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

The dissociation energy of 14N14 is greater than that of 14N143cN14 (option c).

Step 1: Understanding the Concepts

Dissociation energy refers to the amount of energy required to break a molecular bond between atoms. For diatomic nitrogen ( N14), this energy is particularly high due to the triple bond. When 14N14 is ionized to form 14N143cN14, one electron is removed. This changes the electronic configuration and bonding characteristics of the molecule.

Step 2: Assessing the Effect of Ionization

When 14N14 is ionized to form 14N143cN14, the removal of an electron means the positive ion has a different electron configuration and potentially different bond strength. In most cases, the loss of the electron weakens the bond due to decreased electron density responsible for bonding.

Step 3: Comparing Bond Strength

The bond in neutral 14N14 is generally stronger than in 14N143cN14 because the removal of an electron decreases the overlap of the bonding orbitals. The bond order in 14N14 is 3 (triple bond), while in 14N143cN14, it becomes slightly less than 3, making it weaker.

Step 4: Determining the Correct Answer

Based on the concepts and the effect of ionization, it is understood that the dissociation energy of 14N14 is generally greater than that of 14N143cN14. Thus, the correct choice is option (c), where the dissociation energy of 14N14 is greater than that of 14N143cN14.

Key Concepts

Molecular Bond

A molecular bond is the force that holds atoms together within a molecule. These bonds include ionic, covalent, and metallic bonds.

• Covalent Bonds: Formed when atoms share electrons. This is the type of bond present in nitrogen molecules ( N_2).
• Ionic Bonds: Occur when one atom donates an electron to another, forming a pair of ions that attract each other.
• Metallic Bonds: Involves the sharing of free electrons among a lattice of metal atoms.

In a nitrogen molecule, the bond is covalent and is specific as a triple bond. Triple bonds occur when three electron pairs are shared between two atoms, giving the molecule its strength and considerable stability. Understanding molecular bonds helps in predicting molecule behavior during chemical reactions.

Ionization

Ionization refers to the process of removing or adding electrons to an atom or molecule, creating ions. When an electron is removed from N_2 to form N_2^+, the molecule becomes positively charged.

• Cation Formation: Removing an electron results in a positive ion, known as a cation.
• Energy Requirement: Ionization requires energy to overcome the attraction between the electron and the atomic nucleus.
• Molecular Changes: Ionization can alter properties such as bond length and bond strength.

For nitrogen, ionization weakens its molecular bond due to reduced electron density, impacting its stability and bond characteristics significantly.

Bond Strength

Bond strength indicates how strongly the atoms in a molecule are held together. It is generally measured by dissociation energy, the energy needed to break a bond.

• Dissociation Energy: A useful measure of bond strength, with higher values indicating stronger bonds.
• Impact of Electron Configuration: Electron configuration can enhance or diminish bond strength. In N_2, the triple covalent bond is strong because of optimal electron overlap.
• Effect of Ionization: Removing an electron to form N_2^+ weakens the bond by lowering the electron overlap.

In neutral N_2, the bond is robust due to the full electron overlap forming the triple bond. In contrast, N_2^+ has decreased bond strength due to altered electron configuration and lesser bonding electron density.

Bond Order

Bond order is a concept signifying the number of chemical bonds between a pair of atoms. It provides insight into a molecule's stability and bond length.

• Determination: Calculated as half the difference between the number of bonding and antibonding electrons.
• Impact on Stability and Length: A higher bond order often indicates greater stability and shorter bond length.
• Triple Bonds: N_2 has a bond order of 3, representing three shared electron pairs, contributing to its notable stability.
• Bonds and Ionization: Ionization alters bond order. For instance, N_2^+ has a bond order slightly less than 3.

Changes in bond order due to ionization reflect shifts in bond properties, influencing molecular behavior and interaction potential.