Problem 99 - A Complete Resource Book in Chemistry for JEE Main

Question

The correct order of hydration energy of alkaline earth metal ion is (a) \(\mathrm{Mg}^{2+}>\mathrm{Be}^{2+}>\mathrm{Ba}^{2+}>\mathrm{Ca}^{2+}>\mathrm{Sr}^{2+}\) (b) \(\mathrm{Be}^{2+}>\mathrm{Mg}^{2+}>\mathrm{Ca}^{2+}>\mathrm{Sr}^{2+}>\mathrm{Ba}^{2+}\) (c) \(\mathrm{Ba}^{2+}>\mathrm{Be}^{2+}>\mathrm{Ca}^{2+}>\mathrm{Mg}^{2+}<\mathrm{Sr}^{2}\) (d) \(\mathrm{Be}^{2+}>\mathrm{Ca}^{2+}>\mathrm{Sr}^{2+}>\mathrm{Ba}^{2+}>\mathrm{Mg}^{2}\)

Step-by-Step Solution

Answer

Option (b): \( \text{Be}^{2+} > \text{Mg}^{2+} > \text{Ca}^{2+} > \text{Sr}^{2+} > \text{Ba}^{2+} \).

Step 1: Understanding Hydration Energy

Hydration energy is the energy released when ions are dissolved in water. It is predominantly influenced by the charge and radius of the ion: a higher charge and smaller radius increases the hydration energy.

Step 2: Comparing Ionic Radii

In the alkaline earth metals, as you move down the group from Be to Ba, the ionic radii increase. This means that Mg has a smaller radius compared to Ca, Sr, and Ba, and Be has the smallest radius overall.

Step 3: Determining Higher Hydration Energy

Smaller ions with the same charge have higher hydration energies because the smaller radius allows for stronger interactions with water molecules. Therefore, the order from highest to lowest hydration energy generally follows the trend of decreasing ionic radii.

Step 4: Arranging Alkaline Earth Metal Ions by Hydration Energy

Based on their ionic radii and charges, the order of alkaline earth metal ions by decreasing hydration energy should be \( ext{Be}^{2+}, ext{Mg}^{2+}, ext{Ca}^{2+}, ext{Sr}^{2+}, ext{Ba}^{2+}\), which corresponds to option (b).

Key Concepts

Hydration Energy

Hydration energy is a critical concept in chemistry, especially when discussing the interactions of ions with water. It refers to the amount of energy released when one mole of ions is solvated by water molecules. Essentially, this energy is liberated due to the formation of ion-water interactions, which can lead to a more stable system. For alkaline earth metals, such as beryllium (Be), magnesium (Mg), calcium (Ca), strontium (Sr), and barium (Ba), the hydration energy is significantly influenced by their ionic characteristics.

Key factors affecting hydration energy include:

• Charge of the Ion: Higher charges on the ion typically result in greater hydration energy. This is because the charge creates a stronger electric field, enhancing interactions with water molecules.
• Size of the Ion: Smaller ions have higher hydration energies because they can get closer to the water molecules, once again maximizing attractive forces.

Understanding these traits helps explain why smaller, highly charged ions like \(\text{Be}^{2+}\) have greater hydration energies than larger, less charged ones like \(\text{Ba}^{2+}\). Thus, the order of decreasing hydration energy for alkaline earth metals is based on their size and charge, aligning with the observed trend of \(\text{Be}^{2+}>\text{Mg}^{2+}>\text{Ca}^{2+}>\text{Sr}^{2+}>\text{Ba}^{2+}\).

Ionic Radii

The size of an ion, known as its ionic radius, plays a pivotal role in determining how it interacts with its environment. In the periodic table, especially for the alkaline earth metals, the ionic radius increases as you move down a group. This is due to the addition of electron shells, which naturally causes the size of the ion to expand.

For the alkaline earth metal ions:

• Beryllium (3), being at the top of this group, has the smallest ionic radius.
• Barium (5), situated at the bottom of the group, possesses the largest ionic radius.

The size differences among these ions affect their chemical properties, including hydration energy. Smaller ions have greater charge density, leading to stronger interactions with solvents like water. This is why, as you analyze and compare alkaline earth metal ions, you'll observe that the ionic radius inversely affects the hydration energy.

Hence, in solving problems like the given exercise, recognizing the trend in ionic radii is crucial for determining the hydration energy sequence, further allowing students to confidently arrive at the correct order among these ions.

Charge-to-Radius Ratio

Another important concept when discussing ionic interactions is the charge-to-radius ratio. This ratio essentially encapsulates key factors of ionic size and charge in one metric, offering deep insights into the ion's behavior in various chemical environments.

The charge-to-radius ratio is calculated as follows:

• Formula: \( \text{Charge of Ion} / \text{Ionic Radius} \)

This ratio is crucial because ions with a higher charge-to-radius ratio exhibit increased polarization potential, enhancing their interaction strength with other molecules. For alkaline earth metals:

• Influence on Hydration Energy: Ions with a higher charge-to-radius ratio possess greater hydration energies because they exert a stronger attraction towards water molecules.
• Comparative Scale: \(\text{Be}^{2+}\) with a higher charge-to-radius ratio interacts more strongly with water compared to \(\text{Ba}^{2+}\).

Understanding the charge-to-radius ratio is essential for predicting the reactivity and solvation dynamics of ions, particularly in aqueous solutions. By incorporating this metric, students can better predict trends and explain variations in hydration energy seen across different ions, making chemistry more intuitive and graspable.