional model of a Bronsted or Arrhenius acid. Take BF3 for example. BF3 is a Lewis acid primarily because the boron atom has an incomplete octet---it only has 6 electrons around it coming from the three B-F bonds. BF3 is capable of accepting a lone pair from another molecule to form a bond, and so is considered a Lewis acid. A wonderful example is the reaction between BF3 and NH3. Ammonia has a lone pair of electrons on the nitrogen (so it is a lone-pair donor) and uses it to create a bond with the BF3, giving us a Lewis acid-base reaction: BF3 + NH3 ---> BF3NH3

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