Question

CADMIUM SOLUBILITY AND pH Cadmium is a toxic metal. It can be removed from water by chemical precipitation of solid cadmium hydroxide, Cd(OH), The drinking water standard for cadmium is 5 μg L (0.005 mg L). The solubility product of Cd(OH), is 2 x 10" M. What is the minimum pH necessary to reduce the dissolved cadmium ion concentration to the standard?

Answer 1

Explanation:

It is known that,

      Molar mass of Cd = 112.41 g/mol

Standard concentration of Cd = 0.005 mg/L = $0.005 \times 10^{-3}$ g/L

Hence, we will calculate the molarity as follows.

        Molarity = $\frac{0.005 \times 10^{-3}}{112.41} mol/L$

                       = $4.45 \times 10^{-8}$ M

Equation for the reaction is as follows.

          $Cd(OH)_{2} \rightleftharpoons Cd^{2+} + 2OH^{-}$

         $K_{sp} = [Cd^{2+}][OH^{-}]^{2}]$

          $2 \times 10^{-34} = 4.45 \times 10^{-8} \times [OH^{-}]^{2}$

          $[OH^{-}] = 6.7 \times 10^{-4}$ M

Also,

         $[H^{+}] = \frac{10^{-14}}{[OH^{-}]}$

                      = $\frac{10^{-14}}{6.7 \times 10^{-4}}$

                      = $1.49 \times 10^{-11} M$

Relation between pH and concentration of hydrogen ions is as follows.

               pH = $-log [H^{+}]$

                     = $-log (1.49 \times 10^{-11} M)$

                     = 10.82

Thus, we can conclude that a minimum pH of 10.82 is necessary to reduce the dissolved cadmium ion concentration to the standard.