Chapter 15, Problem 69E

A solution is formed by mixing 50.0 mL of 10.0 M NaX with 50.0 mL of 2.0 × 10⁻³ M CuNO₃. Assume that Cu⁺ forms complex ions with X⁻ as follows:

$\begin{array}{ll}{\text{Cu}}^{\text{+}}(aq)+X^{-}(aq)\rightleftharpoons CuX(aq)\hfill & K_1=1.0\times {10}^2\hfill \\ \text{CuX}(aq)+X^{-}(aq)\rightleftharpoons Cu{X}_2{}^{-}(aq)\hfill & K_2=1.0\times {10}^4\hfill \\ {\text{CuX}}_{\text{2}}{}^{-}(aq)+X^{-}(aq)\rightleftharpoons Cu{X}_3{}^{2-}(aq)\hfill & K_3=1.0\times {10}^3\hfill \end{array}$

with an overall reaction

$\begin{array}{cc}{\text{Cu}}^{\text{+}}(aq)+3X^{-}(aq)\rightleftharpoons Cu{X}_3{}^{2-}(aq)& K=1.0\times {10}^9\end{array}$

Calculate the following concentrations at equilibrium.

a. Cux₃²⁻

b. CuX₂⁻

c. Cu⁺