Question

A solution is 0.0010 M in both Ag+ and Au+. Some solid NaCl is added slowly until the second solid compound just begins to precipitate. What is the concentration of Au+ ions at this point? K_sp for AgCl = 1.8 x 10^-10 and for AuCl is 2.0 x 10^-13

Answer 1

CONCEPT: Determine the concentration of Cl^- ion at which AgCl will begin to precipitate , then at the same concentration of Cl^- ion determine Au+ concentration. Whole procedure is shown below.

AuCl <-----> Au⁺ + Cl^-  Ksp = 2.8 X 10^-13

AgCl <-----> Ag⁺ + Cl^-   Ksp = 2.8 X 10^-10.

Ksp = [Ag⁺ ] [Cl^-]

1.8 x 10^-10 = [Ag⁺ ] [Cl^-]

[Cl^-] = 1.8 x 10^-10 / 0.0010 = 1.8 X 10^-7

Hence AgCl will begin to precipitate when [Cl^-] reaches 1.8 X 10^-7 . Concentration of Au+ at this concentration will be determined as

Ksp = [Au⁺ ] [Cl^-]

2.0 x 10^-13 = [Au⁺ ] [1.8 X 10^-7 ]

[Au⁺ ] = 1.11 X 10^-6