Question

Without performing detailed calculations, show why you would expect the concentrations of the various ammine-aqua complex ions to be negligible compared with that of \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}\) in a solution having a total \(\mathrm{Cu}(\mathrm{II})\) concentration of \(0.10 \mathrm{M}\) and a total concentration of \(\mathrm{NH}_{3}\) of \(1.0 \mathrm{M}\). Under what conditions would the concentrations of these ammine-aqua complex ions (such as \(\left.\left[\mathrm{Cu}\left(\mathrm{H}_{2} \mathrm{O}\right)_{3} \mathrm{NH}_{3}\right]^{2+}\right)\) become more significant relative to the concentration of \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+} ?\) Explain.

Short answer

Under given conditions, the ammine complex ions dominate due to higher ammonia concentration favoring the formation of [Cu(NH_3)_4]2+. The amount of free copper ion is negligible, so the equilibrium for complexes with water ligands doesn’t go far to the right, forming tiny amounts of mixed complexes. The conditions under which these mixed complexes would become significant would be if the concentration of ammonia was lowered, or the concentration of water was increased, or both.

Step-by-step solution

Understanding the equilibrium

In this solution, an equilibrium exists between the copper ion, water, ammonia and each species of the ammine-aqua complex copper ions. The equilibrium constant expression for the fully ammonia bound copper would be: \[ K_f = \frac{[\mathrm{Cu}(NH_3)_4]^{2+}}{[\mathrm{Cu}^{2+}][NH_3]^4} \] Now we should realize that if most of the copper is in the form of \([Cu(NH_3)_4]^2+\), it implies that the equilibrium constant for its formation is large enough, thus favoring the formation of the tetraamminecopper(II) complex. This also implies that the amount of free copper ion in the solution not in the [Cu(NH_3)_4] is negligible.

Considering the competition of ammonium and water

The water ligand can substitute the ammonia in [Cu(NH_3)_4]2+ complex according to the equilibrium. However, under the given conditions, the concentration of ammonia is much larger than the concentration of water. Thus, the ammonia will out-compete the water for the binding site, resulting in the negligible extent to which water binds. This leads to an extremely tiny equilibrium constant, favoring the left side in the equilibria, forming the mixed complex ions such as [Cu(H2O)_3(NH_3)]. Thus, the concentration of these ions will be quite tiny in contrast to the concentration of the [Cu(NH_3)_4]2+ ions.

Conditions for higher concentrations of mixed-complex ions

In order to see a significant amount of mixed complex ions, the conditions should favor the side of the equilibrium with the mixed complex. This can be achieved by either increasing the concentration of water or lowering the concentration of ammonia, or both. Lower concentrations of ammonia will allow more water to bind to the copper ion, hence increasing the concentrations of ammine-aqua complex ions. Increasing the concentration of water also favors the same.

Key concepts

Tetraamminecopper(II) complex

The tetraamminecopper(II) complex, represented as \([\mathrm{Cu}(\mathrm{NH}_3)_4]^{2+}\), plays a crucial role in chemistry due to its stability and vibrant blue color. This complex is formed when four ammonia molecules coordinate to a single copper ion, replacing water molecules that may initially surround the copper ion in aqueous solution.
Ammonia, a neutral ligand, has a strong affinity for copper(II) ions, which contributes to the stability of the tetraamminecopper(II) complex. Once formed, this complex tends to dominate in a solution like the one described, particularly when ammonia is present in high concentrations.
In practical terms, you can expect to see negligible amounts of other copper complexes because the tetraamminecopper(II) complex is energetically favored. This preference is due to the large formation constant \(K_f\), which we'll explore next.

Equilibrium constant

The equilibrium constant, often denoted by \(K_f\) for formation reactions, provides insight into the favorability of forming a particular complex. For the tetraamminecopper(II) complex, \(K_f\) is defined by the equation:
\[ K_f = \frac{[\mathrm{Cu}(\mathrm{NH}_3)_4]^{2+}}{[\mathrm{Cu}^{2+}][\mathrm{NH}_3]^4} \]
This expression shows that a large \(K_f\) value indicates a strong preference for the formation of the complex, meaning more of the initial reactants are converted into the complex.
In our scenario, with ample ammonia and a suitable concentration of copper(II) ions, \([\mathrm{Cu}(\mathrm{NH}_3)_4]^{2+}\) becomes highly predominant. The large \(K_f\) ensures that free copper ions and unbound ammonia become minor components in the mixture.
Therefore, unless conditions change significantly, such as reducing ammonia concentration, the tetraamminecopper(II) complex will remain the major species.

Ligand competition in coordination compounds

Ligand competition in coordination compounds is a critical factor that determines which species form in a solution. In the case of the tetraamminecopper(II) complex, ammonia and water compete to bind with the copper ion.
With a high ammonia concentration, ammonia ligands outcompete water molecules due to their higher binding affinity. This turns the equilibrium in favor of forming \([\mathrm{Cu}(\mathrm{NH}_3)_4]^{2+}\).
If the situation were reversed, with higher water concentration or lower ammonia levels, water would have a better chance of binding, forming mixed complexes like \([\mathrm{Cu}(\mathrm{H}_2\mathrm{O})_3\mathrm{NH}_3]^{2+}\).
Understanding ligand competition helps predict product composition. It's clear that under typical conditions, the preference for ammonia in such equilibria leads to a significant formation of one dominant complex, simplifying the mixture.