Problem 110 - Chemistry: An Atoms-Focused Approach

Question

For which of the following diatomic molecules does the bond order increase with the loss of two electrons, forming the corresponding \(2+\) cation? (a) \(\mathrm{B}_{2} ;\) (b) \(\mathrm{C}_{2} ;\) (c) \(\mathrm{N}_{2} ;\) (d) \(\mathrm{O}_{2}.\)

Step-by-Step Solution

Answer

Answer: None of the given diatomic molecules (B2, C2, N2, and O2) have an increased bond order upon losing two electrons and forming a 2+ cation, according to the molecular orbital theory analysis.

Step 1: Understand Molecular Orbital Theory (MOT)

Molecular Orbital Theory (MOT) is used to describe the distribution of electrons in molecules. In MOT, atomic orbitals of individual atoms overlap and combine to form molecular orbitals. There are bonding orbitals (lower energy) and antibonding orbitals (higher energy). Bond order is calculated by subtracting the number of electrons in antibonding orbitals from the number of electrons in bonding orbitals, divided by 2. A higher bond order indicates a stronger bond.

Step 2: Determine the original bond orders of the diatomic molecules

We will determine the bond order of each molecule using the electron configuration and the given molecular orbital diagram. The electron configuration of each atom is: - B: 1s² 2s² 2p¹ - C: 1s² 2s² 2p² - N: 1s² 2s² 2p³ - O: 1s² 2s² 2p⁴ For the diatomic molecules, the molecular orbital filling order is σ1s, σ*1s, σ2s, σ*2s, π2p, σ2p (for B2 and C2), and σ1s, σ*1s, σ2s, σ*2s, π2p, σ*2p (for N2 and O2). The bond orders of the original molecules are: - B2: (4-2)/2 = 1 - C2: (6-4)/2 = 1 - N2: (8-4)/2 = 2 - O2: (10-6)/2 = 2

Step 3: Determine the bond orders of the corresponding 2+ cations

Remove two electrons from each molecule, and recalculate the bond order for each 2+ cation: - B2²⁺: (2-0)/2 = 1 - C2²⁺: (4-2)/2 = 1 - N2²⁺: (6-2)/2 = 2 - O2²⁺: (8-4)/2 = 2

Step 4: Analyze the bond order changes

Compare the bond orders of the original molecules and the 2+ cations: - B2: bond order 1 -> B2²⁺: bond order 1 (No change) - C2: bond order 1 -> C2²⁺: bond order 1 (No change) - N2: bond order 2 -> N2²⁺: bond order 2 (No change) - O2: bond order 2 -> O2²⁺: bond order 2 (No change) In this case, none of the bond orders increased upon forming the corresponding 2+ cations. Therefore, according to the analysis using the molecular orbital theory, there are no molecules in the given list for which the bond order increases upon losing two electrons and forming a 2+ cation.

Key Concepts

Bond Order

Bond order is a key concept in Molecular Orbital Theory (MOT) that helps explain the strength and stability of a bond between two atoms. It is calculated using the formula:\[ \text{Bond Order} = \frac{(\text{Number of electrons in bonding orbitals} - \text{Number of electrons in antibonding orbitals})}{2} \]A higher bond order means that there are more electrons in bonding orbitals compared to antibonding orbitals.
This indicates a stronger, more stable bond. For example:

• A bond order of 1 suggests a single bond.
• A bond order of 2 indicates a double bond.
• A bond order of 3 suggests a triple bond.

Calculating bond order is crucial when comparing molecules, especially when they undergo changes, like losing or gaining electrons. In this exercise, analyzing changes in bond order helps determine the impact of removing electrons to form cations.

Electron Configuration

Electron configuration is a way to describe the distribution of electrons among the different atomic orbitals. Each atom's electrons are arranged in specific orbitals, following principles like the Pauli exclusion principle and Hund's rule.
The notation used includes the energy level, type of orbital, and number of electrons, such as:

• Boron (B): 1s² 2s² 2p¹
• Carbon (C): 1s² 2s² 2p²
• Nitrogen (N): 1s² 2s² 2p³
• Oxygen (O): 1s² 2s² 2p⁴

Understanding electron configurations is pivotal in determining how electrons from different atoms interact to form molecular orbitals. The configurations provide a roadmap for filling the bonding and antibonding molecular orbitals used to calculate bond order, especially when changes like removing electrons occur, as seen in cation formation.

Diatomic Molecules

Diatomic molecules are composed of only two atoms, which can be of the same or different elements. In this exercise, we focus on homonuclear diatomic molecules, where both atoms are identical, such as B₂, C₂, N₂, and O₂.
These molecules are significant in chemistry due to their simplicity and the foundational role they play in understanding molecular behavior. The formation and properties of diatomic molecules can be comprehensively analyzed using Molecular Orbital Theory. This theory helps explain how atomic orbitals combine to form molecular orbitals, influencing bond strength, stability, and reactivity, as indicated by bond order. Understanding diatomic molecules gives insights into more complex molecular structures and is essential for mastering molecular chemistry fundamentals.