If the solubility product of a base $M(OH)_3$ is $2.7 \times 10^{-11}$,find the concentration of $OH^-$.

If the molar solubility (in $mol \cdot L^{-1}$) of a sparingly soluble salt $AB_4$ is $S$ and the corresponding solubility product is $K_{sp}$,then $S$ in terms of $K_{sp}$ is given by the relation:

Calculate the minimum concentration of sulphate ion required to precipitate $BaSO_4$ in a solution containing $10^{-4} \ mol/L$ of $Ba^{2+}$. $(K_{sp} \ BaSO_4 = 4 \times 10^{-10})$

For the following Assertion and Reason,the correct option is
Assertion $(A) :$ When $Cu^{2+}$ and sulphide ions are mixed,they react together extremely quickly to give a solid.
Reason $(R) :$ The equilibrium constant of $Cu^{2+}_{(aq)} + S^{2-}_{(aq)} \rightleftharpoons CuS_{(s)}$ is high because the solubility product is low.

Determine the solubilities of silver chromate,barium chromate,ferric hydroxide,lead chloride,and mercurous iodide at $298 \, K$ from their solubility product constants. Determine also the molarities of individual ions. (Given $K_{sp}$ values: $Ag_{2}CrO_{4} = 1.1 \times 10^{-12}$,$BaCrO_{4} = 1.2 \times 10^{-10}$,$Fe(OH)_{3} = 1.0 \times 10^{-38}$,$PbCl_{2} = 1.6 \times 10^{-5}$,$Hg_{2}I_{2} = 4.5 \times 10^{-29}$)

The solubility product of $AgBr$ is $4.9 \times 10^{-13}$ at a certain temperature. Calculate the solubility.