If `500 ml` of `0.4 M AgNO_(3)` is mixed with `50 ml` of `2 M NH_(3)` solution then what is the concentration of `[Ag(NH_(3))]^(+)` in solution `(K_(t), [Ag_(NH_(3))]^(+) = 10^(3), K_(f_(2)) [Ag(NH_(3))_(2)]^(+)= 10^(4))`

Options

A. `3.33 xx 10^(-7) M`
B. `3.33 xx 10^(-5) M`
C. `3 xx 10^(-4) M`
D. `10^(-7) M`

Answer

B

Explanation

After mixing `[Ag^(+)] = 0.2M, [NH_(3)] = 1M`
Due to very high value of `K_(f), Ag^(+)` is mainly converted into complex.
`Ag_((aq))^(+)+2NH_(3(aq))hArr[Ag(NH_(3))_(2)]_((aq))^(+)`
`{:(0.2,1,),(x,0.6,02):}`
`{:([Ag(NH_(3))_(2)]_((aq))^(+)hArr,[Ag(NH_(3))]_((aq))^(+),+NH_(3(aq))),(0.2-y,y,0.6+y),(0.2,,0.6):}`
`(1)/(K_(f_(2))) = (y xx 0.6)/(0.2) = (1)/(10^(4))`
`y = [Ag(NH_(3))]^(+) = 3.33 xx 10^(-5) M`