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How many moles of NH(3) must be added to...

How many moles of `NH_(3)` must be added to `1.0L` of `0.75M AgNO_(3)` in order to reduce the `[Ag^(o+)]` to `5.0 xx 10^(-8)M. K_(f) Ag (NH_(3))_(2)^(o+) = 1 xx 10^(8)`.

Text Solution

Verified by Experts

The correct Answer is:
1.89

`Ag^(+) + 2NH_(3) to [Ag(NH_(3))_(2)]^(+)`
`K_(f)=([Ag(NH_(3))_(2)]^(+))/([Ag^(+)][NH_(3)]^(2))=1xx10^(8)`
`[AgNO_(3)]=[Ag^(+)]_("initially")=0.750`
`1xx10^(8)=0.750/(5xx10^(-8)xx[NH_(3)]^(2))`
`[NH_(3)]^(2)=0.15`
`[NH_(3)]`in solution at equilibrium=0.39M
`[NH_(3)]` added=0.39 + `[NH_(3)]` needed to convert 0.750 M `Ag^(+)` to [Ag(NH_(3))_(2)]^(+)`
`0.39+2xx0.750=1.89mol`
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