The least soluble compound (salt) of the following is

Options

A. `CsCI(K_(sp)=10^(-12))`
B. `HgS(K_(sp)=1xx10^(-52))`
C. `PbCI_(2)(K_(sp)=1.7xx10^(-5))`
D. `ZnS(K_(sp)=1.2xx10^(-23))`

Answer

B

Explanation

Let the solubility of the salt be S mol `L^(-1)`
`CsCl(s)hArrCs^(+)(aq.)+Cl^(-)(aq.)`
`K_(sp)=S^(2)`
or `S= sqrt(K_(sp))=sqrt(10^(-12))=10^(-6)mol L^(-1)`
`HgS(s)hArr Hg^(2+)(aq.)+S^(2-)(aq.)`
`K_(sp)=S^(2)`
or `S=sqrt(K_(sp))=sqrt(10^(-52))=10^(-26)mol L^(-1)`
`PbCl_(2)hArr Pb^(2+)(aq.)+2Cl^(-)(aq.)`
`K_(sp)=(S)(2S)^(2)= 4S^(3)`
or `S= ((K_(sp))/(4))^(1//3) = ((1.7xx10^(-5))/(4))^(1//3)`
`ZnS(s) hArr Zn^(2+)(aq.)+S^(2-)(aq.)`
`K_(sp)=S^(2)`
or `S=sqrt(K_(sp))= sqrt(1.2xx10^(-23))`
`=sqrt(12xx10^(-24))`
`=3.5xx10^(-12)mol L^(-1)`
Thus, the least soluble compound is HgS.