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

Let ‘s be the solubility of each salt in `mol//L`
(a) `Ag_(2)CrO_(4)(s) overset(aq)(to) 2Ag^(+)(aq), K_(sp)=1.1xx10^(-12)`
2S S
`K_(sp)=[Ag^(+2)].[CrO_(4)^(2-)]=[2S^(2)].[S]=4S^(3) impliesS^(2)=K_(sp)/4 implies S approx. 6.5xx10^(-5)M`
`implies [CrO_(4)^(2-)] =S = 6.5xx10^(-5)M & [Ag^(+)]=2S=1.3xx10^(-4)M`
` BaCrO_(4) to Ba^(+( + CrO_(4)^(2-), K_(sp)=1.2xx10^(-10)`
S S
`K_(sp)=[Ba^(2+)].[CrO_(4)^(2-)]=1.2xx10^(-10) implies S=sqrt(1.2xx10^(-10)) = 1.1xx10^(-5)M`
`implies [ Ba^(2+)]=[CrO_(4)^(2-)]=S^(2)=1.1xx10^(-5)M`
(c)` Fe[OH]_(3) to Fe^(3+) + 3OH^(-), K_(sp)=1.0xx10^(-38)`
S 3S
`K_(sp)=[Fe^(3+)][OH^(-3)]=s.(3s^(2))=27s^(4) implies s^(4)=K_(sp)/27 implies S approx 1.39xx10^(-10)`
`implies[Fe^(3+)]=1.39xx10^(-10)M & [OH(-)=3S=3xx1.39xx10^(-10)=4.17xx10^(-10)M`
(d) `PbCl_(2) to Pb^(2+) + 2Cl^(-), K_(sp)=1.6xx10^(-5)`
S 2S
`K_(sp)=[Pb^(2+)][Cl^(-2)]=S.(2S)^(2)=4S^(3) implies S^(2)=K_(sp)/4 implies S approx 1.59xx10^(-2)M`
`therefore` Solubility of `PbCl_(2) = 1.59 ×x 10^(-2) M`
`implies[Pb^(2+)]=1.59xx10^(-2)M & [Cl^(-)]=2xx10^(-2)M=3.18xx10^(-8)M`
(e) `Hg_(2)I_(2) to Hg_(2)^(2+) + 2I^(-), K_(sp)=4.5xx10^(-29)`
S 2S
`K_(sp)=[Hg_(2)^(2+)][I^(-2)]=S.(2S)^(2)= 4S^(3) implies S^(3)=K_(sp)/4 implies S=2.241xx10^(-10)M`
Solubility of `Hg_(2)I_(2) = 2.241 ×x 1­0^(-10) M`
`[Hg_(2)^(2+)]=2.24xx10^(-10)M & [I^(-)]=2xx2.241xx10^(-10)M=4.482xx10^(-10)M`