The solubility of $BaCl_2$ is $4 \times 10^{-6} \ M$. Calculate its $K_{sp}$. Also,find its new solubility in the presence of $10^{-2} \ M \ Ba(OH)_2$.

The solubility of a salt of weak acid $(AB)$ at $pH = 3$ is $Y \times 10^{-3} \ mol \ L^{-1}$. The value of $Y$ is (Given that the value of solubility product of $AB$ $(K_{sp}) = 2 \times 10^{-10}$ and the value of ionization constant of $HB$ $(K_{a}) = 1 \times 10^{-8}$)

If the solubility of $Ca_3(PO_4)_2$ in water is $x \ mol \ L^{-1}$, its solubility product in $mol^5 \ L^{-5}$ is (in $x^5$)

If the $pH$ of a $0.001 \, M \, Mg(NO_3)_2$ solution is $9$,will precipitation occur? Given the $K_{sp}$ of $Mg(OH)_2 = 8.9 \times 10^{-12}$.

Using the Gibbs energy change,$\Delta G^{o} = +63.3 \ kJ \ mol^{-1}$,for the following reaction in water at $25 \ ^{\circ}C$,calculate the solubility product constant $(K_{sp})$:
$Ag_{2}CO_{3(s)} \rightleftharpoons 2Ag^{+}_{(aq)} + C{O_{3}}^{2-}_{(aq)}$
$(R = 8.314 \ J \ K^{-1} \ mol^{-1})$

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 $BaCO_3 = 5.1 \times 10^{-9}$)