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) is correct: \\( \mathrm{Be}^{2+}>\mathrm{Mg}^{2+}>\mathrm{Ca}^{2+}>\mathrm{Sr}^{2+}>\mathrm{Ba}^{2+} \\).

Step 1: Understanding Hydration Energy

Hydration energy is the amount of energy released when ions dissolve in water. It depends on the size of the ion and the charge density. Smaller ions with higher charge density will have higher hydration energies.

Step 2: Analyzing Alkaline Earth Metal Ions

The alkaline earth metals are in group 2 of the periodic table: Be, Mg, Ca, Sr, Ba. As we move down the group, the size of the cations increases and charge density decreases, leading to a decrease in hydration energy.

Step 3: Comparing Hydration Energies

Since hydration energy decreases with increasing ionic size, the order from highest to lowest hydration energy should follow the size of the ions from smallest to largest: - \(Be^{2+} > Mg^{2+} > Ca^{2+} > Sr^{2+} > Ba^{2+}\)

Step 4: Selecting the Correct Answer

Compare the derived order of hydration energies \(Be^{2+} > Mg^{2+} > Ca^{2+} > Sr^{2+} > Ba^{2+}\) to the provided options. The correct answer matches option (b).

Key Concepts

Alkaline Earth Metals

Alkaline earth metals are a group of elements found in group 2 of the periodic table. They include beryllium (Be), magnesium (Mg), calcium (Ca), strontium (Sr), and barium (Ba). These metals are known for having two electrons in their outermost shell, which gives them a valency of +2. This means they often form ions with a charge of +2. Alkaline earth metals are similar in many chemical properties due to their group position. However, as you move down the group from Be to Ba, several trends can be observed in their properties:

• Atomic size increases, making the atoms larger.
• Ionization energy decreases, meaning it takes less energy to remove an electron.
• Electronegativity decreases, so they attract electrons less strongly.
• Hydration energy decreases, making them less likely to dissolve in water to release energy.

These trends are primarily because of the increasing atomic radius and the addition of more electron shells as you move down the group.

Ionic Size

Ionic size is a key factor in determining the behavior of ions in chemical reactions, especially when talking about hydration energy. Ionic size refers to the size or radius of an ion and is influenced by the number of electrons and their arrangement around the nucleus. When we compare ions within a group, such as alkaline earth metals, the size of the ions tends to increase as we move down the group. This is because each consecutive element has an additional electron shell:

• For instance, Be²⁺ is the smallest ion in the group due to having fewer electron shells.
• Conversely, Ba²⁺ is the largest ion as it has more electron shells.

The increase in ionic size affects a metal’s chemical properties, including its hydration energy. Smaller ions, such as Be²⁺, tend to have higher hydration energies because they can be more closely packed with water molecules, leading to a stronger interaction.

Charge Density

Charge density is an important concept when talking about ionic compounds and their interactions with water. It refers to the amount of charge per unit area on an ion and is essentially how much charge is 'packed' into an ion's volume. Charge density is influenced by two main factors: the ion's charge and its size. For alkaline earth metal ions, the charge is consistently +2 across the group. However, as the size of these ions increases down the group, their charge density decreases. This means:

• Beryllium ion (Be²⁺) has the highest charge density because it is a small ion with a +2 charge.
• Barium ion (Ba²⁺), being larger, has a lower charge density.

High charge density leads to strong interactions with water molecules, resulting in higher hydration energy. For alkaline earth metals, smaller ions like Be²⁺ will have higher hydration energy due to their higher charge density. As ionic size increases and charge density decreases, the hydration energy correspondingly drops.