Question

Of the following, the number of species having two and more than two electrons in the antibonding molecular orbital is__ \(\mathrm{He}_{2}, \mathrm{He}_{2}^{+}, \mathrm{B}_{2}, \mathrm{O}_{2}^{-}, \mathrm{N}_{2}^{-}\)

Short answer

3 species: He₂, B₂, O₂⁻.

Step-by-step solution

Understand Antibonding Molecular Orbitals

Molecular Orbitals (MOs) are formed by the combination of atomic orbitals. In MO theory, we have bonding and antibonding MOs. Electrons in antibonding MOs weaken the bond between atoms. We need to identify the species with two or more electrons in these orbitals.

Analyze Species He₂

He₂ has 2 electrons in bonding molecular orbitals and 2 in antibonding orbitals due to its electron configuration of \(( ext{σ}1s)^2( ext{σ}1s^*)^2\). Thus, He₂ has 2 electrons in antibonding orbitals.

Analyze Species He₂⁺

He₂⁺ loses one electron from either a bonding or antibonding orbital. Its configuration is \(( ext{σ}1s)^2( ext{σ}1s^*)^1\). Therefore, He₂⁺ has 1 electron in the antibonding orbital.

Analyze Species B₂

The electron configuration for B₂ is \( ( ext{σ}2s )^2 ( ext{σ}2s^* )^2 ( ext{π}2p_x )^1 ( ext{π}2p_y )^1 \). This leaves 2 electrons in the antibonding \( ( ext{σ}2s^*)^2 \) orbitals as the first 4 electrons fill the bonding orbitals.

Analyze Species O₂⁻

O₂⁻ has the configuration \( ( ext{σ}2s )^2 ( ext{σ}2s^* )^2 ( ext{σ}2p_z )^2 ( ext{π}2p_x )^2 ( ext{π}2p_y )^2 ( ext{π}2p_x^*)^2 ( ext{π}2p_y^* )^1 \), resulting in 3 electrons in antibonding orbitals, \( ( ext{π}2p_x^*)^2 ( ext{π}2p_y^* )^1 \).

Analyze Species N₂⁻

N₂⁻ has one more electron than N₂, with the additional electron likely filling a \( ext{π}^* \) orbital. Its configuration becomes \( ( ext{σ}2s )^2 ( ext{σ}2s^* )^2 ( ext{σ}2p_z )^2 ( ext{π}2p_x )^2 ( ext{π}2p_y )^2 ( ext{π}2p_y^*)^1 \), meaning it has 1 electron in antibonding orbitals.

Count Suitable Species

From our analysis, He₂, B₂, and O₂⁻ each have 2 or more electrons in antibonding molecular orbitals. Thus, there are 3 species meeting the criteria.

Key concepts

Molecular Orbital Theory

Molecular Orbital (MO) Theory is a fundamental principle in chemistry used to understand how atomic orbitals combine to form molecular orbitals in molecules. This theory helps explain the bonding and structure of atoms within a molecule by considering the overlap of atomic orbitals.

The combination of atomic orbitals leads to the formation of two types of orbitals: bonding and antibonding. Bonding molecular orbitals are formed from constructive interference between atomic orbitals, leading to increased electron density between the nuclei. This enhances the bond strength and stability of a molecule.

In contrast, antibonding molecular orbitals arise from destructive interference, reducing electron density between the atomic nuclei and weakening the bond between the atoms. Understanding the distribution of electrons in these orbitals is crucial for determining the stability and reactivity of molecules.

Electrons in Antibonding Orbitals

Electrons that occupy antibonding molecular orbitals play a significant role in the stability of molecules. The presence of these electrons generally diminishes the bond order and, consequently, the bond strength.

When electrons are added to antibonding orbitals, they can destabilize a molecule because these orbitals are higher in energy compared to bonding orbitals. A higher number of electrons in antibonding orbitals relative to bonding orbitals implies a weakened attraction between the atoms, potentially making the molecule less likely to exist under normal conditions.

For example, in the species \(\mathrm{O}_2^-\), the configuration includes three electrons in antibonding orbitals, which affects the molecule's stability. Evaluating how many electrons occupy these orbitals helps in species analysis, particularly when predicting molecular stability and reactivity.

Species Analysis

Analyzing a species based on its electron configuration allows chemists to understand its properties, such as stability and reactivity. The electron configuration reveals how electrons are distributed among the molecular orbitals, giving insights into the bond order and overall energy level.

For instance, in understanding species like \(\mathrm{He}_2\), which contains two electrons in both the bonding and antibonding orbitals, we see a simplified case with no net bonding and thus a molecule that is unlikely to exist under normal conditions.

Contrast this with \(\mathrm{B}_2\), where the presence of two electrons in antibonding orbitals still allows the molecule to have some bonding character due to the other electrons in bonding orbitals. Species analysis helps determine which molecules have more stable electronic configurations, making it a fundamental part of computational chemistry and molecular design.

Bonding Molecular Orbitals

Bonding molecular orbitals are an essential concept within the Molecular Orbital Theory, distinguishing those that contribute positively to the bond's formation between two atoms. When atomic orbitals overlap constructively, bonding molecular orbitals are created, leading to increased electron density between atomic nuclei.

These orbitals are lower in energy than the original atomic orbitals and play a pivotal role in holding the atoms together within a molecule. Bonding molecular orbitals enhance the bond order, calculated as the difference between the number of electrons in bonding and antibonding orbitals divided by two.

For example, in isolating the molecular orbital diagram for \(\mathrm{N}_2\), you can observe a strong triple bond facilitated by the electrons filling bonding orbitals such as \(\pi_{2p}\) orbitals. Recognizing the number and type of bonding orbitals provides insight into the molecule's overall bond strength and stability.