Problem 10 - Chemistry and Chemical Reactivity

Question

When salts of \(\mathrm{Mg}^{2+}, \mathrm{Na}^{+},\) and \(\mathrm{Cs}^{+}\) are placed in water, the ions are hydrated. Which of these three cations is most strongly hydrated? Which one is least strongly hydrated?

Step-by-Step Solution

Answer

Mg²⁺ is most strongly hydrated; Cs⁺ is least.

Step 1: Understanding Ion Hydration

When salts dissolve in water, the cations and anions are surrounded by water molecules, a process called hydration. The extent of hydration depends on the charge and size of the ion.

Step 2: Analyzing Ion Charge and Size

The strength of hydration is influenced by the charge density of the ion. Charge density is determined by the ion's charge and size. Higher charge and smaller size result in higher charge density and stronger hydration.

Step 3: Comparing Mg, Na, and Cs

Now let's compare the cations: - \(\text{Mg}^{2+}\): Charge = 2+, Smaller ionic radius- \(\text{Na}^{+}\): Charge = 1+, Intermediate ionic radius- \(\text{Cs}^{+}\): Charge = 1+, Larger ionic radius\(\text{Mg}^ {2+}\) has the highest charge and smallest size, leading to highest charge density, while \(\text{Cs}^{+}\) has the lowest charge density.

Step 4: Identifying Strongest and Weakest Hydration

Since \(\text{Mg}^{2+}\) has the highest charge density, it will be most strongly hydrated. \(\text{Cs}^{+}\), with the lowest charge density (due to its larger size), will be least strongly hydrated.

Key Concepts

Charge Density

Charge density is a crucial factor when determining how strongly an ion will hydrate in water. It refers to the ratio of the ion's charge to its size.
To put it simply, charge density is how "concentrated" an ion's charge is over its surface area.
When an ion has a high charge and a small size, it means its positive charge is packed tightly, leading to a high charge density.

• High charge density means the ion has a strong ability to attract water molecules.
• Low charge density means the ion has a weaker attraction to water molecules.

Mg²⁺ has a higher charge density compared to Na⁺ and Cs⁺ due to its double positive charge and smaller ionic radius. This makes it highly effective at attracting water molecules around itself.

Ion Hydration

Ion hydration is the process where water molecules surround and interact with dissolved ions. This interaction is critical in many chemical processes, including solubility and conductivity of salts in water.
This process is influenced heavily by the ion's charge density.

• Ions with high charge density, such as Mg²⁺, attract more water molecules leading to stronger hydration.
• Ions with low charge density, such as Cs⁺, attract fewer water molecules, resulting in weaker hydration.

The strong attraction due to higher charge and smaller size allows water molecules to form more compact layers around the ion, stabilizing it in solution.

Ionic Radius

The ionic radius is the measure of an ion's size, and it plays a pivotal role in determining the ion's charge density.
In hydration, the ionic radius is as important as the ion's charge.
Smaller ions, like Mg²⁺, tend to have a higher charge density due to the concentrated charge.
On the other hand, larger ions like Cs⁺ have a much lower charge density because their charge is spread over a larger area.

• Smaller ionic radius: Leads to higher concentration of charge, resulting in stronger interaction with water molecules.
• Larger ionic radius: Leads to lower concentration of charge, resulting in weaker interaction with water molecules.

Comparing Mg²⁺, Na⁺, and Cs⁺, the smaller radius of Mg²⁺ means that it has the greatest charge density and thus the strongest hydration, while the larger radius of Cs⁺ results in the weakest hydration.