What is the concentration of `Ag^+` ions in 0.01 M `AgNO_(3)` that is also 1.0 M `NH_(3)?` Will AgCl precipitate from a solution that is 0.01M `AgNO_(3) 0.01 NaCl and 1M NH_(3)? " "K_(d) (Ag[NH_(3)]_(2)^+) =5.88 xx 10^(-8), K_(sp) (AgCl)=1.8 xx 10^(-10)`

Explanation

Let us first assume that 0.01M `AgNO_(3)` shall combine with 0.02M `NH_(3)` to form 0.01M `Ag(NH_(3))_(2)^+` and then consider its dissociation
`underset(0)overset(0.01M) (AgNO_(3))+underset(0.98M)overset(1M)(2NH_(3)) to underset(0.01M)overset(0)(Ag(NH_(3))_(2)^(+)`
`"0.01 M 0 0.98M Initial concn."`
`Ag(NH_(3))_(2)^+ Leftrightarrow Ag^(+) + 2NI_(3)`
`"(0.01-x) x (0.98+2x) Eqb. concn."`
`K_(d)=([Ag^(+)] [NH_(3)]^(2))/([Ag(NH_(3))_(2)^(+)]=5.88 xx 10^(-8)`
`[Ag^(+)]=(5.88 xx 10^(-8) xx 0.01)/((0.98)^2)=6.12 xx 10^(-10)M`
Further, ionic product is smaller than `K_(sp)=1.8 xx 10^(-10)`, no precipitate should form.