A very dilute saturated solution of a sparingly soluble salt `A_(3)B_(4)` has a vapour pressure of `20mm` of `Hg` at temperature T, while pure water exerts a pressure of `20.0126mm Hg` at the same temperature. Calculate the solubility product constant of `A_(3)B_(4)` at the same temperature.

Answer

`5.4xx10^(-13)`

Explanation

Let the solubility of `"A"_(3)"B"_(4)="S"`
`{:(A_(3)B_(4),to,3A^(+),+,4B^(-)),(s,,0,,0),(0,,3S,,4s):}`
Solubility product of `A_(3)B_(4)(k_(s.p))=(3S)^(3)(4S)^(4)=6912 S^(7)`
For `A_(3)B_(4),i=7`
To solve this problem we will assume
`"Malarity=Molality and " w_("solvent")=w_("solution")`
`impliesn_("solute")=S,w_("solvent")=100"gm"`
`n_("solvent")=(1000)/(18)=55.56`
`(P_("solvent")^(0)-P_("solution"))/(P_("solvent"))=ixx(n_("solute"))/(n_("solvent"))`
`(20.0126-20)/(20.0126)=(5xx7)/(55.56)`
`S=5xx10^(-3)M`
`therefore "solubility product of "A_(3)B_(4)(K_(s.p))=6912 S^(7)`
`=6912xx5^(7)xx10^(-21)=5.4xx10^(-13)`