Problem 10 - Chemistry and Chemical Reactivity

Question

When salts of \(\mathrm{Mg}^{2+}, \mathrm{Na}^{+},\) and \(\mathrm{Cs}^{+}\) 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

\( \mathrm{Mg}^{2+} \) is the most strongly hydrated, and \( \mathrm{Cs}^{+} \) is the least strongly hydrated.

Step 1: Understand Ion Hydration

Hydration occurs when water molecules surround ions. The strength of hydration depends on the charge density of ions, which is influenced by both the charge and size of the ion.

Step 2: Analyze Charges of Ions

The ions given are \( \mathrm{Mg}^{2+} \), \( \mathrm{Na}^{+} \), and \( \mathrm{Cs}^{+} \). Note that \( \mathrm{Mg}^{2+} \) has a 2+ charge while \( \mathrm{Na}^{+} \) and \( \mathrm{Cs}^{+} \) both have a 1+ charge.

Step 3: Analyze Sizes of Ions

The size of the ions from smallest to largest is \( \mathrm{Mg}^{2+} < \mathrm{Na}^{+} < \mathrm{Cs}^{+} \). Smaller ions have a higher charge density.

Step 4: Determine Hydration Strength

\( \mathrm{Mg}^{2+} \) has the highest charge density (due to its 2+ charge and smaller size), making it the most strongly hydrated. \( \mathrm{Cs}^{+} \) is largest with a 1+ charge, making it the least strongly hydrated.

Key Concepts

Understanding Charge Density and Its Impact

Charge density is a fundamental concept in chemistry that describes how concentrated the electric charge is around an ion. When a charged particle is small and carries a significant charge, it has high charge density. This increased density enhances the "pull" or attraction that ion exerts on surrounding water molecules during hydration.
A higher charge density generally means stronger hydration. Cations with greater charge densities can attract water molecules more intensely, leading to more pronounced hydration effects. Cations like the magnesium ion (\(\mathrm{Mg}^{2+}\)), which has a higher charge density due to its smaller size and higher charge, are perfect examples for studying these effects.

• More charge, more hydration
• Smaller size, higher charge density

Ion Size and Hydration Relationship

The size of an ion plays a crucial role in determining how strongly it is hydrated. The principle at work here is that smaller ions can pack more charge into a smaller space, leading to higher charge density, which strengthens their interaction with water molecules.
For instance, the magnesium ion (\(\mathrm{Mg}^{2+}\)) is smaller than sodium (\(\mathrm{Na}^{+}\)) and cesium (\(\mathrm{Cs}^{+}\)) ions. This smaller size indicates that water molecules are drawn closer to the magnesium ion's surface, enabling stronger hydration. Meanwhile, cesium, being larger, has a lower charge density, and thus weakly hydrates with water.

• Smaller ions hydrate stronger
• Larger ions have lower charge density

The Phenomenon of Cation Hydration

Cation hydration occurs when positively charged ions attract surrounding water molecules due to the ions' charge. This process is often observed with common cations such as \(\mathrm{Mg}^{2+}\), \(\mathrm{Na}^{+}\), and \(\mathrm{Cs}^{+}\). During hydration, water molecules align themselves in a particular manner around cations to stabilize the charge.
Cations that are smaller and more charged will pull water molecules more tightly, causing a stronger hydration effect. For example, \(\mathrm{Mg}^{2+}\), with its smaller radius and 2+ charge, draws water molecules closely and forms a compact and stable hydration shell compared to \(\mathrm{Cs}^{+}\), which due to its size, forms a looser hydration shell.

• Strong cation-water attraction
• Highly charged cations form tight hydration shells

Unique Properties of Magnesium Ion Hydration

Magnesium ions (\(\mathrm{Mg}^{2+}\)) exhibit unique hydration properties, primarily due to their high charge and small ionic size, resulting in exceptionally high charge density. These characteristics make magnesium ions highly effective at drawing in water molecules and forming a tight, stable hydration shell.
This intense hydration has practical implications. It influences many biological processes and even industrial applications, where magnesium's capacity to attract water is critical. Compared to other cations like sodium or cesium, the magnesium ion's hydration phenomenon is significantly more pronounced, making it a topic of interest in the study of ionic interactions in water.

• High charge density enhances magnesium hydration
• Crucial in biological and industrial applications