Diprotic acids are those acids in their molecules contain two hydrogen acids, potentially separable.
Remember that for the acids oxygenates (or oxyacids), the hydrogens acids are those of -OH groups.
Examples of common diprotic acids are hydrogen sulfide (H 2 S), sulfurous acid (H 2 SO 3), sulfuric acid (H 2 SO 4), orthophosphorous acid (H 3 PO 3) and carbonic acid (H 2 CO 3).
The complete dissociation of a diprotic acid door in solution two moles of H 3 O + per mole of acid.
However, usually, the only significant dissociation is the first.
For certain acids, the first dissociation is quantitative (K a1 very large). And 'the case for example of H 2 SO 4:
For other acids instead, also the first dissociation is partial only. And 'the case for example of H 2 S:
The second dissociation usually is almost insignificant, or at least it is for the purposes of calculation of pH. We take the specific case of the H 2 S. His first dissociation constant is very low. In fact, H 2 S is an acid weak. HS - is its conjugate base, and being the conjugate base of an acid weak and relatively strong and its tendency to donate the second proton acid is really poor.
For further clarification about the calculation of pH see → calculation of pH - solutions of polybasic acids