if 500 mL of 0.4 M `AgNO_3` is mixed with 500 mL of `2M NH_3` solution the what is the concentration of ` Ag (NH_3 ) ^(+) ` in solution?
[Given : ` K_(f_1) [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) `

Answer

B

Explanation

After mixing , ` [Ag^(+) ] =0.2 M, [NH_3]=1M`
` K_(f_1) xx K_(f_2) =10 ^(7) `
Due to high `K_f` value , most of the `Ag^(+) ` converted into ` [Ag(NH_3)_2]^(+) `
`{:( Ag^(+) +,2NH_3 hArr, [Ag(NH_3)_2 ]^(+)), (0.2 M, 1M, 0), (, 1-04-0.6M, 0.2M):} `
` {:([Ag(NH_3)_2]^(+) ,hArr ,Ag(NH_3)^(+), +NH_3) ,( 0.2 M, 0, 0.6M),( 0.2-y, y, 0.6+y),(~~0.2 , , ~~0.6):}`
` (1)/(10^(4) )= (yxx 0.6)/(0.2) =3y rArry =3.33 xx 10 ^(-5) M`