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

If the $[F^{-}] = 2.0 \times 10^{-5} \ M$ in water,how many grams of $CaCl_{2}$ must be added to initiate the precipitation of $CaF_{2}$? Given: $K_{sp}$ for $CaF_{2} = 1.7 \times 10^{-10}$ and the molar mass of $CaCl_{2} = 111 \ g \ mol^{-1}$. Assume the volume of the solution is $1 \ L$.

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 of $BaSO_{4}$ in water is $2.42 \times 10^{-3} \ g \ L^{-1}$ at $298 \ K$. The value of solubility product $(K_{sp})$ will be (Given molar mass of $BaSO_{4} = 233 \ g \ mol^{-1}$)

The solubility of $AgCl$ in water is $1.43 \times 10^{-3} \ g \ L^{-1}$. What is the value of $K_{sp}$ for $AgCl$ at $25 \ ^oC$?

The molar solubility of $PbI_2$ in $0.2 \ M \ Pb(NO_3)_2$ solution in terms of solubility product of $PbI_2$ is