Problem 97 - Chemistry The Central Science In Si Units

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 \(\mathrm{Ga}^{3+}\).

Step-by-Step Solution

Answer

(a) Cu²⁺, (b) Fe³⁺, (c) Al³⁺ produce more acidic solutions.

Step 1: Understanding Acidity of Aqueous Solutions

The acidity of an aqueous solution containing metal ions is related to the metal ion's ability to polarize and weaken O-H bonds in water molecules, thereby facilitating the release of H⁺ ions. Generally, metal ions with higher charge and smaller radius have a greater polarizing effect and lead to a more acidic solution.

Step 2: Comparing K⁺ and Cu²⁺ for Acidity

K⁺ is a Group 1 element with a +1 charge and a relatively larger ionic radius. Conversely, Cu²⁺ has a +2 charge and a smaller ionic radius. The higher charge and smaller size of Cu²⁺ enable it to polarize water molecules more effectively than K⁺, thus Cu²⁺ produces a more acidic aqueous solution.

Step 3: Comparing Fe²⁺ and Fe³⁺ for Acidity

Fe²⁺ and Fe³⁺ are oxidation states of iron. Fe³⁺ has a higher charge than Fe²⁺, which increases its polarizing power on water molecules. Despite having similar ionic sizes, the higher charge of Fe³⁺ makes it more efficient in generating acidity in an aqueous solution.

Step 4: Comparing Al³⁺ and Ga³⁺ for Acidity

Al³⁺ and Ga³⁺ both have a +3 charge. Though they have similar charges, the position of the elements in the periodic table indicates that Al³⁺ has a smaller atomic radius than Ga³⁺. The smaller size of Al³⁺ results in a stronger polarization of water molecules, leading to a more acidic solution.

Key Concepts

Metal Ion Polarization

Metal ion polarization refers to the ability of a metal ion to distort the cloud of electrons in surrounding molecules, such as water. This distortion weakens the bonds in the molecule, like the O-H bond in water, and often results in the release of hydrogen ions (H⁺), making the solution more acidic. When we compare metal ions:

• Their charge and size play significant roles in how much they can polarize other molecules.
• Higher charged ions have a greater electric field and thus a stronger polarizing effect.
• Smaller ions can get closer to other molecules, enhancing their polarizing ability.

To summarize, a metal ion that is small and highly charged can make an aqueous solution very acidic by strongly polarizing the water molecules deteriorating the O-H bonds.

Charge Density

Charge density is an important concept for understanding the behavior of metal ions in solutions. It is defined as the ratio of the charge of an ion to its volume. When predicting the acidity of the solutions, it can help us identify which ions are more likely to polarize water molecules.

• Higher charge density implies a higher concentration of charge over a smaller area.
• This results in a stronger electric field around the ion, which can attract and distort the electronic structures of nearby molecules.
• In essence, ions with high charge density, typically due to high charge and small size, are excellent at polarizing water molecules, leading to increased acidity.

Thus, charge density offers a clear explanation as to why certain metal ions are more successful in creating acidic environments in their aqueous solutions.

Oxidation States

The oxidation state of a metal ion refers to the effective charge of the ion within a compound. It is directly linked to how many electrons the metal has lost or gained through bonding. In the context of metal ions in aqueous solutions:

• Higher oxidation states mean the metal ion has given up more electrons and usually has a higher positive charge.
• This increased charge often results in a smaller ionic radius due to greater attraction between the remaining electrons and the nucleus.
• Consequently, higher oxidation states correlate with increased metal ion polarization power, leading to greater acidity.

Understanding oxidation states helps us predict the tendencies of metal ions to create acidic solutions by looking at their ability to alter the electronic environment of surrounding water molecules.