##### J. W. Hill, R. H. Petrucci, T. W. McCreary, & S. S. Perry General Chemistry 4th edition

Problem 16.72

Which of the following complex ions would you expect to have the lowest [Ag+] in a solution that is 0.10 M in the complex ion and 1.0 M in the free ligand? Explain.

(a) [Ag(NH3)2]+   (b) [Ag(CN)2]   (c) [Ag(S2O3)2]3–

Let L = ligand in each case, so the formation reaction is

Ag+(aq) + 2 Lm–(aq)[AgL2](m–1)–(aq)

The mass action expression is:

Now the silver ion concentration can be calculated for each case:

(a) Kf = 1.6×107 so [Ag+] = [0.10]/(1.6×107)[1.0]2 = 6.3×10–9 M

(b) Kf = 5.6×1018 so [Ag+] = [0.10]/(5.6×1018)[1.0]2 = 1.8×10–20 M

(c) Kf = 1.7×1013 so [Ag+] = [0.10]/(1.7×1013)[1.0]2 = 5.9×10–15 M

The [Ag(CN)2] solution has the lowest silver ion concentration. Since all of these complex ions have the same stoichiometry, a comparison of the formation constants would have sufficed to answer the question: the largest formation constant leads to the lowest silver ion concentration.