Problem 93 - Chemistry and Chemical Reactivity

Question

When salts of \(\mathrm{Mg}^{2+}, \mathrm{Ca}^{2+},\) and \(\mathrm{Be}^{2+}\) are placed in water, the positive ion is hydrated (as is the negative ion). Which of these three cations is most strongly hydrated? Which one is least strongly hydrated?

Step-by-Step Solution

Answer

\(\mathrm{Be}^{2+}\) is most strongly hydrated; \(\mathrm{Ca}^{2+}\) is least.

Step 1: Understanding Cation Hydration

Hydration of cations involves the attraction between the cation and water molecules. The strength of hydration depends on the charge density of the ion, which is determined by its charge-to-radius ratio.

Step 2: Analyze Charge Density

Of \(\mathrm{Mg}^{2+}, \mathrm{Ca}^{2+}, \mathrm{and} \mathrm{Be}^{2+},\) all have a charge of +2. Therefore, the determining factor for hydration strength is the ionic radius; the smaller the radius, the higher the charge density.

Step 3: Ionic Radius Comparison

The ionic radii of the cations are: \(\mathrm{Be}^{2+}\) with the smallest radius, followed by \(\mathrm{Mg}^{2+}\), and \(\mathrm{Ca}^{2+}\) with the largest radius. This ordering indicates \(\mathrm{Be}^{2+}\) has the highest charge density, and \(\mathrm{Ca}^{2+}\) the lowest.

Step 4: Determine Hydration Strength

Given the ionic radius comparison, \(\mathrm{Be}^{2+}\), with the smallest radius, is the most strongly hydrated. Conversely, \(\mathrm{Ca}^{2+}\), having the largest radius, is the least strongly hydrated.

Key Concepts

Charge Density

Charge density is a crucial concept for understanding cation hydration. It represents how much electric charge is present per unit volume in a cation. A higher charge density means the cation's positive charge is more concentrated. This concentration influences how strongly the cation can attract negatively charged water molecules.
For cations such as \(\mathrm{Mg}^{2+}\), \(\mathrm{Ca}^{2+}\), and \(\mathrm{Be}^{2+}\), charge density plays a key role in determining their hydration strength. Although all these cations have the same positive charge (+2), their charge density differs. This variation is due to differences in their ionic radius.

• Cations with smaller ionic radii typically have higher charge densities. This is because the positive charge is packed into a smaller volume.
• Higher charge density increases the electrostatic attraction between the cation and water molecules, enhancing the hydration strength.

Ionic Radius

The ionic radius of a cation significantly affects its hydration. It refers to the size of an ion in a crystal lattice or when dissolved in solution.Knowing the ionic radius helps us understand why different cations have different hydration strengths.
For \(\mathrm{Be}^{2+}\), \(\mathrm{Mg}^{2+}\), and \(\mathrm{Ca}^{2+}\), their ionic radii determine how tightly they interact with water molecules:

• \(\mathrm{Be}^{2+}\) has the smallest ionic radius. This means that it has the highest charge density and is most strongly hydrated when dissolved in water.
• \(\mathrm{Mg}^{2+}\) has a moderate ionic radius, giving it a medium level of hydration strength, standing between \(\mathrm{Be}^{2+}\) and \(\mathrm{Ca}^{2+}\).
• \(\mathrm{Ca}^{2+}\) possesses the largest ionic radius, resulting in a lower charge density and the weakest hydration strength of the three cations.

Smaller ionic radii mean more concentrated charge, leading to stronger hydration forces.

Hydration Strength

Hydration strength measures how effectively a cation attracts and binds water molecules when it is in solution. This process depends on the cation's charge density and ionic radius.
Here's how these two factors contribute to hydration strength:

• A higher charge density leads to a stronger electrostatic pull on water molecules, thus a higher hydration strength.
• Cations with smaller ionic radii, like \(\mathrm{Be}^{2+}\), exhibit stronger hydration because their charges are more densely packed. This enables these cations to create more robust bonds with water molecules.
• On the contrary, cations such as \(\mathrm{Ca}^{2+}\) with larger radii have a weaker charge pull. Their bonds with water are not as strong, resulting in lower hydration strength.

Understanding these interactions helps explain why some cations dissolve more effectively in water and interact more vigorously with other ions or molecules.