Question

The solubility product of magnesium hydroxide in pure water is $ 8.2 \times {10^{ - 5}} $ mol per 500 ml of water. The solubility product of magnesium hydroxide is:

A.  $ 6.72 \times {10^{ - 9}}{M^2} $ 

B.  $ 5.51 \times {10^{ - 13}}{M^3} $ 

C.  $ 8.84 \times {10^{ - 12}}{M^3} $ 

D.  $ 1.77 \times {10^{ - 11}}{M^3} $ 

Answer 1

Hint: Solubility product of a solution is defined as the product of concentration of its ions in a saturated solution with each concentration raised to the power equal to the number of ions produced on dissociation of one molecule of the solution. It is denoted by Ksp and for a molecule  $ {A_x}{B_y} $  it is calculated using the formula shown below:

$ {K_{sp}} = {[{A^{y + }}]^x}[{B^{x - }}^y] $ 

Complete step by step answer:

As per above question, the solubility of Magnesium hydroxide is given for 500ml of water, so the solubility per litre of the molecule is found as:

$ 2 \times 8.2 \times {10^{ - 5}} $  mol per litre

$  \Rightarrow 1.64 \times {10^{ - 4}} $  mol per litre

Now as we know on dissociation, Magnesium Hydroxide ( $ Mg{(OH)_2} $ ) dissociates into one ion of Magnesium ( $ M{g^{2 + }} $ ) and two ions of hydroxide ( $ O{H^ - } $ ). The resulting equation is shown below:

$ Mg(OH) _{2} \to Mg^{2 +} + 2OH^{-} $ 

We are given the solubility(s) for Magnesium hydroxide and it the solubility for Magnesium will be equal to the solubility for Magnesium Hydroxide and that for Hydroxide ion will be twice that of Magnesium. Hence, the solubility product  $ K_{sp} $  is shown as:

$ {K_{sp}} = [M{g^{2 + }}]{[O{H^ - }]^2}  $ 

$ \Rightarrow {K_{sp}} = (1.64 \times {10^{ - 4}}){(2 \times 1.64 \times {10^{ - 4}})^2}  $ 

$ \Rightarrow {K_{sp}} = (1.64 \times {10^{ - 4}}){(3.28 \times {10^{ - 4}})^2}  $ 

$ \Rightarrow {K_{sp}} = (1.64 \times {10^{ - 4}})(10.7584 \times {10^{ - 8}})  $ 

$ \Rightarrow {K_{sp}} = 17.643 \times {10^{ - 12}}  $ 

$ \Rightarrow {K_{sp}} = 1.77 \times {10^{ - 11}}{M^3}  $ 

Hence, the answer is option (D).

Note: The product of the concentrations of ions in the solution, raised to the power equal to the number of ions, when one molecule is dissociated in the solution by Ionic Product. The basic difference between Ionic and solubility product are:

Ionic products are more general and are applicable to both saturated and unsaturated solutions, whereas solubility products are defined for the saturated solution.

Ionic products depend on the concentrations of ions and whereas solubility products are constant at constant temperature.