Problem 58 - Chemistry and Chemical Reactivity

Question

List the following ions in order of hydration energies: \(\mathrm{Na}^{+}, \mathrm{K}^{+}, \mathrm{Mg}^{2+}, \mathrm{Ca}^{2+} .\) Explain how you determined this order.

Step-by-Step Solution

Answer

The order is \(\mathrm{Mg}^{2+} > \mathrm{Ca}^{2+} > \mathrm{Na}^{+} > \mathrm{K}^{+}\).

Step 1: Understanding Hydration Energy

Hydration energy refers to the amount of energy released when ions are surrounded by water molecules. It depends on the charge and size of the ion. Higher charge and smaller size result in higher hydration energy.

Step 2: Analyzing Ion Charges and Sizes

Examine the charges: \(\mathrm{Na}^{+}\) and \(\mathrm{K}^{+}\) have a charge of +1, while \(\mathrm{Mg}^{2+}\) and \(\mathrm{Ca}^{2+}\) have a charge of +2. Higher charges increase hydration energy.

Step 3: Comparing Similar Charges by Size

Compare the ions with the same charge by size. For \(+1\) ions, \(\mathrm{Na}^{+}\) is smaller than \(\mathrm{K}^{+}\), thus \(\mathrm{Na}^{+}\) has a higher hydration energy. For \(+2\) ions, \(\mathrm{Mg}^{2+}\) is smaller than \(\mathrm{Ca}^{2+}\), thus \(\mathrm{Mg}^{2+}\) has a higher hydration energy.

Step 4: Arranging Ions by Hydration Energy

Combine charge and size effects to order the ions. Since a high charge has more impact than size, \(\mathrm{Mg}^{2+}\) will have the highest hydration energy, followed by \(\mathrm{Ca}^{2+}\) (both +2). Among the +1 ions, \(\mathrm{Na}^{+}\) will have more than \(\mathrm{K}^{+}\). Therefore, the order is \(\mathrm{Mg}^{2+} > \mathrm{Ca}^{2+} > \mathrm{Na}^{+} > \mathrm{K}^{+}\).

Key Concepts

Ion Size

The size of an ion plays a crucial role in determining its hydration energy, which is the energy released when ions interact with water molecules. Smaller ions are more effective at interacting with water molecules because they allow water to get closer, leading to stronger interactions.
In our exercise, two sets of ions are analyzed based on size with the same charge. For instance, between

• the +1 charge ions:
  • \(\mathrm{Na}^+\)
  • \(\mathrm{K}^+\)

\(\mathrm{Na}^+\) is smaller, meaning it will have a larger hydration energy than \(\mathrm{K}^+\). Similarly, between the +2 charge ions:

• \(\mathrm{Mg}^{2+}\) and \(\mathrm{Ca}^{2+}\)

\(\mathrm{Mg}^{2+}\) is smaller; therefore, it will release more energy upon hydration compared to \(\mathrm{Ca}^{2+}\).
When considering ion size, always remember that smaller ions bring in greater interaction with surrounding water molecules, enhancing hydration energy.

Ionic Charge

The charge of an ion is another factor influencing the hydration energy. The higher the charge, the greater the attraction to water molecules, and thus, the greater the energy released. This is due to a stronger electric field created by higher charged ions.
In our exercise, we see ions like:

• \(\mathrm{Mg}^{2+}\) and \(\mathrm{Ca}^{2+}\) with a +2 charge
• \(\mathrm{Na}^{+}\) and \(\mathrm{K}^{+}\) with a +1 charge

The +2 ions exhibit higher hydration energies than those with a +1 charge. This is because the increased charge of +2 attracts more water molecules, leading to a higher interaction energy when these ions are hydrated. Between ions with different charges, always expect the higher charged ion to have a greater influence on the energy released during hydration.

Energy Released

Energy released during the hydration of ions is essentially the hydration energy. Hydration occurs as water molecules align around the ion, reducing its energy state, and releasing energy in the process.
This release of energy depends on specific factors:

• The ionic size: Smaller ions mean shorter distances for interaction, leading to stronger interactions.
• The ionic charge: Higher charges cause stronger electric attractions with water molecules.

Using these principles:

• \(\mathrm{Mg}^{2+}\) with its small size and high charge, releases the most energy.
• \(\mathrm{K}^+\) with a larger size and lower charge, releases the least amount of energy.

The combination of ion size and charge culminates in the total energy released via hydration, highlighting why different ions release varying amounts of energy upon interacting with water.

Cation Hydration

Hydration of cations involves the surrounding of positively charged ions by polar water molecules. As cations are surrounded by water molecules, several effects occur which influence their hydration energy.

• Ionic charge: Cations with a higher positive charge interact more strongly with dipolar water molecules.
• Ionic size: Smaller cations allow water molecules to approach more closely, strengthening the hydration interactions.

When applying these facts to our ions:

• \(\mathrm{Mg}^{2+}\), with its small size and high charge, demonstrates strong cation hydration, leading to high energy release.
• \(\mathrm{Na}^{+}\), although lower in charge, benefits from being smaller in size compared to \(\mathrm{K}^{+}\).

By understanding these principles, you'll find that cation hydration explains why \(\mathrm{Mg}^{2+}\) and \(\mathrm{Ca}^{2+}\) appear before \(\mathrm{Na}^{+}\) and \(\mathrm{K}^{+}\) in terms of hydration energy sequence.