Complex Ion Question?

Question

What is the concentration of Ag+(aq) in 0.010 M AgNO3 that is also 1.00 M NH3?

Kf for Ag(NH3)2 + ion is 1.7 x 107.

Answer 1

I find it useful to do equilibrium problems like this, that have huge equilibrium constants, to assume the reaction has gone to completion, and calculate the equilibrium from the reverse reaction. When this is done, we have to use the reciprocal for the original Kf.

Ag(NH3)2+ (aq) ↔ Ag+ (aq) + 2 NH3 (aq) 1/Kf = 5.9x10^-8

1/Kf = [Ag(NH3)2+] / [Ag+] [NH3]²

Since we are assuming the reverse reaction, we assume [Ag(NH3)2+] = 0.01M initially, and it loses x in going to equilibrium. [Ag+] goes from 0 to x, and [NH3] gains x from 0.99 M. Substituting:

5.9x10^-8 = (0.01-x) / (x) (0.99+x)²

We can see x will be very small, so we can ignore it in the numerator and the squared parentheses in the denominator. The equation becomes:

5.9x10^-8 = (0.01) / (x) (0.99)²

Solving, x = [Ag+] = 5.8x10^-6 M, or pAg+ = 5.3.