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

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 $(K_{sp})$:
$Ag_{2}CO_{3(s)} \rightleftharpoons 2Ag^{+}_{(aq)} + C{O_{3}}^{2-}_{(aq)}$
$(R = 8.314 \ J \ K^{-1} \ mol^{-1})$

For the equilibrium reaction: $Fe(OH)_3(s) \rightleftharpoons Fe^{3+}(aq) + 3OH^-(aq)$,if the concentration of $OH^-$ is reduced to $\frac{1}{4}$ of its initial value,by what factor will the concentration of $Fe^{3+}$ increase at equilibrium?

Zirconium phosphate $[Zr_3(PO_4)_4]$ dissociates into three zirconium cations of charge $+4$ and four phosphate anions of charge $-3$. If molar solubility of zirconium phosphate is denoted by $S$ and its solubility product by $K_{sp}$,then which of the following relationships between $S$ and $K_{sp}$ is correct?

The solubility of $AgCl$ is $1 \times 10^{-5} \ mol/L$. Its solubility in $0.1 \ M$ sodium chloride solution is

The $pH$ at which $Mg(OH)_2$ $[K_{sp} = 1 \times 10^{-11}]$ begins to precipitate from a solution containing $0.10 \ M$ $Mg^{2+}$ ions is . . . . . .