Determine the number of mole of AgI which may be dissolved in `1.0` litre of `1M CN^(-)` solution. `K_(SP)` for AgI and `K_(C)` for `Ag(CN)_(2)^(-)` are `1.2xx10^(-17)M^(2)` and `7.1xx10^(19)M^(-2)` respectively.

Options

A. `1.0` mole
B. `0.5` mole
C. `4.0` mole
D. `2.5` mole

Answer

B

Explanation

`Agl(s)hArrAg^(+)(aq)+I^(-)(aq)`
`K_(sp)=[Ag^(+)(aq)][I^(-)(aq)]`
`Ag^(+)(aq)+2CN^(-)(aq)hArr[Ag(CN)_(2)]_((aq))^(-)`
`K_(r)=([Ag(CH)_(2)]^(-))/([Ag^(+)][CN^(-)])`
Now, let a moles of `Agl` dissolved in `CN^(-)` solution
`Agl(s)+underset((1-2x)"mole") underset(1"mole")(2CN_((aq))^(-))hArr underset(x"mole")underset(0)([Ag(CN)_(2)]_((aq))^(-))+underset(x"mole")underset(0)(I_((aq))^(-))`
As `[CN^(-)]=M.V=1xx1=1"mole"`
`:.K_(c)=(x.x)/((1-2x)^(2))`
also `k_(c)=K_(f).K_(sp)`
`:.(x^(2))/((1-2x)^(2))=1.19xx10^(-17)M^(2)xx7.11xx10^(19)M^(-2)`
`implies x=0.5`