Calculate the mass of AgBr?

Question

To a 250.0 mL volumetric flask are added 1.00 mL volumes of three solutions: 0.0100 M AgNO3, 0.145M NaBr, and 0.100 M NaCN. The mixture is diluted with deionized water to the mark and shaken vigorously. The Ksp of AgBr is 5.40×10–13 and the Kf of Ag(CN)2– is 1.00×1021.

Answer 1

AgNO3(aq) + NaBr(aq) ==>AgBr(s) + NaNO3(aq) .... Eq. 1
This is the original precipitation reaction. The addition of the cyanide anion forms a soluble complex. These reactions are shown below.

AgBr(s) ===> Ag+(aq) + Br-(aq) Ksp = 5.40x10-13 ... Eq. 2
Ag+(aq) + 2CN-(aq) ===> Ag(CN)2-(aq) Kf = 1.00x1021 ... Eq. 3
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AgBr(s) + 2CN-(aq) ===> Ag(CN)2-(aq) + Br-(aq) K = Ksp x Kf = 5.40x108 ... Eq. 4

Calculate molarity of each species present. The AgBr(s) formed in first rx will be limited by moles AgNO3. Calculate molarity of Ag(CN)2- formed in 3rd rx.

Using K in Eq. 4 (Ksp x Kf) find solubility of Ag+ and Br- and from that you can then determine the mass of precipitate not dissolved, if any. Given the large value of Kf (and K), it seems that all the AgBr will dissolve.