The question is:
What is the pH of equal weights of borax and boric acid dissolved in distilled water? I used 15 g/L of both.
To help with pH measurements, I decided to create a reference-buffer near the pH of the developer I'm working on, and noticed that equal weights of borax and boric acid were close to what I wanted according to the Henderson-Hasselbalch equation. I calculated a pH of 8.28 (at 30C), but measured 8.05, so I was far off. I used a pKa of 9.139 for boric acid at 30C. Furthermore, I know that borax splits into boric acid and its conjugate base upon dissolution, so I added the concentration of borax to that of boric acid. Here's my math:
g = grams of powder per litre
b = 381.37 = mw of Borax
a = 61.83 = mw of boric acid
B = g / b
A = g * (1/b + 1/a)
pH = pKa + log(B/A) = pKa + log(1/(b*(1/b + 1/a)) = pKa + log(1/(1+b/a)) = pKa - log(1 + b/a)
Plugging in the numbers: 9.139 - log(1 + 381.37/61.83) = 8.28
But boric acid is polyprotic, and according to wikipedia, has pKa2=12.74 and pKa3=13.8. I don't know how to account for those. Would they cause my calculation to be in error by 0.23?
Also, before adding the boric acid, I measured the pH of the borax solution as 9.164 (at 30C). It should be 9.14, so my (home-made) pH meter was off by .024, which is accurate enough. So the measurement of 8.05 should be close, so I really am .23 off. Any clue why?