H2CO3 = OC(OH)2 so pKa1 ~ 8 – 5(1) ~ 3 and pKa2 ~ 3 + 5 = 8. These do not match the experimental values at all. The reason is due to the instability of carbonic acid towards dissociation carbon dioxide and water. Thus, there are competing equilibria:
H2CO3(aq) + H2O(l) ⇄H3O+(aq) + HCO3–(aq)
H2CO3(aq) ⇄CO2(g) + H2O(l)
The second equilibrium reduces the amount of hydronium ion available in solution, reducing the apparent pKa of carbonic acid. The reported values are better thought of as the pKa values for CO2(aq).