Problem 52 - A Complete Resource Book in Chemistry for JEE Main

Question

Let IP stand for ionization potential. The IP, and \(\mathrm{IP}_{2}\) of \(\mathrm{Mg}\) are 178 and \(348 \mathrm{kcal} \mathrm{mol}^{-1} .\) The energy required for the following reaction is \(\mathrm{Mg} \longrightarrow \mathrm{Mg}^{2+}+2 \mathrm{e}-\) (a) \(+178 \mathrm{kcal}\) (b) \(+526 \mathrm{kcal}\) (c) \(-170 \mathrm{kcal}\) (d) \(-526 \mathrm{kcal}\)

Step-by-Step Solution

Answer

The correct answer is (b) \(+526 \mathrm{kcal}\).

Step 1: Understand the Reaction

We need to determine the energy required for the reaction \( \text{Mg} \rightarrow \text{Mg}^{2+} + 2\, \text{e}^{-} \). This reaction represents the removal of two electrons from a neutral magnesium atom to form a doubly charged magnesium ion \( \text{Mg}^{2+} \).

Step 2: Identify Given Information

We are given the first ionization potential, \( \mathrm{IP}_1 = 178 \text{kcal/mol} \), for the reaction \( \text{Mg} \rightarrow \text{Mg}^+ + \text{e}^- \), and the second ionization potential, \( \mathrm{IP}_2 = 348 \text{kcal/mol} \), for the reaction \( \text{Mg}^+ \rightarrow \text{Mg}^{2+} + \text{e}^- \).

Step 3: Calculate Total Energy

The total energy required to remove two electrons from magnesium is the sum of the first and second ionization potentials: \( \mathrm{IP}_1 + \mathrm{IP}_2 = 178 \text{kcal/mol} + 348 \text{kcal/mol} = 526 \text{kcal/mol} \).

Step 4: Choose the Correct Answer

From the options provided, \(+526 \text{kcal} \) corresponds to the total energy required to remove both electrons. Therefore, option (b) is correct.

Key Concepts

Magnesium Ionization

Magnesium is a chemical element found in Group 2 of the periodic table, known as the alkaline earth metals. An important aspect of magnesium's chemistry is its ionization potential, which determines how much energy is needed to remove electrons from a neutral magnesium atom. With magnesium, we often talk about the two-step ionization process because magnesium usually loses two electrons to achieve a stable electronic configuration.

When a magnesium atom undergoes ionization, it first loses one electron to become a singly charged ion, denoted as \( \text{Mg}^+ \). This is referred to as the first ionization. The resulting \( \text{Mg}^+ \) ion then loses another electron to form a doubly charged ion, \( \text{Mg}^{2+} \). This process is known as the second ionization. Ultimately, magnesium tends to form a \( \text{Mg}^{2+} \) ion because this configuration is more energetically favorable due to the complete emptying of its outer shell.

Understanding magnesium's ionization is crucial for grasping its chemical properties and behavior in reactions, particularly in situations where magnesium plays a role in forming compounds or conducting electricity.

Electron Removal Energy

In the context of magnesium, the term "electron removal energy" refers to the energy required to sequentially remove electrons from a magnesium atom. This energy is typically measured in kilocalories per mole (kcal/mol).

The process consists of two main stages:

• First Ionization Energy: This is the energy needed to remove the first electron from a neutral magnesium atom, resulting in the formation of \( \text{Mg}^+ \). For magnesium, this first ionization potential is \( 178 \text{kcal/mol} \).
• Second Ionization Energy: After the formation of \( \text{Mg}^+ \), more energy is required to remove the second electron, further ionizing the atom to \( \text{Mg}^{2+} \). The second ionization potential for magnesium is \( 348 \text{kcal/mol} \).

Electron removal energy is significant as it helps predict how likely an element is to form ionic bonds, which is essential for understanding reaction dynamics and compound formation.

Ionization Energy Calculation

Calculating the ionization energy for magnesium involves understanding the individual energies required for both ionizations involved in forming \( \text{Mg}^{2+} \).

The total energy required to remove both electrons from a neutral magnesium atom is simply the sum of the first and second ionization potentials. For magnesium:

• \( IP_1 = 178 \text{kcal/mol} \)
• \( IP_2 = 348 \text{kcal/mol} \)

Therefore, the total ionization energy, which reflects the energy to transition from \( \text{Mg} \to \text{Mg}^{2+} \), can be calculated as follows: \[ IP_{total} = IP_1 + IP_2 = 178 \text{kcal/mol} + 348 \text{kcal/mol} = 526 \text{kcal/mol}\] This calculation confirms that removing two electrons from magnesium requires \( 526 \text{kcal/mol} \), aligning with option (b) from the original exercise. Accurate ionization energy calculations are vital for predicting element behavior in different chemical environments.