Question

The hydroxide ion has the formula OH−. The solubility-product constants for three generic hydroxides are given here.

Generic hydroxide	Ksp
XOH	2.70×10−8
Y(OH)2	2.60×10−10
Z(OH)3	7.00×10−15

The removal of an ion is sometimes considered to be complete when its concentration drops to 1.00×10−6  M. What concentration of hydroxide would cause Y2+ to "completely" precipitate from a solution?

Answer 1

     XOH ---------------> X^+ (aq) + OH^-                            

Ksp   = [X^+][OH^-]

2.7*10^-8   = 1*10^-6 *[OH^-]

[OH^-]           = 2.7*10^-8/1*10^-6    = 0.027M

Y(OH)2 --------------> Y^2+ (aq) + 2OH^-

     Ksp   = [Y^2+][OH^-]^2

    2.6*10^-10   = 1*10^-6*[OH^-]^2

    [OH^-]^2      = 2.6*10^-10/1*10^-6   = 2.6*10^-4 M

Z(OH)3 ---------------> Z^3+ (aq) + 3OH^-

      Ksp   = [Z^3+][OH^-]^3

    7*10^-15   = 1*10^-6 *[OH^-]^3

    [OH^-]^3    = 7*10^-15/10^-6    = 7*10^-9 M

   [OH^-]     = 1.9*10^-3M