Problem 91 - A Complete Resource Book in Chemistry for JEE Main

Question

The relationship between the dissociation energy of \(\mathrm{N}_{2}\) and \(\mathrm{N}_{2}{\underline{\phantom{xx}}}^{+}\)is (a) dissociation energy of \(\mathrm{N}_{2}^{+}>\)dissociation energy of \(\mathrm{N}_{2}\) (b) dissociation energy of \(\mathrm{N}_{2}=\) dissociation energy of \(\mathrm{N}_{2}^{+}\) (c) dissociation energy of \(\mathrm{N}_{2}>\) dissociation energy of \(\mathrm{N}_{2}^{+}\) (d) dissociation energy of \(\mathrm{N}_{2}\) can either be lower or higher than the dissociation energy of \(\mathrm{N}_{2}\)

Step-by-Step Solution

Answer

(c) dissociation energy of \(\mathrm{N}_2 >\) dissociation energy of \(\mathrm{N}_2^+\)

Step 1: Define Dissociation Energy

Dissociation energy is the amount of energy needed to break a bond in a molecule to separate it into its constituent atoms. For example, the dissociation energy of \(\mathrm{N}_2\) is the energy required to break the nitrogen-nitrogen triple bond and form two nitrogen atoms.

Step 2: Understand Molecule Ionization Effect

Ionizing a molecule like \(\mathrm{N}_2\) to form \(\mathrm{N}_2^+\) generally weakens the bond between atoms. This occurs because removing an electron usually reduces the bond strength by lowering the bond order, which increases the molecule's dissociation energy.

Step 3: Compare \(\mathrm{N}_2\) and \(\mathrm{N}_2^+\)

The \(\mathrm{N}_2\) molecule has a triple bond, which is very strong. When \(\mathrm{N}_2\) is ionized to form \(\mathrm{N}_2^+\), it loses an electron, reducing the bond order from three to approximately two and a half, thus decreasing the bond strength and dissociation energy.

Step 4: Analyze Options

Given that ionization generally results in a decrease in bond strength, the dissociation energy for \(\mathrm{N}_2\) is greater than that for \(\mathrm{N}_2^+\). Thus, the correct relationship is option (c): dissociation energy of \(\mathrm{N}_2 > \) dissociation energy of \(\mathrm{N}_2^+\).

Key Concepts

Nitrogen Molecule

The nitrogen molecule, \(\mathrm{N}_2\), is a simple diatomic molecule made up of two nitrogen atoms paired together by a triple bond, one of the strongest types of chemical bonds. This triple bond consists of one sigma bond and two pi bonds. Due to this triple bond, the \(\mathrm{N}_2\) molecule is very stable and requires a significant amount of energy to break apart the atoms, which is known as dissociation energy.

• The ability of \(\mathrm{N}_2\) to maintain such a robust triple bond is a primary reason for its abundance in the Earth's atmosphere, where it accounts for about 78% of the air we breathe.


• The strength of this bond plays a crucial role in various industrial processes, like the production of ammonia through the Haber process, and even natural processes like plant nutrition via nitrogen fixation.

Ionization Effect

Ionization is the process of removing one or more electrons from a molecule, converting it into an ion. In the case of the nitrogen molecule, \(\mathrm{N}_2\), ionization leads to the formation of \(\mathrm{N}_2^+\), where the molecule has lost an electron, making it a positively charged ion. This ionization has a diminishing effect on the molecule's bond strength.
When \(\mathrm{N}_2\) is ionized:

• The overall bond order decreases. Originally, the nitrogen molecule has a bond order of 3, due to the triple bond.


• Once ionized to \(\mathrm{N}_2^+\), the bond order decreases to approximately 2.5.

This decrease in bond order reflects a weakening in the molecular bond strength, making it easier to dissociate the bonded atoms, ultimately leading to a lower dissociation energy for the ionized molecule compared to the neutral nitrogen molecule.

Bond Order

Bond order is a concept that helps describe the strength and stability of a chemical bond in a molecule. It is generally calculated as the difference between the number of bonding and antibonding electrons, divided by two.
For the nitrogen molecule, \(\mathrm{N}_2\):

• The bond order is calculated from the number of covalent bonds, which is three due to the triple bond.


• For its ionized form, \(\mathrm{N}_2^+\), bond order becomes approximately 2.5. This is because the formation of the positive ion results in a loss of a bonding electron.

A higher bond order correlates to a stronger bond and indicates greater stability of the molecule. Thus, the \(\mathrm{N}_2\) molecule, with its bond order of 3, is more stable and has a higher dissociation energy compared to \(\mathrm{N}_2^+\), with its bond order decreased after ionization.

Molecular Chemistry

Molecular chemistry is a branch of chemistry focused on the study of molecules and their interactions, properties, and structures. In the context of our nitrogen example, understanding molecular chemistry allows us to delve into how molecules like \(\mathrm{N}_2\) are structured and how their inherent properties, like bond and dissociation energies, contribute to both chemical stability and reactivity.
Key aspects of molecular chemistry in relation to nitrogen molecules include:

• The understanding of molecular orbitals and how electrons are distributed within the \(\mathrm{N}_2\) and \(\mathrm{N}_2^+\) molecules, influencing their overall stability.


• Application of molecular chemistry knowledge to real-world scenarios such as chemical synthesis, pharmaceuticals, and industrial processes.

Molecular chemistry bridges our understanding from atomic-level interactions to clear explanations of macroscopic phenomena, providing a framework for predicting molecule behavior under various conditions.