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I tried working this problem out a few different ways and keep getting different answers. The last calculation I tried gave me a pKa of 4.44.

I'm using pH = pKa + log [A-]/[HA] I used pH = pKa-log[HA] / 2 to get an HA of 1.38. I plugged 8.17 and 4.2 in respectively as pH and pKa. Looking at it now that doesn't seem right.

But where I get stuck is how to add the 0.01 moles of HCl into the equation. I also was wondering if the answer is much more simple than I think it is. At the second ionizable group's pKa it would equal the pH right? So if that's the case is the pKa just 8.17? Or am I just completely wrong?