Up to what $pH$ must a solution containing a precipitate of $Cr(OH)_3$ be adjusted so that the precipitate just dissolves? (Given: $[Cr^{3+}] = 0.1 \ mol/L$,$K_{sp} = 6 \times 10^{-31}$)

The solubility product of $Cr(OH)_3$ at $298 \ K$ is $6.0 \times 10^{-31}$. The concentration of hydroxide ions in a saturated solution of $Cr(OH)_3$ will be

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

Let the solubility of an aqueous solution of $Mg(OH)_2$ be $x$,then its $K_{sp}$ is:

Observe the following solutions:
$(i)$ $1 \ L$ of $10^{-6} \ M \ AgNO_3$
$(ii)$ $1 \ L$ of $10^{-7} \ M \ AgNO_3$
$(iii)$ $1 \ L$ of $10^{-9} \ M \ AgNO_3$
$(iv)$ $1 \ L$ of $10^{-3} \ M \ AgNO_3$
$(v)$ $1 \ L$ of $10^{-5} \ M \ NaCl$
Which of the above two solutions when mixed will give a white precipitate,$AgCl$?
$(Given \ K_{sp} \ of \ AgCl = 1 \times 10^{-10})$

Consider the following salts: $NaCl, HgCl_{2}, Hg_{2}Cl_{2}, CuCl_{2}, CuCl$ and $AgCl$. Identify the correct set of insoluble salts in water.