Solubility Equilibria

Calculate the concentrations of Ag\(^+\), Ag(S\(_2\)O\(_3\))\(^-\), and Ag(S\(_2\)O\(_3\))\(_2^{3-}\) in a solution prepared by mixing 150.0 mL of 1.00 x 10\(^{-3}\) M AgNO\(_3\) with 200.0 mL of 5.00 M Na\(_2\)S\(_2\)O\(_3\). The stepwise formation equilibria are:

Ag\(^+\) + S\(_2\)O\(_3^{2-}\) \(\leftrightharpoons\) Ag(S\(_2\)O\(_3\))\(^-\)    K\(_{f1}\) = 7.4 x 10\(^{8}\)

Ag(S\(_2\)O\(_3\))\(^-\) + S\(_2\)O\(_3^{2-}\) \(\leftrightharpoons\) Ag(S\(_2\)O\(_3\))\(_2^{3-}\)    K\(_{f2}\) = 3.9 x 10\(^{4}\)