What is the $pH$ at which $Mg(OH)_2$ starts to precipitate from a solution containing $0.1 \ M \ Mg^{2+}$ ions? (Given $K_{sp}$ for $Mg(OH)_2 = 1.0 \times 10^{-11}$)

Sodium sulfate is soluble in water,whereas barium sulfate is sparingly soluble. Why?

Formula	Solubility product $(K_{sp})$
$AgBrO_3$	$2.5 \times 10^{-10}$
$MgSO_4$	$2.7 \times 10^{-27}$
$CaCO_3$	$2.7 \times 10^{-18}$
$FeC_2O_4$	$2.4 \times 10^{-15}$

Which of the following salts has the maximum solubility?

Solid $Ba(NO_3)_2$ is gradually added to a $1.0 \times 10^{-4} \, M \, Na_2CO_3$ solution. At what concentration of $Ba^{2+}$ will precipitation start? (Given $K_{sp}$ for $BaCO_3 = 5.1 \times 10^{-9}$)

The $K_{sp}$ value of $AgCl$ at $25^{\circ}C$ is $1.8 \times 10^{-10}$. If $10^{-5} \ mol$ of $Ag^{+}$ is added to the solution,the new $K_{sp}$ value will be:

For a compound $AB$,the degree of ionization is $80\%$. What is the solubility $(s)$ of $AB$ if its solubility product $(K_{sp})$ is $6.4 \times 10^{-9}$?