Question

3. Silver ion reacts with excess CN- to form colorless complex ion, Ag(CN)2-, which has the formation constant Kf = 3.0 x 1020. Calculate the concentration of Ag+ in a solution prepared by mixing equal volumes of 2.0 X 10-3 M AgNO3 and 0.20 M NaCN.

Answer 1

                Ag+        +         2CN- ------------> [Ag(CN)2]-

I          2 x 10^-3                0.20                           -

C             -x                        -2x                            +x

E      (2 x 10^-3 - x)       (0.20 - 2x)                       x

Now,

Kf = [Ag(CN)2]-/[Ag+][CN-]^2

feeding the equilibrium values,

3 x 10^20 = x/(2 x 10^-3 - x)(0.2 - 2x)^2

3 x 10^20 = x/(- 1.6 x 10^-3x + 0.808x^2 - 0.04 - 4x^3)

-1.2 x 10^21x^3 + 2.424 x 10^20x^2 - 4.8 x 10^17x - 1.2 x 10^19 = x

1.2 x 10^21x^3 - 2.424 x 10^20x^2 + 4.8 x 10^17x + 1.2 x 10^19 = 0

x = -0.165 M

So,

concentration of [Ag+] = 2 x 10^-3 - (-0.165) = 0.167 M