To calculate the pH of a mixture of 100 mL of 0.20 M acetic acid (HOAc) and 100 mL of 0.10 M barium hydroxide (Ba(OH)2), one must consider the equivalents of the reactants. The initial calculation shows 20 mmol of HOAc and 10 mmol of Ba(OH)2, leading to a net of 10 mmol of acetic acid remaining. However, the discussion highlights that Ba(OH)2 is dibasic, which means it can provide two hydroxide ions per molecule, affecting the neutralization process. The correct approach involves using the Kb of the acetic acid's conjugate base to find the hydroxide concentration and subsequently the pH. The initial conclusion of a pH of 12.7 is incorrect, as the presence of excess acetic acid suggests a pH below 7.