What is the [Tl3+] in a solution that is buffered at pH 11.50 at 25 °C? The Ksp of Tl(OH)3 is 2 × 10–44 at 25 °C.?

pOH = pKw - pH = 14.00 - 11.50 = 2.50
[OH⁻] = 10⁻²·⁵⁰ M

       Ti(OH)₃(s)  ⇌  Ti³⁺(aq)  +  3OH⁻(aq)        Ksp = 2 × 10⁻⁴⁴
Initial:                      0 M           10⁻²·⁵⁰ M
Change:                +s M            +3s M
Eqm:    　　　        s M        (10⁻²·⁵⁰ + 3s) M
                                                ≈ 10⁻²·⁵⁰ M

At equilibrium:
Ksp = [Ti³⁺] [OH⁻]³
2 × 10⁻⁴⁴ = s (10⁻²·⁵⁰)³
s = (2 × 10⁻⁴⁴) / (10⁻²·⁵⁰)³
s = 6.3 × 10⁻³⁷
[Ti³⁺] = 6.3 × 10⁻³⁷ M