Help with buffer solutions (triprotic)?

Question

Hi, I am having a bit of trouble with my Chemistry homework. I understand the basics of buffers, but this question is a mite complicated and I'm not quite sure how to approach it:

A buffer consists of 0.25 M NaH2PO4 and 0.15 M Na2HPO4. Phosphoric acid is triprotic with Ka1 = 7.5 × 10^-3, Ka2 = 6.3 × 10^-8, and Ka3 = 4.8 × 10^-13.
A. Which Ka value is most important to this buffer system?
B. What is the pH of the buffer?

For the first one, I'm inclined to say that Ka1 is the most important, but that is just a guess, and I don't know why any one of them would be more important than the others. Please help!

Answer 1

Ka2 is the most important constant, since it involves the equilibrium between the 2 phosporic acid salt species you have.

First, write your equation.
H2PO4 -1 = HPO4 -2 + H+
Let x be [H2PO4] -1 converted to [HPO4] =
Then:
[HPO4]= = 0.15+x
[H2PO4]- = 0.25-x
[H]+ = x
Then: [0.15+x][x]/[0.25-x] = 6.3x10-8
If you look at these numbers, the fraction
[0.15+x]/[0.25-x] can't vary by very much, since x is going to be a number << either term. So we can neglect the x's in these term without losing much accuracy. Then 0.15 x / 0.25 = 6.3x10-8
Then x = 11.5x10-8 or 1.15x10-7.
Finally, pH= -( 10-x) = 7 - log 1.15 = 6.9 appx.

Answer 2

Which Ka value is most important to this buffer system?