Question

Consider the molecular orbital electron configurations for \(\mathrm{N}_{2}\) \(\mathrm{N}_{2}^{+},\) and \(\mathrm{N}_{2}^{-} .\) For each compound or ion, fill in the table below with the correct number of electrons in each molecular orbital.

Short answer

For N₂, N₂⁺, and N₂⁻, the molecular orbital electron configurations are as follows: For N₂ (14 electrons): 1. σ(1s) - 2 electrons 2. σ*(1s) - 2 electrons 3. σ(2s) - 2 electrons 4. σ*(2s) - 2 electrons 5. π(2p) - 2 electrons 6. π(2p) - 2 electrons 7. σ(2p) - 2 electrons 8. π*(2p) - 0 electrons 9. π*(2p) - 0 electrons 10. σ*(2p) - 0 electrons For N₂⁺ (13 electrons): 1. σ(1s) - 2 electrons 2. σ*(1s) - 2 electrons 3. σ(2s) - 2 electrons 4. σ*(2s) - 2 electrons 5. π(2p) - 2 electrons 6. π(2p) - 2 electrons 7. σ(2p) - 1 electron 8. π*(2p) - 0 electrons 9. π*(2p) - 0 electrons 10. σ*(2p) - 0 electrons For N₂⁻ (15 electrons): 1. σ(1s) - 2 electrons 2. σ*(1s) - 2 electrons 3. σ(2s) - 2 electrons 4. σ*(2s) - 2 electrons 5. π(2p) - 2 electrons 6. π(2p) - 2 electrons 7. σ(2p) - 2 electrons 8. π*(2p) - 1 electron 9. π*(2p) - 0 electrons 10. σ*(2p) - 0 electrons

Step-by-step solution

Determine the total number of electrons in each species

First, let's calculate the total number of electrons in each of the given species: 1. Nitrogen has 7 electrons, so N₂ will have 7(2) = 14 electrons. 2. N₂⁺ has one less electron than N₂, so it will have 14 - 1 = 13 electrons. 3. N₂⁻ has one extra electron than N₂, so it will have 14 + 1 = 15 electrons.

Understand the molecular orbital order in N₂, N₂⁺, and N₂⁻ and fill the electrons

For nitrogen and other diatomic molecules lighter than oxygen (O₂) and fluorine (F₂), the molecular orbital energy order is as follows: 1. σ(1s) 2. σ*(1s) 3. σ(2s) 4. σ*(2s) 5. π(2p) 6. π(2p) 7. σ(2p) 8. π*(2p) 9. π*(2p) 10. σ*(2p) Now let's fill the electrons in molecular orbitals for each species: For N₂, 14 electrons: 1. σ(1s) - 2 electrons 2. σ*(1s) - 2 electrons 3. σ(2s) - 2 electrons 4. σ*(2s) - 2 electrons 5. π(2p) - 2 electrons 6. π(2p) - 2 electrons 7. σ(2p) - 2 electrons 8. π*(2p) - 0 electrons 9. π*(2p) - 0 electrons 10. σ*(2p) - 0 electrons For N₂⁺, 13 electrons: 1. σ(1s) - 2 electrons 2. σ*(1s) - 2 electrons 3. σ(2s) - 2 electrons 4. σ*(2s) - 2 electrons 5. π(2p) - 2 electrons 6. π(2p) - 2 electrons 7. σ(2p) - 1 electron 8. π*(2p) - 0 electrons 9. π*(2p) - 0 electrons 10. σ*(2p) - 0 electrons For N₂⁻, 15 electrons: 1. σ(1s) - 2 electrons 2. σ*(1s) - 2 electrons 3. σ(2s) - 2 electrons 4. σ*(2s) - 2 electrons 5. π(2p) - 2 electrons 6. π(2p) - 2 electrons 7. σ(2p) - 2 electrons 8. π*(2p) - 1 electron 9. π*(2p) - 0 electrons 10. σ*(2p) - 0 electrons Now, we have the number of electrons in each molecular orbital for N₂, N₂⁺, and N₂⁻.

Key concepts

Diatomic Molecules

Diatomic molecules are molecules made up of only two atoms, which can either be of the same element or of different elements. A familiar example of a homonuclear diatomic molecule, where both atoms are the same element, is nitrogen, represented as \( \mathrm{N}_2 \). Understanding diatomic molecules is crucial because they serve as simple models for learning about molecular bonding and structure.

These molecules follow specific rules for filling their molecular orbitals with electrons. For elements like nitrogen, this process is integral to predicting properties such as magnetism, reactivity, and bond strength. The configurations of their electrons in molecular orbitals pinpoint why \( \mathrm{N}_2 \) is such a stable molecule and why its ions, \( \mathrm{N}_2^+ \) and \( \mathrm{N}_2^- \), behave differently in chemical reactions.

Molecular Orbital Theory

Molecular Orbital Theory (MOT) offers a method for determining molecular structure and properties by considering how atomic orbitals combine to form molecular orbitals. When two atoms bond to form a molecule, their atomic orbitals overlap to produce these molecular orbitals, which can be bonding, antibonding, or nonbonding.

Each molecular orbital can hold two electrons with opposite spins, following Pauli's exclusion principle. In a bonding orbital, electrons are in a lower energy state than in the individual atomic orbitals, thus stabilizing the molecule. Conversely, electrons in antibonding orbitals are at a higher energy level, which tends to destabilize the molecule.

The principle of Aufbau (building up) applies, where electrons fill the lowest energy orbitals first. Moreover, Hund's rule tells us that electron pairs in the same energy level won't pair up until they have to. Diatomic nitrogen, for instance, has a unique ordering of these energy levels, which is crucial when considering its electron configuration.

Electron Counting

Electron counting is a fundamental process in chemistry used to understand the electron configuration of molecules. It is essential to know the total number of electrons to distribute them correctly among available molecular orbitals, according to energy levels and rules of MOT.

For diatomic molecules, knowing the number of valence electrons for each atom enables us to count the total electrons and thus predict the distribution in molecular orbitals. We count electrons to determine whether a molecule or ion is paramagnetic (has unpaired electrons and is attracted to a magnetic field) or diamagnetic (all electrons are paired and thus repelled by a magnetic field).

As seen in the molecular orbital electron configurations for \( \mathrm{N}_2 \), \( \mathrm{N}_2^+ \) and \( \mathrm{N}_2^- \) from the exercise, electron counting helped us identify the presence and absence of unpaired electrons which is crucial for determining the magnetic properties and the stability of these species. Accurate electron counting also aids in understanding chemical reactions and bonding, like assessing which molecular orbitals are filled for \( \mathrm{N}_2 \) and its ions, impacting reactivity and bond orders.