If the $K_{sp}$ of $Mg(OH)_2$ is $1 \times 10^{-12}$,at what $pH$ will $Mg(OH)_2$ precipitate from a $0.01 \ M$ solution of $Mg^{2+}$ ions?

Derive the solubility product $(K_{sp})$ expression for the following sparingly soluble salts:
$(i)$ Two ions having $MX$ formula
$(ii)$ Three ions having $MX_{2}$ or $M_{2}X$ types
$(iii)$ Four ions having $AX_{3}$ or $A_{3}X$ type salts
$(iv)$ Five ions $A_{2}X_{3}$ or $A_{3}X_{2}$ type salts.

The solubility product of Lead sulphate,$PbSO_4$ is $1.3 \times 10^{-8}$. Calculate its solubility in pure water. The molecular mass of $PbSO_4 = 303 \ g \ mol^{-1}$.

The $K_{sp}$ of $CaF_2$ is $1.7 \times 10^{-10}$. What is the volume in $mL$ of a saturated solution containing $10 \ mg$ of $CaF_2$? (Molecular mass of $Ca = 40, F = 19$).

$K_{sp}$ for $BaSO_4$ at $25 \, ^oC$ is $1.1 \times 10^{-10}$. To make the new solubility equal to $1.1 \times 10^{-8} \, M$,it is necessary to use a solution of $Na_2SO_4$ of the following concentration $....... \ M$

Solubility of calcium phosphate (molecular mass,$M$) in water is $W \ g$ per $100 \ mL$ at $25^{\circ} C$. Its solubility product at $25^{\circ} C$ will be approximately.