[Ben Cohen]

The question is: "Calculate the hydronium ion concentration in 50.0 mL of 0.10M NaH2AsO4. K1 = 6.0 x 10^-3. K2 = 1.1 x 10^-7. K3 = 3.0 x 10^-13.

So I know the 50.0 mL doesn't matter, and it's basically H2AsO4^(1-). Other than that, I am confused as to which Ka (or possibly Kb?) or combination of the both to use. I know how to write Ka and Kb expressions, but I don't know how to start the problem.

[AWK]

For pH calculation forget about K₂ and K₃. Treat this acid analogously to  monoprotic acids.

[Borek]

Also check http://www.chembuddy.com/?left=pH-calculation&right=pH-polyprotic-simplified

[AhBeng]

If the question was asking the pH of the fully protonated form (eg. H3AsO4), then as AWK mentioned, treat polyprotic acids as a monoprotic acid and use only Ka1 to calculate pH. For a solution of H3AsO4, only Ka1 is relevant.

If the question was asking the pH of a solution containing only the fully deprotonated form (eg. AsO4 3-), then treat polyprotic bases simply as a monoprotic base and use only the relevant Kb value to calculate pH. For a solution of AsO4 3-, only Kb3 is relevant (to be precise : Kb3 as defined mathematically by Ka3 x Kb3 = Kw).

For a solution containing only an amphiprotic species (ie. a species that has the capacity to both accept a proton and donate a proton), the pH of the solution may be approximated to :
pH = (1/2)(pKa1 + pKa2)

For a solution of H2AsO4 -, pKa1 and pKa2 are relevant.
For a solution of HAsO4 2-, pKa2 and pKa3 are relevant.

For a solution containing both members of any conjugate acid-base pair (eg. H3AsO4 and H2AsO4 -, or H2AsO4 - and HAsO4 2-, or HAsO4 2- and AsO4 3-), then we have a buffer system, in which case you should use the Henderson-Hasselbalch equation, involving the relevant pKa (ie. of the acidic species present) in the formula :

pH = pKa + log ( [basic] / [acidic] )