Ionization of sulfuric acid in water and its final pH?

ume a certain m of H2SO4 were dissolved in water giving a solution with a certain molarity.does the pH depend solely on the first ionization ONLY or does the second dissociation,ie, HSO4- -----> SO4 2- + H+,too influences the pH?if so how do we calculate the final pH or the hydronium concentration at equilibrium given tht we knw the second ionization acid constant?do we add the H+ conc in both ionizations?