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

Order: \(\mathrm{Mg}^{2+} > \mathrm{Ca}^{2+} > \mathrm{Na}^{+} > \mathrm{K}^{+}\).

Step 1: Understanding Hydration Energy

Hydration energy is the energy released when ions are surrounded by water molecules. It depends on two main factors: the charge of the ion and the size of the ion. Generally, higher charge and smaller size lead to higher hydration energy.

Step 2: Compare Sizes and Charges of Ions

We have the ions: \(\mathrm{Na}^{+}, \mathrm{K}^{+}, \mathrm{Mg}^{2+}, \mathrm{Ca}^{2+}\). Both \(\mathrm{Mg}^{2+}\) and \(\mathrm{Ca}^{2+}\) have a +2 charge, while \(\mathrm{Na}^{+}\) and \(\mathrm{K}^{+}\) have a +1 charge. In terms of size, \(\mathrm{K}^{+}\) is larger than \(\mathrm{Na}^{+}\), and \(\mathrm{Ca}^{2+}\) is larger than \(\mathrm{Mg}^{2+}\). Higher charge and smaller size imply stronger hydration energy.

Step 3: Determine the Order Based on Charge

Start with charge: since \(\mathrm{Mg}^{2+}\) and \(\mathrm{Ca}^{2+}\) have higher charges (+2) compared to \(\mathrm{Na}^{+}\) and \(\mathrm{K}^{+}\) (+1), \(\mathrm{Mg}^{2+}\) and \(\mathrm{Ca}^{2+}\) will have higher hydration energies compared to \(\mathrm{Na}^{+}\) and \(\mathrm{K}^{+}\).

Step 4: Determine the Order Based on Size Within Charge Categories

Within ions with the same charge, a smaller ionic size leads to higher hydration energy. For the +2 charged ions, \(\mathrm{Mg}^{2+}\) is smaller than \(\mathrm{Ca}^{2+}\), so \(\mathrm{Mg}^{2+}\) has a higher hydration energy than \(\mathrm{Ca}^{2+}\). For the +1 charged ions, \(\mathrm{Na}^{+}\) is smaller than \(\mathrm{K}^{+}\), so \(\mathrm{Na}^{+}\) has a higher hydration energy than \(\mathrm{K}^{+}\).

Step 5: Final Order of Hydration Energies

Combining the findings: \(\mathrm{Mg}^{2+}\) has the highest hydration energy due to its high charge and small size, followed by \(\mathrm{Ca}^{2+}\), \(\mathrm{Na}^{+}\), and finally \(\mathrm{K}^{+}\) with the lowest hydration energy. Thus, the order is: \(\mathrm{Mg}^{2+} > \mathrm{Ca}^{2+} > \mathrm{Na}^{+} > \mathrm{K}^{+}\).

Key Concepts

Charge of Ions

The charge of an ion is a fundamental property affecting its interaction with water molecules. Ions are atoms or molecules that have lost or gained electrons, resulting in a net electric charge.

Higher charged ions tend to have greater hydration energies because they produce stronger electric fields. This increased field strength means they can attract water molecules more strongly than ions with lower charges.

• Ions with a high positive charge (like \(\mathrm{Mg}^{2+}\) and \(\mathrm{Ca}^{2+}\)) have a stronger attraction to the negatively charged polar molecules of water.
• Ions with a lower charge such as \(\mathrm{Na}^{+}\) and \(\mathrm{K}^{+}\) have weaker interactions due to a less intense electric field.

Understanding the influence of the ion's charge helps explain why certain ions are more "hydrated" than others, which simply means they tightly bind to more water molecules, releasing energy.

Ionic Size

The size of an ion, which is determined by the number of electron shells around its nucleus, has a significant inpact on hydration energy.

Smaller ions tend to have greater hydration energies. This is because smaller ions have their positive charge concentrated in a smaller area, increasing the attraction to water molecules.

Here's how it works:

• Smaller ions can come closer to the water molecules, resulting in a stronger attraction because the distance between charges in physics is key in determining force strength.
• Larger ions, like \(\mathrm{K}^{+}\), have a distributed charge over a larger volume, which weakens the electrostatic attraction to water molecules compared to smaller ions like \(\mathrm{Na}^{+}\).

Therefore, an ion like \(\mathrm{Mg}^{2+}\) not only benefits from its higher charge but also from its smaller size, enhancing its hydration energy.

Ionic Hydration

Ionic hydration refers to how ions interact and are stabilized by water molecules. When ions dissolve in water, they become surrounded by water molecules in a structured arrangement.

This interaction releases energy known as hydration energy. The process is more pronounced in ions with higher charges or smaller sizes.

• Hydration is essential because it reflects how well ions can dissolve in water.
• For instance, \(\mathrm{Mg}^{2+}\) ions release more energy upon hydration compared to \(\mathrm{Ca}^{2+}\) ions, attributable to its smaller size and greater charge.

The concept highlights why some ions are more soluble in water than others.

It also aids in predicting the behavior of different ions in various chemical environments, which is crucial in fields like biochemistry and engineering.

Ion-Water Interaction

The interaction between ions and water molecules is a delicate interplay of electrostatic forces. Water, due to its polar nature, is very responsive to electric charges.

• Positively charged ions like \(\mathrm{Na}^{+}\) and \(\mathrm{Mg}^{2+}\) attract the partly negative oxygen end of water molecules.
• Conversely, a negatively charged ion would attract the hydrogen ends, which carry a slight positive charge.

The strength of the ion-water interaction is a determinant of hydration energy. The stronger the attraction between an ion and water, the greater the energy released and the more stable the ion-water complex.

Understanding this fundamental concept helps explain many phenomena in chemistry, such as why magnesium and calcium ions are prevalent in hard water or how ions affect the boiling and freezing points of solutions.