Question

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

Short answer

In summary, the more acidic members of each pair are: (a) Cu²⁺ produces a more acidic aqueous solution than K⁺ due to its higher charge and charge density. (b) Fe³⁺ is more acidic than Fe²⁺ because it has a higher charge and stronger electrostatic attraction for water molecules. (c) Al³⁺ creates a more acidic aqueous solution than Ga³⁺ due to its smaller size and higher charge density.

Step-by-step solution

Understand acidity of ions

An aqueous solution of a cation (a positively charged ion) can be acidic if the cation can attract an electron pair from water and create a hydronium (H₃O⁺) ion. This process is called hydrolysis. Meanwhile, small and highly charged cations have a greater tendency to undergo hydrolysis since they have a higher charge density and stronger electrostatic attractions for water molecules. Thus, they produce more acidic solutions.

Comparing K⁺ and Cu²⁺ acidity

From the periodic table, potassium (K) is from group 1 (alkali metals) and has a charge of +1 (K⁺). Copper (Cu) is from group 11 (transition metals) and has a charge of +2 (Cu²⁺). Since Cu²⁺ has a higher charge than K⁺, it has a higher charge density and a stronger electrostatic attraction for water molecules. The result is that Cu²⁺ has a higher tendency for hydrolysis than K⁺. Therefore, Cu²⁺ produces a more acidic aqueous solution.

Comparing Fe²⁺ and Fe³⁺ acidity

In this case, we're comparing two different oxidation states of the same element (iron). Fe²⁺ has a charge of +2, while Fe³⁺ has a charge of +3. Comparing their charges, Fe³⁺ has a higher charge, more charge density, and stronger electrostatic attraction for water molecules. Thus, Fe³⁺ has a higher tendency for hydrolysis and will produce a more acidic solution than Fe²⁺.

Comparing Al³⁺ and Ga³⁺ acidity

Both aluminum (Al) and gallium (Ga) are in group 13 and have a charge of +3. Therefore, both Al³⁺ and Ga³⁺ have the same charge, and we need to compare their sizes to determine their charge density. Aluminum has a smaller atomic radius than gallium since it is above gallium in the periodic table. Smaller size means higher charge density, so Al³⁺ has a stronger electrostatic attraction for water molecules and a higher tendency to undergo hydrolysis. Therefore, Al³⁺ produces a more acidic aqueous solution than Ga³⁺. In summary, the more acidic members of each pair are: (a) Cu²⁺ (b) Fe³⁺ (c) Al³⁺

Key concepts

Hydrolysis

Hydrolysis is a chemical process where a molecule interacts with water, often resulting in the breaking of chemical bonds and the formation of new molecules. In the context of metal ions, hydrolysis occurs when positively charged ions (cations) can attract electrons from water molecules. This interaction typically leads to the formation of hydronium ions \( \text{(H}_3\text{O}^+\text{)}\), thus increasing the acidity of the solution.
Cations that undergo hydrolysis tend to be smaller and have higher charges. These properties allow them to polarize surrounding water molecules more effectively, breaking the \( \text{H–O} \) bonds and improving hydronium formation.
When ions such as \( \text{Cu}^{2+} \) or \( \text{Fe}^{3+} \) hydrolyze, they do so because their charge density and size promote interactions that favor water molecule dissociation. Consequently, understanding hydrolysis in metal ions involves recognizing how these ions manipulate water molecules to transition the solution towards acidity.
In summary:

• Hydrolysis involves the interaction of water with metal ions.
• Leads to the formation of \( \text{H}_3\text{O}^+ \) ions, increasing acidity.
• Influenced by the ion's size and charge.

Charge Density

Charge density is a crucial concept to understand the acidity of metal ions. It describes how much electric charge is distributed over the space occupied by an ion. Higher charge density means that the charge is concentrated in a smaller area, which can lead to strong interactions with other charged or polar molecules, like water.
In essence, charge density is determined by two factors:

• The magnitude of the charge: Ions with higher charges, such as \( \text{Fe}^{3+} \) compared to \( \text{Fe}^{2+} \), have higher charge densities.
• The size of the ion: Smaller ions, such as \( \text{Al}^{3+} \) compared to \( \text{Ga}^{3+} \), have greater charge densities due to their compactness.

High charge density cations exert stronger force on the surrounding water molecules, enhancing the hydrolysis process. By polarizing the \( \text{H--O} \) bonds in water, the ions facilitate proton donation to solutions, increasing acidity. This concept is pivotal in comparing ions like \( \text{Cu}^{2+} \) and \( \text{K}^{+} \), where charge density differences explain varying acidities in solutions.

Electrostatic Attraction

Electrostatic attraction is the force that brings oppositely charged ions or polar molecules together. In the context of metal ion acidity, this attraction is vital as it underlies the ion's ability to influence water molecules.
Cations with higher charges, such as \( \text{Cu}^{2+} \) and \( \text{Fe}^{3+} \), exhibit stronger electrostatic attractions towards the partially negatively charged oxygen atoms in water. This attraction encourages the distortion of water molecule structures, facilitating hydrolysis.
Through electrostatic attraction:

• Larger ion charges lead to greater attraction, promoting more substantial interactions with water.
• This can result in a higher tendency for water molecules to dissociate into \( \text{H}_3\text{O}^+ \) ions, increasing the solution's acidity.

Overall, electrostatic attraction provides the driving force for the ion-water interactions that explain why certain metal ions lead to more acidic solutions. Understanding these attractions helps us predict acidity differences, such as more acidic solutions formed by \( \text{Cu}^{2+} \) over \( \text{K}^{+} \).