If 1.1 moles of HCl were mixed with 1.0 moles Na2CO3, the final pH would fall into which of the following ranges?
(for carbonic acid, pKa1 = 6.4 and pKa2 = 10.8)
A. pH < 3.0
B. 3.0 < pH < 6.4
C. 6.4 < pH < 10.8
D. pH > 10.8
Answer: C
I eliminated A and D right off the bat. But how do you decide between B and C?
So with 1 mole of sodium carbonate and 1.1 moles HCl, we know that the CO3 (2-) will be completely neutralized, with enough HCl left over to neutralize some of the HCO3-... 0.1 moles to be exact. So, we have
some H2CO3, corresponding to the pKa1 of 6.4, and the rest is HCO3-, corresponding to the pKa2 of 10.8. So, given that we have only these two species with the majority being HCO3-, we know that the pH has to be between 6.4 and 10.8.
This can also be proven mathematically using a slight variation of the Henderson-Hasselbach equation. We all know this as:
pH = pKa + log ([B-]/[HA]).
But there's a similar version for bases, stating:
pOH = pKb + log([BH]/[B-]) where BH is the protonated base in question.
For our purposes, we have 0.1 moles left of HCl after the first equivalence. So there will be 0.1 moles of H2CO3 created, and 0.9 moles left of HCO3-. The pKb for H2CO3 is 14 - pKa1 = 14 - 6.4 = 7.6. Plugging the values into the equation, we get:
pOH = 7.6 + log (0.1/0.9) = 6.65
To find the pH, we take 14 - pOH, or 14 - 6.65 = 7.35. So the pH at this point is 7.35, confirming what we already know, namely that it's between 6.4 and 10.8.
