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Question: The solubility product of \(CuS\), \(A{g_2}S\) and \(HgS\) are \({10^{ - 31}},{10^{ - 44}},{10^{ - 5...

The solubility product of CuSCuS, Ag2SA{g_2}S and HgSHgS are 10−31,10−44,10−54{10^{ - 31}},{10^{ - 44}},{10^{ - 54}} respectively. The solubilities of these sulphides are in the order.
A. HgS>Ag2S>CuSHgS > A{g_2}S > CuS
B. CuS>Ag2S>HgSCuS > A{g_2}S > HgS
C. Ag2S>CuS>HgSA{g_2}S > CuS > HgS
D. Ag2S>HgS>CuSA{g_2}S > HgS > CuS

Explanation

Solution

Solubility is a property which is referred to the ability for a given substance for a solute to dissolve in a given solvent. It is measured in terms of the maximum amount of solute dissolved in a solvent at equilibrium. This resulting solution is called a saturated solution.

Complete step-by-step answer:
In the question above, it’s clear that we have to solve the solubility of the given sulphides. Therefore, to find out the solubility, we have to put in the solubility product constant Ksp{K_{sp}} and check the most soluble sulphide in the three provided in the question. Now when we put the solubility product constant and check the highest soluble sulphide and lowest soluble sulphide.
As we look into CuSCuS, Solubility is (10−31)1/2=(10−31/2){\left( {{{10}^{ - 31}}} \right)^{1/2}} = \left( {{{10}^{ - 31/2}}} \right)
As we look into HgSHgS, Solubility is (10−54)1/2=(10−54/2)=(10−27){\left( {{{10}^{ - 54}}} \right)^{1/2}} = \left( {{{10}^{ - 54/2}}} \right) = \left( {{{10}^{ - 27}}} \right)
As we now look into Ag2SA{g_2}S, is (10−44)1/3=(10−44/3){\left( {{{10}^{ - 44}}} \right)^{1/3}} = \left( {{{10}^{ - 44/3}}} \right)
Now it is clear when we look into the values above which is by applying a solubility product constant that Ag2SA{g_2}S stands highest in solubility and HgSHgS is the lowest in the solubility.
Therefore it goes like- Ag2S>CuS>HgSA{g_2}S > CuS > HgS

Additional information:
Now there are several factors which can affect the rate or amount of solubility:
Temperature: with an increase in temperature the solute gets more easily dissolved in the solvent.
Polarity: when the solute and solvent are of similar polarity then it dissolves easily, therefore, there goes the term “ like dissolves like”.
Pressure: pressure does not affect solubility.
Molecular size: with an increase in the molecular size of the solute the solubility decreases therefore smaller molecules are easily soluble.
Stirring: stirring makes the rate of solution faster.

Hence, the right option is C.

Note: Solubility can also be viewed in the point of view of dissociation of an ionic compound. as we dissolve ionic salts in the water they get dissociated into cation and anion where both of the ions are attracted to the opposite charges of a water molecule.