Chemistry - Ionic Equilibrium Question with Solution | TestHub

Given:

Al(OH)₃ ⇌ Al³⁺ + 3OH⁻, $K_{sp}=1.3\times 10^{-33}$

At precipitation threshold:

$K_{sp}=[A{l}^{3+}][O{H}^{-}{]}^3$

$1.3\times 10^{-33}=0.075\times [O{H}^{-}{]}^3$

$[O{H}^{-}{]}^3=\frac{1.3\times 10^{-33}}{0.075}\approx 1.73\times 10^{-32}$

Taking the cube root:

$[O{H}^{-}]\approx 2.57\times 10^{-11}$

$pOH=-\log (2.57\times 10^{-11})\approx 10.59$

$pH=14-10.59=3.41$