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The definition of bronstead acid/base is that it is a proton donor/acceptor. Looking at NH3, the hydrogen atoms bound to the nitrogen are not likely to fall off and bind to another atom since NH bonds are not polar enough to give the hydrogen a sufficiently positive charge to allow it to bind to an electronegative atom on another molecule; therefore, NH3 is not likely to be a proton donor. However, there are two lone pair atoms on the nitrogen atom that can form a coordinate covalent bond with proton(H+) donated by another molecule; therefore, NH3 is more likely to be a proton acceptor(bronsted base).
You need to look at the chemical formula and see if the molecule is more likely to accept or donate an H+ ion. Since NH3 has a lone pair on the N, it is more likely to accept a proton and is therefore considered a weak base. However, it's also good to memorize common acids and bases.
Bronsted acids and bases are determined by whether they donate or accept protons. Remember, protons are just H+ ions. Since this is just a hydrogen atom with no electrons, it is attracted to lone pairs, almost like a ligand. Since NH3 has a lone pair, it readily accepts hydrogen atoms, therefore it is a Bronsted base.
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