solubility product of M(OH)₂ If its saturated solution has PH 10 at 25 celsius?

The chemical equation:

Mg(OH)₂ ⇌ Mg²⁺ + 2OH¯

2) The K_sp expression:

K_sp = [Mg²⁺] [OH¯]²

3) Use the pH to get the pOH:

14.00 - 10.17 = 3.83

4) Use the pOH to get the [OH¯]:

[OH¯] = 10¯^pOH = 10¯^3.83 = 1.479 x 10¯⁴M

5) From the chemical equation, we note that the [Mg²⁺] is half the value of the [OH¯], therefore:

[Mg²⁺] = 1.479 x 10¯⁴ M divided by 2 = 7.395 x 10¯⁵ M

6) We now have the necessary values to put into the K_sp expression:

K_sp = (7.395 x 10¯⁵) (1.479 x 10¯⁴)²

K_sp = 1.62 x 10¯¹²