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Can a solution have [H3O+] = 2×[OH]? Can a solution have pH = 2×pOH? If so, will the two solutions be the same?
Assume 25 oC so [H3O+][OH] = Kw = 1.0×1014 and pH + pOH = 14.00.
If [H3O+] = 2×[OH], then 1.0×1014 = [H3O+][OH] = (2×[OH])[OH] = 2[OH]2
or [OH] = 7.1×108 M and [H3O+] =1.4×107 M. There is no reason why a solution could not have these concentrations.
If pH = 2×pOH, 14.00 = pH + pOH = 2×pOH + pOH = 3 pOH
or pOH = 4.67 and pH = 9.33. Again, these are perfectly reasonable and there is no reason why such a solution could not be prepared.
However, the two solutions are not the same. In the first case, the pH = log[H3O+] = log[1.4×107] = 6.85, which is different from the second solution having pH = 9.33.