Solution
Barium hydroxide is a strong base for both stages of dissociation:
Ba(OH)
2
(s)→Ba
2+
+2OH
−
So the solution will have 0.20M hydroxide ions. Now use the autodissociation product for water:
[H
+
][OH
−
]=1.0×10
−14
M
[OH
−
]=2.0×10
−1
M
[H
+
]=5.0×10
−14
M
And then
pH=−log
10
([H
+
]=5.0×10
−14
)=13.30.