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Question: \[{K_{sp}}\] of \(CuS\) , \(A{g_2}S\) and \(HgS\) are \({10^{ - 31}}\) ,\({10^{ - 44}}\) and \({10^{...

Ksp{K_{sp}} of CuSCuS , Ag2SA{g_2}S and HgSHgS are 10−31{10^{ - 31}} ,10−44{10^{ - 44}} and 10−54{10^{ - 54}} mol2mo{l^2} litre−2litr{e^{ - 2}} respectively. Select the correct order for their solubility in water.
1. Ag2SA{g_2}S>HgSHgS>CuSCuS
2. HgSHgS>CuSCuS>Ag2SA{g_2}S
3. HgSHgS>Ag2SA{g_2}S>CuSCuS
4. Ag2SA{g_2}S>CuSCuS>HgSHgS

Explanation

Solution

The solubility product constant is the equilibrium constant for the dissolution of a solid substance into an aqueous solution. It is denoted by the symbol Ksp{K_{sp}}. It is found out by using the solubility product of the components given.

Complete Step by step answer:
Equilibrium reaction for dissolution reaction of CuSCuS is:
CuS⇌[Cu+2]+[S−2]CuS \rightleftharpoons [C{u^{ + 2}}] + [{S^{ - 2}}]
So, Ksp{K_{sp}}= [Cu+2][S−2][C{u^{ + 2}}][{S^{ - 2}}] = 10−31{10^{ - 31}}
Hence, we get S2{S^2} =10−31{10^{ - 31}}
Therefore S= 3.16 ×10−16 \times {10^{ - 16}}
Equilibrium reaction for dissolution reaction of Ag2SA{g_2}S is:
Ag2S⇌2Ag++S−2A{g_2}S \rightleftharpoons 2A{g^ + } + {S^{ - 2}}
So, Ksp{K_{sp}}=[Ag+]2[S−2]{[A{g^ + }]^2}[{S^{ - 2}}] = 10−44{10^{ - 44}}
Hence, we get (2S)2(S){(2S)^2}(S) = 10−44{10^{ - 44}}
Therefore, 4S3{S^3} = 10−44{10^{ - 44}}
So, S= 1.357×10−15 \times {10^{ - 15}}
Equilibrium reaction for dissolution of HgSHgS is:
HgS⇌Hg+2+S−2HgS \rightleftharpoons H{g^{ + 2}} + {S^{ - 2}}
So, Ksp{K_{sp}}=[Hg+2][S−2][H{g^{ + 2}}][{S^{ - 2}}] =10−54{10^{ - 54}}
Hence, we get S2{S^2}= 10−54{10^{ - 54}}
Therefore, S= 1×10−271 \times {10^{ - 27}}

Therefore solubility of CuSCuS , Ag2SA{g_2}S and HgSHgS are 3.16×10−16 \times {10^{ - 16}} , 1.357×10−15 \times {10^{ - 15}}and1×10−271 \times {10^{ - 27}}. This implies that the highest solubility is that of Ag2SA{g_2}S and lower than this is of CuSCuS. And lowest solubility is that of HgSHgS according to the values found. So the correct order according to the solubility in water is Ag2SA{g_2}S>CuSCuS>HgSHgS.

So the correct option is 4th.

Note: The solubility product is a kind of equilibrium constant and its value depends on temperature. Ksp{K_{sp}} Usually increases with an increase in temperature due to increased solubility. It should be kept in mind that solubility products represent the extent of dissolution of any compound.