Question

Given: `Ag(NH_(3))_(2)^(+)hArrAg^(+)2NH_(3), K_(C)=6.2xx10^(-8)` and `K_(SP)` of `AgCI=1.8xx10^(-10)` at 298 K. Calculate the concentration of the complex in `1.0M` aqueous ammonia.

Answer 1

`Ag(NH_(3))_(2(aq.))^(+)hArr underset(a+b)(Ag_((aq.))^(+))+underset(2a)(2NH_(3(aq.))`
`:. K_(C )=([NH_(3)]^(2)[Ag^(+)])/([Ag(NH_(3))_(2)^(+)])` ….(1)
`AgCI_((s))hArr underset(a+b)(Ag_((aq.))^(+)+underset(b)(CI_((aq.))^(-)`,
`:. K_(SP)=[Ag^(+)][CI^(-)]` ......(2)
In case of simultaneous solubility `Ag^(+)` remains same in solution. Given `[NH_(3)]= 2a=1M, also [Ag(NH_(3))_(2)^(+)]=[CI^(-)]=b` becauser `Ag^(+)` obtained from `AgCI` passes in `[Ag(NH_(3))_(2)^(+)]` state.
Thus, by eqs. (1) and (2),
`(K_(C ))/(K_(SP))= ([NH_(3)]^(2))/([CI^(-)][Ag(NH_(3))_(2)^(+)])=(1^(2))/(b^(2))`
or `b^(2)=(1.8xx10^(10))/(6.2xx10^(-8))=0.29xx10^(-2)`
`:. b= 0.539xx10^(-1)=0.0539`
or `[Ag(NH_(3))_(2)^(+)]= 0.0539`