Problem 56 - A Complete Resource Book in Chemistry for JEE Main

Question

The hydration energy or \(\mathrm{Mg}^{2+}\) ions is higher than that of (a) \(\mathrm{Al}^{3+}\) (b) \(\mathrm{Be}^{2+}\) (c) \(\mathrm{Na}^{+}\) (d) none of these

Step-by-Step Solution

Answer

The hydration energy of \(\mathrm{Mg}^{2+}\) is higher than that of \(\mathrm{Na}^{+}\) (option c).

Step 1: Understanding Hydration Energy

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

Step 2: Compare Ion Charges

List the charges of the given ions: \(\mathrm{Mg}^{2+}\) has a +2 charge, \(\mathrm{Al}^{3+}\) has a +3 charge, \(\mathrm{Be}^{2+}\) has a +2 charge, and \(\mathrm{Na}^{+}\) has a +1 charge.

Step 3: Compare Ion Sizes

The size of an ion affects its hydration energy. Generally, the smaller the ion size, the higher the hydration energy. Consider the periodic trend that the size decreases across a period and increases down a group.

Step 4: Analyze \(\mathrm{Al}^{3+}\) versus \(\mathrm{Mg}^{2+}\)

\(\mathrm{Al}^{3+}\) has a higher charge than \(\mathrm{Mg}^{2+}\) and a smaller ionic size, resulting in a higher hydration energy for \(\mathrm{Al}^{3+}\).

Step 5: Analyze \(\mathrm{Be}^{2+}\) versus \(\mathrm{Mg}^{2+}\)

Both \(\mathrm{Be}^{2+}\) and \(\mathrm{Mg}^{2+}\) have the same charge. However, \(\mathrm{Be}^{2+}\) is smaller than \(\mathrm{Mg}^{2+}\), leading to a higher hydration energy for \(\mathrm{Be}^{2+}\).

Step 6: Analyze \(\mathrm{Na}^{+}\) versus \(\mathrm{Mg}^{2+}\)

\(\mathrm{Na}^{+}\) has a lower charge (+1) compared to \(\mathrm{Mg}^{2+}\) and is larger in size. Thus, \(\mathrm{Mg}^{2+}\) has a higher hydration energy than \(\mathrm{Na}^{+}\).

Step 7: Conclusion: Determine the Correct Answer

From the analyses, the hydration energy of \(\mathrm{Mg}^{2+}\) is higher than \(\mathrm{Na}^{+}\) due to its higher charge and smaller size.

Key Concepts

Ion Charge

Ion charge is a fundamental concept in understanding the behavior of ions in various chemical reactions. It refers to the electrical charge that an ion has as a result of losing or gaining electrons. The charge of an ion strongly affects its chemical properties, including hydration energy.

When an ion has a higher charge, it creates a stronger electric field around itself. This means that it can attract water molecules more powerfully, leading to a higher hydration energy. For instance,

• Aluminum Ion (\(\mathrm{Al}^{3+}\)): This ion has a +3 charge. Since it has a high charge, it attracts water molecules more strongly, thus resulting in high hydration energy.
• Magnesium Ion (\(\mathrm{Mg}^{2+}\)): With a +2 charge, it also shows considerable hydration energy, though less than that of \(\mathrm{Al}^{3+}\) because the charge is lower.
• Sodium Ion (\(\mathrm{Na}^{+}\)): This ion only has a +1 charge, which means it has lower hydration energy compared to other ions with higher charges.

Understanding ion charge is essential for predicting and comparing the hydration energies of different ions.

Ion Size

Ion size, also known as ionic radius, is another crucial factor that influences hydration energy. Generally, smaller ions can pack water molecules more densely around them, increasing the interaction and, consequently, hydration energy.

This is because smaller ions have their charge spread over a smaller area, creating a higher charge density. Let's take a closer look:

• Beryllium Ion (\(\mathrm{Be}^{2+}\)): This ion is smaller than the \(\mathrm{Mg}^{2+}\) ion despite having the same charge. Thus, it has higher hydration energy as more water molecules can closely surround it.
• Magnesium Ion (\(\mathrm{Mg}^{2+}\)): Although smaller than sodium, it is bigger than beryllium, making its hydration energy less than \(\mathrm{Be}^{2+}\) but more than \(\mathrm{Na}^{+}\).
• Sodium Ion (\(\mathrm{Na}^{+}\)): This ion is relatively larger, meaning it cannot attract water molecules as closely as smaller ions, resulting in lower hydration energy.

Ion size is thus a vital factor when comparing hydration energies, especially between ions with similar charges.

Periodic Trends

Periodic trends help us understand the patterns in ionic radii, ionization energies, and charges across the periodic table, which are essential for predicting ion behaviors.

These trends can explain why certain ions have higher or lower hydration energies:

• Across a Period: As you move from left to right across a period, the ionic size generally decreases. The decreasing size is due to the increasing nuclear charge pulling the electrons closer. As seen with \(\mathrm{Be}^{2+}\) being smaller than \(\mathrm{Mg}^{2+}\), leading to higher hydration energy.
• Down a Group: Moving down a group in the periodic table, ionic size generally increases even if the charge is the same, because you are adding more electron shells. This is why \(\mathrm{Na}^{+}\) is larger than \(\mathrm{Mg}^{2+}\) and has lower hydration energy.

Understanding these periodic trends helps predict the ion size and charge, thus making it easier to compare the hydration energies of different ions.