[doodlebug]

I've been trying for the past hour trying to figure this out, I keep getting the wrong answer. Can someone please walk through this problem?

1.0 L of an aqueous solution in which [H2CO3]=[HCO3–]= 0.10 M, has [H+]= 4.2 x 10–7.
What is the [H+] after 0.005 mole of NaOH has been added?

[DevaDevil]

first calculate the Ka of H₂CO₃ / HCO₃^- with the given values
 
then assume the NaOH is fully neutralized by the buffer (every H₂CO₃ takes a OH^- to form HCO₃^- and water), and neglect the volume change of adding the NaOH
this will give you the new concentrations of H₂CO₃ and HCO₃^-

then recalculate the (new) concentration of H+ with the new values for [H₂CO₃] and [HCO₃^-] (Henderson-Hasselbalch equation for pH)