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

`5.4 xx10^(-13)`

Explanation

`P_(s) = 20 P^(@) = 20.0126`
`(P^(@)-P_(s))/(P^(@)) = (0.0126)/(20.0126) = (n)/(n+N) =(n)/(N)`
`("mole of solute")/("moles of" H_(2)O) = 0.00063`
1 mole `H_(2)O = 18g = 18 mL`
`18 mL` solution `= 0.00063` mole
`1L` solution `= (0.000063)/(18) xx 1000 = 0.035` mole/L
Let solubility of salt `A_(3)B_(4)` is s then
`7s = 0.035`
`s = 0.005` mole/L
`k_(sp) = 3^(3).4^(4) (s)^(7) = 27 xx 256 xx (0.005)^(7)`
`k_(sp) = 5.4 xx 10^(-13)`