Calculate moles of bicarbonate and carbonate:
HCO3¯: (0.384 mol/L)(0.2250 L) = 0.0864 mol
CO32¯: (0.239 mol/L)(0.2250 L) = 0.053775 mol
The hydroxide reacts with the acid (the bicarbonate):
HCO3¯ decreases: 0.0864 - 0.0464 = 0.0400 mol
CO32¯ increases: 0.053775 + 0.0464 = 0.100175 mol
Need pKa of bicarbonate:
Ka of HCO3¯ is the same as the Ka2 of H2CO3.
Ka of HCO3¯ = 4.7 x 10¯11
pKa = 10.252
Use Henderson-Hasselbalch Equation:
pH = 10.328 + log (0.100 / 0.04)
pH = 10.328 + 0.398 = 10.726