Determine the solubilities of silver chromate, barium chromate, ferric hydroxide, lead chloride and mercurous iodide at `298K` from their solubility product constants given in Table `7.9`. Determine also the molarities of individual ions.

Explanation

(i)Silver chromate , `Ag_2CrO_4`
`Ag_2CrO_4 hArr 2Ag^(+) + CrO_4^(2-)`
`[Ag^+]=2s , CrO_4^(2-) =s`
`K_(sp)=(2s)^2 (s) =4s^3`
`therefore 4s^3 =1.1xx10^(-12)`
`s=((1.1xx10^(-12))/4)=6.5 xx10^(-5)`
`[Ag^+]=1.30xx10^(-4)` M, `[CrO_4^(2-)]=6.5xx10^(-5)` M
(ii) Barium chromate , `BaCrO_4`
`BaCrO_4 hArr Ba^(2+) +CrO_4^(2-)`
`[Ba^(2+)]=s, CrO_4^(2-) =s`
`K_(sp)=(s)(s)=s^2`
`s^2=1.2xx10^(-10)`
`s=(1.2xx10^(-10))^(1//2)=1.09xx10^(-5)` M
`[Ba^(2+)]=1.09xx10^(-5)` M , `[CrO_4^(2-)] = 1.09xx10^(-5)` M
(iii) Ferric hydroxide , `Fe(OH)_3`
`Fe(OH)_3 hArr Fe^(3+) + 3OH^-`
`[Fe^(3+)]=s, [OH^-]=3s`
`K_(sp)=(s)(3s)^3 =27s^4`
`27s^4 =1.0xx10^(-38)`
`s=((1.0xx10^(-38))/27)^(1//4)=1.38xx10^(-10)` M
`[Fe^(3+)]=1.38xx10^(-10)` M , `[OH^-]=4.14xx10^(-10)` M
(iv) Lead chloride , `PbCl_2`
`PbCl_2 hArr Pb^(2+) + 2Cl^(-)`
`[Pb^(2+)]=s, [Cl^-]=2s`
`K_(sp)=(s) xx(2s)^2=4s^3`
`4s^3 =1.6xx10^(-5)`
`s=((1.6xx10^(-5))/4)^(1//3)=1.59xx10^(-2)` M
`[Pb^(2+)]=1.59xx10^(-2)` M
`[Cl^-]=3.18xx10^(-2)` M
(v)Mercurous iodide , `Hg_2I_2`
`Hg_2I_2 hArr 2Hg^(+) + 2I^-`
`[Hg^+]=2s, [I^-]=2s`
`K_(sp)=(2s)^2 (2s)^2`
`=16s^4`
`16s^4=4.5xx10^(-29)`
`s=((4.5xx10^(-29))/16)^(1//4)=4.09xx10^(-8)` M
`[Hg^+]=8.18xx10^(-8)` M
`[I^-]=8.18xx10^(-8)`M .