What is the molar solubility of $Ag_{2}CO_{3}$ $(K_{sp} = 4 \times 10^{-13})$ in $0.1 \ M \ Na_{2}CO_{3}$ solution?

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

Match the following metal sulfides with their respective solubility product $(K_{sp})$ values:

Metal sulfide	Solubility product
$A$. $PbS$	$I$. $4.0 \times 10^{-53}$
$B$. $HgS$	$II$. $8.0 \times 10^{-28}$
$C$. $MnS$	$III$. $1.6 \times 10^{-24}$
$D$. $ZnS$	$IV$. $2.5 \times 10^{-13}$

If the solubility of salts $M_2X$,$QY_2$,and $PZ_2$ is the same,what is the relationship between their $K_{sp}$ values?

Assign $A, B, C, D$ from the given type of reaction: $PbCl_2(s) + \text{Hot water} \longrightarrow Pb^{2+}(aq) + 2Cl^{-}(aq)$

If $K_{sp}$ of $Ag_2CO_3$ is $8 \times 10^{-12},$ the molar solubility of $Ag_2CO_3$ in $0.1 \ M \ AgNO_3$ is