[Big-Daddy]

Problem:
Calculate the concentration of hydrogen ions in a solution of sodium sulfite (c = 0.010 molL-1), at 25°C, from the following data:

SO₂(aq) + 2H₂O(l)  HSO₃^-(aq) + H₃O⁺(aq) K_a1 = 10^-1,92 molL-1
HSO₃^-(aq) + H₂O(l)  SO₃^2-(aq) + H₃O⁺(aq) K_a2 = 10^-7,18 molL-1.

Comments:
I'm guessing water's auto-ionization can be neglected. Question is, once Na₂SO₃ is fully dissolved, how can I get an approximate answer for how much H₃O⁺ is produced? I could do the full-length mass balance, charge balance, +2 equilibrium equations (in fact these are all the same as for the case of SO2 itself being dissolved in water, or sodium hydrogensulfite being dissolved in water: 0.010=[SO2]+[HSO3-]+[SO32-], [H3O+]=[HSO3-]+2[SO32-] and the two equilibria given) thing but is that the only way for this sum?

Also, since the equations are the same as they would be if SO2 of original concentration c = 0.010 molL-1 were dissolved in water, or NaHSO3 of this same concentration were dissolved in water, then is it ok to say the same equilibrium concentrations of all 4 variables ([SO₂], [HSO₃^-], [SO₃^2-], [H₃O⁺], neglecting [OH-], which by the way would also be the same) would be present in all 3 of these proposed solutions?