Polyprotic acids like H2SO4 dissociate in solution to produce two (or more, for H3PO4, for example) protons in a stepwise manner, as shown here:
H2SO4↔ H˄+ + HSO4˄-
HSO4˄- ↔ H˄+ + SO4˄2-
While the first proton is removed from a neutral molecule, the second (and any subsequent) proton is removed from a species that has negative charge upon itself. Removing a second proton is more difficult because of electrostatic force of attraction between the positively charged proton (H+) and the negatively charged residue. If the acid were triprotic it would still be harder to remove the third proton. The phenomenon is well evidenced in the K1, K2 and K3 values of polyprotic acids such as:
H2SO4, K1 = very large, K2 = 1.2 × 10˄-2
H3PO4, K1 = 7.1 × 10˄-3, K2 = 6.3 × 10˄-8, K3 = 4.5 × 10˄-13
H2CO3, K1 = 4.5 × 10˄-7, K2 = 4.7 × 10˄-11
H2C2O4, K1 = 5.36 × 10˄-2, K2 = 5.34 × 10˄-5.