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

Step-by-step explanation:

It is known that,

Molar mass of Cd = 112.41 g/mol

Standard concentration of Cd = 0.005 mg/L =
`0.005 * 10^(-3)` g/L

Hence, we will calculate the molarity as follows.

Molarity =
`(0.005 * 10^(-3))/(112.41) mol/L`

=
`4.45 * 10^(-8)` M

Equation for the reaction is as follows.

`Cd(OH)_(2) \rightleftharpoons Cd^(2+) + 2OH^(-)`

`K_(sp) = [Cd^(2+)][OH^(-)]^(2)]`

`2 * 10^(-34) = 4.45 * 10^(-8) * [OH^(-)]^(2)`

`[OH^(-)] = 6.7 * 10^(-4)` M

Also,

`[H^(+)] = (10^(-14))/([OH^(-)])`

=
`(10^(-14))/(6.7 * 10^(-4))`

=
`1.49 * 10^(-11) M`

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

pH =
`-log [H^(+)]`

=
`-log (1.49 * 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.