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 energy required is +526 kcal, so the answer is (b).

Step 1: Understanding Ionization Potentials

Ionization potential (IP) is the energy required to remove an electron from an atom or ion. For magnesium (Mg), the first ionization potential, IP₁, is 178 kcal/mol. This is the energy required to remove the first electron, converting Mg to Mg⁺. The second ionization potential, IP₂, is 348 kcal/mol. This energy is required to remove a second electron, converting Mg⁺ to Mg²⁺.

Step 2: Calculating Total Energy Required

The total energy required to remove two electrons from Mg to form Mg²⁺ is the sum of the first and second ionization potentials. Therefore, the total energy needed is 178 kcal/mol (for the first electron) plus 348 kcal/mol (for the second electron).

Step 3: Performing the Calculation

Add the ionization potentials together: \[ 178 \text{kcal/mol} + 348 \text{kcal/mol} = 526 \text{kcal/mol} \]

Step 4: Finding the Correct Answer

The question asks for the total energy required for the reaction \(\mathrm{Mg} \longrightarrow \mathrm{Mg}^{2+}+2 \mathrm{e}^-\). According to our calculation, the energy required is 526 kcal/mol, matching option (b).

Key Concepts

Energy Required for Ionization

Ionization energy, also known as ionization potential, is the essential amount of energy needed to remove an electron from an atom or ion. This concept is fundamental in chemistry when dealing with atomic structure and electron configurations. The energy required varies depending on how tightly an electron is bound to the atom's nucleus. Thus, the closer an electron is to the nucleus, the more energy is required to remove it. Ionization energy is typically measured in kilocalories per mole (kcal/mol) or electronvolts (eV).

Understanding ionization energy allows us to predict and explain chemical reactivity and trends in the periodic table. For example:

• Elements with lower ionization energy easily lose electrons, forming cations.
• Higher ionization energy indicates a stable electron configuration, making it harder for the atom to lose an electron.

The concept is particularly useful when studying reactions involving the formation of ions.

Magnesium Ionization

Magnesium (Mg) is an alkaline earth metal that is commonly found in the earth's crust. It is known for its metallic properties and reactivity. One important characteristic of magnesium is its tendency to lose electrons, particularly two of them, to achieve a stable electron configuration.

When discussing magnesium ionization, there are typically two main ionization potentials of interest:

• **First Ionization Potential (IP₁):** This is the energy needed to remove the first electron from a neutral magnesium atom. For magnesium, this energy is 178 kcal/mol.
• **Second Ionization Potential (IP₂):** After removing the first electron, more energy is required to remove the second electron from the now positively charged Mg⁺ ion. This energy amounts to 348 kcal/mol.

These ionization potentials reflect magnesium's reactivity and predict its behavior in chemical reactions, as it readily forms a Mg²⁺ ion in reactions.

Step-by-Step Calculation of Ionization Energy

Calculating the energy required for the complete ionization of magnesium involves a straightforward procedure. We need to understand this in terms of removing electrons across two stages, each requiring energy known as ionization potential.

The initial step is recognizing the energy needed for the first electron. We have:

• The first ionization energy, IP₁, for removing the first electron from magnesium is 178 kcal/mol.

Next, we consider the second electron:

• The second ionization energy, IP₂, is 348 kcal/mol.

To find the total energy needed for magnesium to go from a neutral atom to a doubly charged ion (Mg²⁺), we sum these two energies:

The calculation is straightforward: \[ 178 \, \text{kcal/mol} + 348 \, \text{kcal/mol} = 526 \, \text{kcal/mol} \]
The result, 526 kcal/mol, informs us of the energy requisite for this ionization process. This result coincides with option (b) in the provided multiple-choice question, confirming our understanding and calculation.