Determine the solubilities of silver chromate, barium chromate, ferric hydroxide, lead chloride and mercurous iodide at 298 K form their solubility product constants given below. Determine also the molarities of individual ions.
`K_(SP(Ag_(2)CrO_(4)))=1.1xx10^(-12)`,
`K_(SP(BaCrO_(4)))=1.2xx10^(-10)`,
`K_(SP[Fe(OH)_(3)])=1.0xx10^(-38)`,
`K_(SP(PbCI_(2)))=1.6xx10^(-5)`,
`K_(SP(Hg_(2)I_(2)))=4.5xx10^(-29)`.

Explanation

For `Ag_(2)CrO_(4): K_(SP)= 4S^(3)`
`Ag_(2)CrO_(4)hArr2Ag^(+)+CrO_(4)^(2-)`
`S=3sqrt((K_(SP))/(4))=3sqrt((1.1xx10^(-12))/(4))`
`=6.5xx10^(-5)M`
`[Ag^(+)]=2xx6.5xx10^(-5)`
`=1.30xx10^(-4)M`
`[CrO_(4)^(2-)]=6.5xx10^(-5)M`
For `BaCrO_(4):`
`BaCrO_(4)hArr underset(S)(Ba^(2+))+underset(S)(CrO_(4)^(2))`
`K_(SP)=S^(2)`
`S=sqrt(K_(SP))=sqrt(1.2xx10^(-10))`
`=1.1xx10^(-5)M`
`[Ba^(2+)=1.1xx10^(-5)M=[CrP_(4)^(2)]`
For `Fe(OH)_(3):`
`Fe(OH)_(3)hArr underset(S)(Fe^(3+))+underset(3S)(3OH^(-))`
`K_(SP)=27S^(4)`
`:. S=4sqrt((K_(SP))/(27))=4sqrt((1.0xx10^(-38))/(27))`
`=1.39xx10^(-10)M`
`:. [Fe^(3+)]=1.39xx10^(-10)M`
`[OH^(-)]=1.39xx10^(-10)xx3`
`=4.17xx10^(-10)M`
For `PbCI_(2):`
`PbCI_(2)hArr underset(S)(Pb^(2+))+underset(2S)(2CI^(-))`
`K_(SP)=4S^(3)`
`:. S=3sqrt((K_(SP))/4)=3sqrt((1.6xx10^(-5))/(4))`
`=1.59xx10^(-2)M`
`[Pb^(2+)]= 1.59xx10^(-2)M`
`[CI^(-)]=2xx1.59xx10^(-2)`
`=3.18xx10^(-2)M`
For `Hg_(2)I_(2): Hg_(2)I_(2)hArrunderset(S)(Hg_(2)^(2+))+underset(2S)(2I^(-))`
`K_(SP)=4S^(3)`
`S=3sqrt((K_(SP))/(4))=3sqrt((4.5xx10^(-29))/(4))`
`=2.24xx10^(-10)M`
`[Hg_(2)^(2+)]=2.24xx10^(-10)M`
`[I^(-)]=2xx2.24xx10^(-10)M`
`=4.48xx10^(-10)M`