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 strongly hydrated.

Step 1: Understand the Concept of Hydration

Hydration refers to the attraction and subsequent attachment of water molecules to ions. The strength of this hydration is influenced by the size and charge of the ion; smaller and more highly charged ions will typically be more strongly hydrated due to a higher charge density.

Step 2: Analyze the Cations' Characteristics

Evaluate the charge and size of the given cations: - \(\mathrm{Mg}^{2+}\) has a +2 charge and a relatively small ionic radius.- \(\mathrm{Na}^{+}\) has a +1 charge and a larger ionic radius than \(\mathrm{Mg}^{2+}\).- \(\mathrm{Cs}^{+}\) also has a +1 charge but an even larger ionic radius than both \(\mathrm{Mg}^{2+}\) and \(\mathrm{Na}^{+}\).

Step 3: Determine the Most Strongly Hydrated Ion

Smaller ions with higher charges tend to have a higher charge density, leading to stronger hydration. \(\mathrm{Mg}^{2+}\) is both smaller and has a higher charge compared to the other two, so \(\mathrm{Mg}^{2+}\) is most strongly hydrated.

Step 4: Determine the Least Strongly Hydrated Ion

Larger ions with lower charges have lower charge densities, resulting in weaker hydration. \(\mathrm{Cs}^{+}\) is the largest ion with the lowest charge, making it the least strongly hydrated among the three cations.

Key Concepts

Cation Hydration

Cation hydration is a process where water molecules surround and interact with positively charged ions, known as cations. When a salt dissolves in water, cations become surrounded by water molecules due to the attraction between the water's partial negative charge (oxygen end) and the positive charge of the cation. This interaction helps stabilize the ion in solution and is crucial for various biological and chemical processes.

Factors influencing the strength of cation hydration include:

• Charge of the ion: Higher charged ions attract more water molecules.
• Size of the ion: Smaller ions can get closer to water molecules, enhancing the interaction.

Overall, smaller cations with higher charges will generally experience stronger hydration.

Ion Charge Density

Ion charge density is key to understanding how ions interact with surrounding molecules. It is defined as the amount of charge an ion carries spread over its volume. Ions with higher charge densities exert stronger forces on nearby particles, affecting how they are managed in solutions.

Here's why it's important:

• Higher charge: Increases attraction forces with surrounding molecules like water.
• Smaller volume: Means the charge is concentrated, further enhancing interactions.

For instance, \(abla^{2+}\) has a high charge density due to its +2 charge and small size, resulting in more intense hydration compared to ions with lower charge densities.

Ionic Radius

The ionic radius refers to the effective size of an ion in a crystal lattice or in a solution. It affects how ions interact with each other and with molecules like water.

Understanding ionic radius involves knowing:

• Comparison between ions: Smaller ionic radii indicate smaller ions that typically fit more easily into spaces and interact more closely with other molecules.
• Effects on hydration: Smaller ions with higher charge densities (like \(abla^{2+}\)) lead to stronger hydration due to their ability to get closer to water molecules.

In a series like \(abla^{2+}\), \(abla^{+}\), and \(abla^{+}\), the ion with the smallest radius and highest charge is often more hydrated.

Chemical Bonding

Chemical bonding involves the interactions between atoms and ions that lead to the formation of chemical compounds. Understanding chemical bonding is fundamental in determining how ions like \(abla^{2+}\) behave in solution.

Key components of chemical bonding include:

• Electrostatic interactions: These play a significant role in the formation of bonds, especially in ionic compounds where positive and negative ions attract each other.
• Hydration effects: When ions enter water, their interaction with water molecules forms a kind of bonding that stabilizes them in solution.

These concepts help predict why certain ions are more strongly hydrated than others, based on their size, charge, and resulting charge density.