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Determine the mol. Of AgI which may be d...

Determine the mol. Of `AgI` which may be dissolved in `1.0L` of `1.0MCN^(Theta)` solution. `K_(sp)` for `AgI` and `K_(c)` for `Ag(CN)_(2)^(Theta)` are `1.2 xx 10^(-17)M^(2)`and `7.1 xx 10^(-19) M^(-2)`, respectively.

A

`1.0` mole

B

`0.5` mole

C

`4.0` mole

D

`2.5` mole

Text Solution

Verified by Experts

The correct Answer is:
B
`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`
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