Question

Predict which member of each pair produces the more acidic aqueous solution: (a) \(\mathrm{K}^{+}\) or \(\mathrm{Cu}^{2+},(\mathrm{b}) \mathrm{Fe}^{2+}\) or \(\mathrm{Fe}^{3+},(\mathrm{c}) \mathrm{Al}^{3+}\) or \(\mathrm{Ga}^{3+} .\) Explain.

Short answer

In summary, the more acidic aqueous solutions are produced by: (a) Cu2+ compared to K+ (b) Fe3+ compared to Fe2+ (c) Al3+ compared to Ga3+ This is due to their higher oxidation states, stronger metal-ligand interactions, and greater stability of hydroxo complexes in water.

Step-by-step solution

(a) Comparing K+ and Cu2+ in aqueous solution

: First, we will assess the relative acidity of K+ and Cu2+ when placed in an aqueous solution. K+ is an alkali metal ion and it does not form stable hydroxo complexes in water, so it will not result in acidic conditions. In contrast, Cu2+ is a transition metal ion and has a greater tendency to form hydroxo metal complexes in water. Here, the higher oxidation state of Cu2+ compared to K+ leads to stronger metal-ligand interactions, which enhance the acidity of Cu2+ ions in aqueous solutions. Therefore, Cu2+ will produce a more acidic aqueous solution than K+.

(b) Comparing Fe2+ and Fe3+ in aqueous solution

: Now, we will compare the acidic behavior of Fe2+ and Fe3+ in an aqueous solution. Both ions belong to the same element but have different oxidation states. In general, the acidity of ions in aqueous solutions increases with the increase in the oxidation state. Fe3+ has a higher oxidation state than Fe2+, making its metal-ligand interactions stronger and its hydroxo complexes more stable. Therefore, Fe3+ will produce a more acidic aqueous solution than Fe2+.

(c) Comparing Al3+ and Ga3+ in aqueous solution

: Finally, we will compare the acidic behavior of Al3+ and Ga3+ in an aqueous solution. Both ions are members of the same group in the periodic table (Group 13) and have the same oxidation state, but they differ in their atomic size and charge density. In general, the acidity of ions in aqueous solutions increases with decreasing atomic size and increasing charge density. Since Al3+ has a smaller atomic size and higher charge density than Ga3+, it will form stronger metal-ligand interactions and more stable hydroxo complexes in water. Therefore, Al3+ will produce a more acidic aqueous solution than Ga3+. In conclusion: (a) Cu2+ produces a more acidic aqueous solution than K+ (b) Fe3+ produces a more acidic aqueous solution than Fe2+ (c) Al3+ produces a more acidic aqueous solution than Ga3+

Key concepts

Metal-ligand Interactions

Understanding metal-ligand interactions is crucial when exploring the behavior of metals in aqueous solutions. These interactions occur between a central metal ion and surrounding molecules or ions called ligands, which often have lone pairs of electrons that they can donate to the metal. In the context of our exercise, water acts as a ligand, forming hydroxo complexes with metal ions.

In a typical metal-ligand interaction, the ligand's lone pair forms a coordinate bond with the metal ion, which can alter the properties of the metal ion, including changes in solubility, color, and acidity. For example, the Cu²⁺ ion in an aqueous solution forms stronger bonds with water molecules compared to the K⁺ ion. This is due to Cu²⁺ having a higher charge and smaller ionic radius, which increases its affinity for ligands and contributes to stronger metal-ligand interactions. As a result, the solution becomes more acidic as Cu²⁺ forms hydroxo complexes that can release H⁺ ions.

These interactions are influenced by factors including the charge and size of the metal ion, the identity of the ligands, and the geometry of the resulting metal-ligand complex. Therefore, the strength of metal-ligand interactions plays a significant role in determining the acidity of aqueous solutions of different metal ions.

Oxidation States

The concept of oxidation states describes the degree of oxidation of an atom within a compound or complex. These states are represented by integers, which can be positive, negative, or zero, and indicate the hypothetical charge an atom would have if all bonds to atoms of different elements were completely ionic.

In our exercise, we look at ions such as Fe²⁺ and Fe³⁺. We see that the higher the oxidation state of the ion, the greater its acidity in aqueous solutions. This is because a high oxidation state typically indicates a stronger pull on the surrounding water molecules, leading to a greater tendency to release protons (H⁺ ions) and thereby increasing acidity. The Fe³⁺ ion, with an oxidation state of +3, has stronger metal-ligand interactions and forms more acidic solutions compared to the Fe²⁺ ion with an oxidation state of +2.

Essentially, the oxidation state of a metal can affect its electron density, and thus its ability to attract ligands. This interaction, in turn, can influence the stability of hydroxo complexes and play a part in the metal's acidity in aqueous solutions.

Hydroxo Metal Complexes

Hydroxo metal complexes are formed when metal ions in aqueous solutions interact with water, acting as a ligand, to form complexes that contain hydroxide (OH⁻) ions. This process is also known as hydrolysis. When these complexes are formed, they can affect the pH of the solution, often making it more acidic.

In the context of the exercise, we analyze how certain metal ions, like Al³⁺, create a more acidic environment as compared to others like Ga³⁺. This is influenced by the size and charge density of the metal ion. Al³⁺, which is smaller and has a higher charge density, can attract more water molecules and form stronger bonds, leading to the release of H⁺ ions when hydroxo complexes are formed.

These hydroxo complexes play a vital role in the chemistry of metal ions in water and can significantly affect their behavior in various chemical processes, including catalysis, environmental chemistry, and biological systems. Understanding these complexes is key to predicting and explaining the acidic nature of solutions with different metal ions.