The solubility product of $PbS$ is $3.4 \times 10^{-28}$. If $[Pb^{2+}] = 1 \times 10^{-2} \ mol/L$,what concentration of $[S^{2-}]$ is required to precipitate $PbS$?

Solubility product constant $(K_{sp})$ of salts of types $MX$,$MX_2$ and $M_3X$ at temperature '$T$' are $4.0 \times 10^{-8}$,$3.2 \times 10^{-14}$ and $2.7 \times 10^{-15}$,respectively. Solubilities $(\text{mol } dm^{-3})$ of the salts at temperature '$T$' are in the order:

The solubility products of $NiS$,$ZnS$,$CdS$,and $HgS$ are $4.7 \times 10^{-5}$,$1.6 \times 10^{-24}$,$8 \times 10^{-27}$,and $4 \times 10^{-53}$ respectively. An aqueous solution contains $Ni^{2+}$,$Zn^{2+}$,$Cd^{2+}$,and $Hg^{2+}$ of equal concentration. $H_2S$ gas was passed into this solution very slowly. The first and the last ions that precipitate as sulphides are respectively.

At $298 \ K$,the solubility of silver chloride in water is $1.434 \times 10^{-3} \ g \ L^{-1}$. The value of $-\log K_{sp}$ for silver chloride is $........$ (Given: molar mass of $Ag = 107.9 \ g \ mol^{-1}$ and $Cl = 35.5 \ g \ mol^{-1}$)

Derive the solubility product $(K_{sp})$ expression for the following sparingly soluble salts:
$(i)$ Two ions having $MX$ formula
$(ii)$ Three ions having $MX_{2}$ or $M_{2}X$ types
$(iii)$ Four ions having $AX_{3}$ or $A_{3}X$ type salts
$(iv)$ Five ions $A_{2}X_{3}$ or $A_{3}X_{2}$ type salts.

The solubility product of a binary weak electrolyte is $4 \times 10^{-10}$ at $298 \ K$. Its solubility in $\text{mol} \ dm^{-3}$ at the same temperature is