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Calculate the concentration of free silv...

Calculate the concentration of free silver ion `[Ag^(+) ]` in an aqueous solution that is prepared as `0.1 M AgNO_3 and 3.0 M NH_3 ,Ag^(+) (aq) +2 NH_3 (aq) hArr [Ag(NH_3) _2]^(+) (aq) K_(f) = 1.6 xx 10^(7) ` . If answer is ` x xx 10^(-10) M ` then x= ______?

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The correct Answer is:
8
` Ag^(+) +2NH_3 hArr 2NH_3 hArr [Ag(NH_3]_2]^(+) `
` ([Ag(NH_3)_2]^(+) )/([Ag^(+) ][NH_3]^(2) ) = K_f`
` (0.1)/( [Ag^(+) ](3-0.2)^(2)) = 1.6 xx 10^(7) `
` [Ag^(+) ]= (0.1)/(1.6 xx 10^(-7) xx (2.8) ^(2)) ~~8 xx 10 ^(-10) `
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