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

(c) \(\mathrm{Na}^{+}\)

Step 1: Understand the Concept of Hydration Energy

Hydration energy refers to the amount of energy released when ions interact with water molecules. It's influenced by the charge density of an ion; the higher the charge and the smaller the radius, the greater the hydration energy.

Step 2: Analyze the Charge and Size of Ions

Examine the charge and radius of each ion: - \(\mathrm{Mg}^{2+}\) has a +2 charge. - \(\mathrm{Al}^{3+}\) has a +3 charge. - \(\mathrm{Be}^{2+}\) has a +2 charge but is smaller than \(\mathrm{Mg}^{2+}\). - \(\mathrm{Na}^{+}\) has a +1 charge.

Step 3: Compare the Charge Density

Charge density is determined by the ion charge over its volume. Since \(\mathrm{Al}^{3+}\) has the highest charge and smallest ionic radius among these, its charge density is the highest, giving it higher hydration energy than \(\mathrm{Mg}^{2+}\). Similarly, \(\mathrm{Be}^{2+}\), being smaller than \(\mathrm{Mg}^{2+}\), also has higher hydration energy. \(\mathrm{Na}^{+}\), with lower charge, will have lower hydration energy than \(\mathrm{Mg}^{2+}\).

Step 4: Determine the Ion with Lower Hydration Energy

\(\mathrm{Mg}^{2+}\) has higher hydration energy than \(\mathrm{Na}^{+}\) because \(\mathrm{Na}^{+}\) has a lower charge, leading to lower charge density.

Key Concepts

Charge Density

Charge density is a key concept when understanding why certain ions have higher or lower hydration energies. It refers to how much charge is concentrated in a particular volume of an ion. This is determined by the ratio of the ion's charge to its volume. To simplify:

• Higher charge = potentially higher charge density.
• Smaller radius (or volume) = higher charge density.

Analyzing the ions involved, such as \(\mathrm{Mg}^{2+}\), \(\mathrm{Na}^{+}\), \(\mathrm{Be}^{2+}\), and \(\mathrm{Al}^{3+}\):

• \(\mathrm{Al}^{3+}\) has a high charge and a compact size, resulting in the highest charge density among the ions considered.
• \(\mathrm{Be}^{2+}\), though having the same charge as \(\mathrm{Mg}^{2+}\), also possesses a smaller ionic radius, ensuring a higher charge density than \(\mathrm{Mg}^{2+}\).
• \(\mathrm{Na}^{+}\) has the least charge density due to its single positive charge combined with a larger radius.

Charge density significantly impacts how ions interact with water molecules, as greater charge density means stronger attraction and interaction, leading to higher hydration energy.
Understanding charge density helps to predict and compare how different ions behave in an aqueous environment.

Ion Charge

The charge of the ion is an intrinsic property that affects its interactions with other particles, including water molecules. The higher the ion's charge, the more strongly it will attract the polar water molecules during hydration. This is because:

• Positive ions can attract the negative ends of the dipolar water molecules.
• A larger charge results in a stronger electric field around the ion.

For instance, with \(\mathrm{Mg}^{2+}\), we have a +2 charge. Contrast this with \(\mathrm{Na}^{+}\), which carries only a +1 charge, making its attraction to water weaker and, subsequently, resulting in lower hydration energy.
On the other hand, \(\mathrm{Al}^{3+}\) possesses a +3 charge, leading to the strongest attraction among the ions discussed. Thus, the ion charge not only dictates the strength of the attraction but also significantly influences the hydration process, determining the equilibrium and stability of such systems in water.

Ionic Radius

The ionic radius is the size of an ion, and it plays a crucial role in determining its chemical behavior, including hydration energy. Smaller ions can pack more charge per unit volume, contributing to high charge density and, therefore, greater hydration energy.

• A smaller ionic radius means the ion can come closer to water molecules, enhancing the interaction and the resulting energy release.
• For example, \(\mathrm{Be}^{2+}\) has a smaller ionic radius compared to \(\mathrm{Mg}^{2+}\), leading to higher hydration energy.

Conversely, larger ions, like \(\mathrm{Na}^{+}\), have a more spread-out charge over a larger volume, decreasing interaction strength with water molecules.
This inverse relationship between size and hydration energy means that knowing the ionic radius helps predict how energetically favorable an ion's interaction with water will be. Therefore, considering ionic radius is essential when comparing the hydration energies across different ions.