Question

The simulaneous solubility of `AgCN (Ksp = 2.5 xx 10^(-16))` and `AgCl (Ksp = 1.6 xx 10^(-10))` in `1.0 M NH_(3(aq))` are respectively `(K_(f)[Ag(NH_(3))_(2)]^(+) = 10^(7))`
A. `0.037, 5.78 xx 10^(-8)`
B. `5.78 xx 10^(-8), 0.037`
C. `0.04, 6.258 xx 10^(-8)`
D. `1.58 xx 10^(-3), 1.26 xx 10^(-5)`

Answer 1

Correct Answer - B
`underset((s))(AgCl)+underset((aq))(2NH_(3))hArr [Ag(underset((aq))(NH_(3)))_(2)]^(+) + underset((aq))(Cl)^(-)`
`K_(1) = 1.6 xx 10^(-10) xx 10^(7)`
`= 1.6 xx 10^(-3)`
`= ([Ag(NH_(3))_(2)]^(+)[Cl^(-)])/([NH_(3)]^(2))`
`AgCH_((s))+2NH_(3(aq)) hArr[Ag(NH_(3))_(2)]_((aq))^(+) + CN_(aq)^(o.)`
`K_(2) = 2.5 x 10^(-16) xx 10^(7) = 2.5 xx 10^(-9)`
`= ([Ag(NH_(3))_(2)]^(+)[CN^(-)])/([NH_(3)]^(2))`
`([Cl^(-)])/([CN^(-)]) = (1.6 xx 10^(-3))/(2.5 xx 10^(-9)) = 6.4 xx 10^(5)`
`K_(1) = (x^(2))/((1-2x)^(2))`
`(x)/(1-2x) = 0.04`
`x = 0.037`
`[CN^(-)] = (0.037)/(6.4 xx 10^(5)) = 5.78 xx 10^(-8) M`