pH of M/500 barium hydroxide is
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pH=13.30 .
Barium hydroxide is a strong base for both stages of dissociation:
Ba(OH)2(s)→Ba2++2OH−
So the solution will have 0.20 M hydroxide ions. Now use the autodissociation product for water:
[H+][OH−]=1.0×10−14M
[OH−]=2.0×10−1M
[H+]=5.0×10−14M
And then
pH=−log10([H+]=5.0×10−14)=13.30 .