91Ó°ÊÓ

A complex ion is formed when a metal ion binds with surrounding molecules or ions, known as ligands. These ligands donate their electron pairs to the metal ion, forming a coordination bond. In the case of our exercise, the complex ion is \(\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}^{2+}\), which consists of a central copper ion \(\mathrm{Cu}^{2+}\) surrounded by four ammonia molecules \(\mathrm{NH}_3\).
This type of structure allows the metal ion to stabilize, as the electrons from the ligands fill the vacant orbitals of the metal ion.
Ammonia acts as a neutral ligand, contributing to the formation of the complex ion without changing its charge. As a result, the copper ion holds a 2+ charge within this complex.

In any chemical reaction, equilibrium concentrations mean the amounts of reactants and products present when the reaction is in a state where the forward and backward reactions occur at the same rate. In our problem, it's crucial to understand the concentrations of \([\mathrm{Cu}^{2+}]\), \([\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}^{2+}]\), and \([\mathrm{NH}_{3}]\).

• The copper ion \([\mathrm{Cu}^{2+}]\) is given as \(1.8 \times 10^{-17} M\).
• The complex ion \([\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}^{2+}]\) has a concentration of \(1.0 \times 10^{-3} M\).
• Ammonia \([\mathrm{NH}_{3}]\) is in a much larger concentration of \(1.5 M\).

These values are plugged into the equilibrium expression to help calculate the formation constant, capturing the balance point for the chemical reaction.

The formation constant, or \(K_{\mathrm{overall}}\), is a special equilibrium constant that quantifies the stability of a complex ion in solution.
In our scenario, the formula used to compute \(K_{\mathrm{overall}}\) is derived from the equilibrium reaction:
\(\mathrm{Cu}^{2+}(a q)+4 \mathrm{NH}_{3}(a q)\rightleftharpoons \mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}^{2+}(a q)\).
The expression is:
\[K_{\mathrm{overall}}=\frac{[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}^{2+}]}{[\mathrm{Cu}^{2+}][\mathrm{NH}_{3}]^4}\]
By substituting the equilibrium concentrations into this formula, we've calculated the \(K_{\mathrm{overall}}\) to be approximately \(1.097 \times 10^{14}\).
A high \(K_{\mathrm{overall}}\) value suggests a highly stable complex ion, showing that at equilibrium, the species exist largely as the complex rather than dissociated into \(\mathrm{Cu}^{2+}\) and \(\mathrm{NH}_3\) reactants. This indicates the strong affinity between copper ions and ammonia.