H3BO3 -> H+ + H2BO3-

Why doesn't H3BO3 break down to something with H3O+ because it is a weak acid? I know many weak acids break down to something with H3O+ like HCN, C6H5COOH, HNO2, and HF.

It does. It is a Lewis acid but not a Bronsted-Lowry acid.

H3BO3 or B(OH)3.
B(OH)3 + HOH ==> H^+ + B(OH)4^
You can read more about it here.

http://en.wikipedia.org/wiki/Boric_acid-

To understand why H3BO3 doesn't break down into H3O+ like other weak acids such as HCN, C6H5COOH, HNO2, and HF, we need to consider its acid-base behavior and the structure of the molecule.

H3BO3, also known as boric acid, is a unique weak acid due to its chemical structure. It contains a boron atom surrounded by three hydroxyl groups (-OH). The hydrogen atom bonded to the hydroxyl group can dissociate, resulting in the formation of the H+ ion and a negative ion, H2BO3-.

The reason H3BO3 doesn't produce H3O+ is due to the weak acidity of the hydroxyl groups attached to the boron atom. In water, weak acids like H3BO3 do not contribute many H3O+ ions because they only partially dissociate. The hydroxyl groups in boric acid are not very acidic, and they do not readily donate protons (H+ ions) to water molecules to form H3O+.

On the other hand, other weak acids like HCN (hydrogen cyanide), C6H5COOH (benzoic acid), HNO2 (nitrous acid), and HF (hydrofluoric acid) have more readily dissociable protons. They are able to donate protons to water molecules more easily, leading to the formation of H3O+ in solution.

In summary, the weak acidity of H3BO3 can be attributed to the relatively low tendency of its hydroxyl groups to donate protons to water molecules. This results in the formation of H+ and H2BO3-, rather than H3O+.