Which of the following is most soluble?

Options

A. `Bi_(2)S_(3)(K_(sp) =1xx10^(-70))`
B. `MnS(K_(sp)=7 xx 10^(-16))`
C. `CuS(K_(sp)=8 xx 10^(-37))`
D. `Ag_(2)S(K_(sp)=6 xx 10^(-51))`

Answer

B

Explanation

Let S be the solubility in each case
`Bi_(2)S_(3) hArr 2Bi^(2+)+3S^(2-)`
`:. K_(sp)=(2S)^(2)(3S)^(3)=108S^(5)`
`:. S=((1xx10^(-70))/(108))^(1//5)~~3.9 xx 10^(-15)M`
`MnS hArr Mn^(2+)+S^(2-),S=(7 xx 10^(-16))^(1//2)~~2.6 xx 10^(-8)M`
`CuShArr Cu^(2+)+S^(2-),S=(8 xx 10^(-37))^(1//2)~~8.9xx10^(-19)M`
`Ag_(2)S hArr 2Ag^(+)+S^(2),S=((6 xx 10^(-51))/(4))~~1.4 xx 10^(-17)M`
Thus, most soluble is MnS.