The simultaneous solubility of Ag CN `(K_(f) =2.5 xx 10^(-16) ) and AgCl (Ksp =1.6 xx 10^(-10 ) ) ` in 1. 0M `NH_3` (aq) are respectively : `[Given ,K_f [Ag(NH_3)_2^(+) ]= 10^(7) ]`

Options

A. ` 0.037 , 5.78 xx 10 ^(-8) `
B. ` 5. 78 xx 10^(-8) , 0. 037`
C. ` 0.04 , 6.25 xx 10 ^(-8) `
D. ` 1. 58 xx 10 ^(-3) , 1.26 xx 10 ^(-5)`

Answer

A

Explanation

` AgCN +2NH_3hArr [Ag(NH_3) _2]^(+) +CN^(-) `
` K_f xx K_(Sp) =([Ag(NH_3)_2]^(+) [CN^(-)])/([NH_3]^(2))`
` 2.5 xx 10 ^(-9) =([Ag(NH_3)_2]^(+) [CN^(-) ])/([NH_3]^(2))`
` AgCl+2NH_3 hArr [Ag(NH_3)_2 ]^(+) +Cl^(-) `
` 1.6 xx 10^(-3) =([Ag(NH_3)_2]^(+) [Cl^(-)])/([NH_3]^(2))`
` ([CN^(-)])/([Cl^(-)]) =(25)/(16) xx 10^(-6) , 16 xx 10^(-4) =(x^(2))/((1-2x)^(2))`
` x= 0.037`
`[CN^(-)] =(0.037)/(6.4 xx 10^(5) ) = 5.78 10 ^(-8) `