Question

The $ {K_{sp}} $ of $ H{g_2}{I_2} $ in aqueous solution is given by $ {x^x}.{y^y}.{s^{x + y}} $ . What is the value of $ (x + y) $ ?

Answer 1

Hint: Solubility Product is defined as the equilibrium constant for sparingly soluble substances or salts in a solution. In sparingly soluble compounds the concentration of undissociated compounds will be more than that of the dissociated ions present in the solution.

Complete answer:
Mercurous Iodide is very less or sparingly soluble in water due to the strong bond between Mercury and iodine. Hence for sparingly soluble salts the solubility product is defined and not equilibrium constant. The solubility constant for sparingly soluble salts is very less. Hence we can say that higher the value of $ {K_{sp}} $ more will be the solubility.
The chemical formula for mercurous iodide is $ H{g_2}{I_2} $ and it is very less dissociated when dissolved in water. Hence the dissociation of the compound can be given as:
  $ H{g_2}{I_2} \rightleftharpoons {[H{g_2}]^{ + 2}} + 2{[I]^ - } $

s

s

2s

The equilibrium constant hence can be given as the ratio of the products to the reactants as:
 $ K = \dfrac{{[H{g_2}^{ + 2}]{{[{I^ - }]}^2}}}{{[H{g_2}{I_2}]}} $
Since the concentration of undissociated ions will be much greater than the dissociated ions, the denominator can be ignored. Hence the solubility product is given as:
 $ {K_{sp}} = [H{g_2}^{ + 2}] \times {[{I^ - }]^2} $
Substituting the concentrations of $ [H{g_2}^{ + 2}]\& [{I^ - }] $ we get the value as:
 $ {K_{sp}} = {(s)^1} \times {(2s)^2} $
 $ {K_{sp}} = {(1)^1}{(2)^2}{s^{2 + 1}} = 4{s^3} $
Thus, the value of $ x = 1 $ and $ y = 2 $
Hence $ x + y = 1 + 2 = 3 $ .

Additional Information:
The Solubility product is affected by various factors:
Common Ion Effect: Presence of an common ion decreases the solubility
Diverse Ion Effect: Presence of diverse or different ions increases the solubility
Ion Pairs: If ion pairs are being present the value of $ {K_{sp}} $ is found to be less than the observed value.

Note:
In mercurous iodide the oxidation state of Hg is $ + 1 $ . Mercury also exists in the $ + 2 $ state and is known as mercuric. Mercurous Iodide is sparingly soluble in water because of its large size and strong covalent bond between Mercury and Iodine. Mercurous Iodide is a common drug used in the $ {19^{th}} $ century to treat acne, kidney diseases etc.