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 correct answer is (c) \( \mathrm{Na}^{+} \).

Step 1: Understand the Concept of Hydration Energy

Hydration energy is the amount of energy released when ions are surrounded by water molecules. It is affected by the charge and size of the ion: higher charge and smaller size contribute to higher hydration energy.

Step 2: Analyze the Charge of Ions

Compare the ionic charges. The magnesium ion \( \mathrm{Mg}^{2+} \) has a charge of +2, whereas the aluminum ion \( \mathrm{Al}^{3+} \) has a charge of +3, the beryllium ion \( \mathrm{Be}^{2+} \) has a charge of +2, and the sodium ion \( \mathrm{Na}^{+} \) has a charge of +1. Generally, more highly charged ions have greater hydration energies.

Step 3: Analyze the Size of Ions

Next, consider the ionic size. \( \mathrm{Al}^{3+} \), \( \mathrm{Mg}^{2+} \), and \( \mathrm{Be}^{2+} \) have smaller radii compared to \( \mathrm{Na}^{+} \), which leads to higher hydration energy due to closer interaction with water molecules.

Step 4: Compare Hydration Energies

Compare \( \mathrm{Mg}^{2+} \) with other ions: \( \mathrm{Al}^{3+} \) ions, having a higher charge and smaller size, have higher hydration energy than \( \mathrm{Mg}^{2+} \) ions. \( \mathrm{Be}^{2+} \) has similar charge but is much smaller, potentially leading to higher hydration energy. \( \mathrm{Na}^{+} \), having a lower charge and larger size, has a lower hydration energy than \( \mathrm{Mg}^{2+} \).

Step 5: Determine the Correct Option

Since \( \mathrm{Na}^{+} \) ions have a lower hydration energy compared to \( \mathrm{Mg}^{2+} \), the correct answer is (c) \( \mathrm{Na}^{+} \).

Key Concepts

Ionic Charge

Ionic charge is an essential concept when discussing hydration energy. Ions are atoms or molecules that have gained or lost electrons, resulting in a net positive or negative charge. This charge is indicated by the superscript number and symbol (e.g., "+2", "-3") following the element or molecule notation. The charge of an ion dictates how strongly it can interact with polar molecules like water.
The more charged an ion is, the stronger its interaction with water molecules, which in turn increases the hydration energy. For instance:

• \( \mathrm{Mg}^{2+} \) has a charge of +2;
• \( \mathrm{Na}^{+} \) has a charge of +1.

Typically, ions with higher charges, like \( \mathrm{Al}^{3+} \), have higher hydration energies. This is because the higher the charge, the more the ion can attract the polar water molecules, thus releasing more energy in the process.

Ionic Size

The size of an ion is another factor that affects its hydration energy. Ionic size is determined by the radius of the ion. Generally, smaller ions can approach water molecules more closely than larger ions. This proximity allows for a stronger interaction, leading to greater hydration energy.
A smaller ion with a given charge will typically have a higher hydration energy compared to a larger ion with the same charge. For example:

• \( \mathrm{Be}^{2+} \) is smaller than \( \mathrm{Mg}^{2+} \);
• \( \mathrm{Na}^{+} \) is larger than both \( \mathrm{Be}^{2+} \) and \( \mathrm{Mg}^{2+} \).

Therefore, even if two ions share the same charge, the one with the smaller radius will release more energy when hydrated.

Chemical Ions

Chemical ions are charged particles formed from atoms or molecules. They play a significant role in a variety of chemical processes, including the dissolution and hydration in solutions. In aqueous solutions, these ions interact with water, leading to the release or absorption of energy based on their charge and size.
These interactions can be influenced by other factors such as ionic charge and size. For instance, an ion like \( \mathrm{Al}^{3+} \), due to its high charge, engages more effectively with surrounding water molecules, enhancing its hydration energy. Understanding the behavior of chemical ions in such contexts is crucial for predicting their reactions and stability in different environments.

Energy Release in Chemistry

Energy release is a fundamental concept in chemistry, especially in processes such as dissolution and hydration. When ions dissolve in water, they become surrounded by water molecules, a process known as hydration. This process releases energy, referred to as hydration energy.
The amount of energy released depends on factors including ionic charge and size. For example, ions with higher charges and smaller sizes release more energy when hydrated, as they attract water molecules more strongly. This is why ions like \( \mathrm{Mg}^{2+} \) have higher hydration energy compared to larger or less charged ions such as \( \mathrm{Na}^{+} \).

• Stronger interactions lead to more significant energy release.
• Larger ions have weaker interactions and thus release less energy.

Thus, understanding how and why energy is released during chemical processes is key to mastering chemistry homework problems related to ions and their behaviors.