Liquid `NH_(3)` ionises to a slight extent. At `-50^(@)C`, its ionic product `K_(NH_(3)) = [overset(Θ)Nh_(4)] [overset(Θ)NH_(2)]` is `10^(-30)`. How many amide ions, `overset(o+)NH_(2)` are present per `mm^(3)` of pure liquid `NH_(3)`?

Options

A. `6xx10^(6)ions`
B. `6xx10^(5)ions`
C. `6xx10^(-5)ions`
D. `6xx10^(-6)ions`

Answer

B

Explanation

`2NH_(3)hArrNH_(4)^(+)+NH_(2)^(-)` (self ionisation)
and `K = [NH_(4)^(+)][NH_(2)^(-)]`
`:. [NH_(4)^(+)]=[NH_(2)^(-)]`
`:. [NH_(2)^(-)]=sqrt(K)= sqrt(10^(-30))=10^(-15)M`
Number of amide ions in `10^(3) cm^(3)`
`=10^(-15)xx6xx10^(23)`
`:.` Number of amide ions in `10^(3)cm^(3)`
`=(10^(-15)xx6xx10^(23))/(10^(3))`
`= 6xx10^(5)ions`