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

The molecular orbital electron configurations for \(\mathrm{N}_{2}\), \(\mathrm{N}_{2}^{+}\), and \(\mathrm{N}_{2}^{-}\) are as follows: | MO | \(\mathrm{N}_{2}\) | \(\mathrm{N}_{2}^{+}\) | \(\mathrm{N}_{2}^{-}\) | |------------|--------|-------------|-------------| | \(\mathrm{1\sigma_{g}}\) | 2 | 2 | 2 | | \(\mathrm{1\sigma_{u}^{*}}\) | 0 | 0 | 0 | | \(\mathrm{2\sigma_{g}}\) | 2 | 2 | 2 | | \(\mathrm{2\sigma_{u}^{*}}\) | 0 | 0 | 0 | | \(\mathrm{3\sigma_{g}}\) | 2 | 2 | 2 | | \(\mathrm{3\sigma_{u}^{*}}\) | 0 | 0 | 0 | | \(\mathrm{1\pi_{u}}\) | 6 | 5 | 6 | | \(\mathrm{1\pi_{g}^{*}}\) | 2 | 0 | 3 | | \(\mathrm{4\sigma_{g}}\) | 0 | 0 | 0 | | \(\mathrm{4\sigma_{u}^{*}}\) | 0 | 0 | 0 |

Step-by-step solution

Determine the number of electrons for each compound

For \(\mathrm{N}_{2}\), each nitrogen atom contributes 7 electrons, so total electrons = 7 * 2 = 14 electrons. For \(\mathrm{N}_{2}^{+}\), one electron is removed; hence total electrons = 14 - 1 = 13 electrons. For \(\mathrm{N}_{2}^{-}\), one electron is added; hence total electrons = 14 + 1 = 15 electrons. Step 2: Fill in the molecular orbitals

Fill electrons in the molecular orbitals for each compound

For \(\mathrm{N}_{2}\), we have 14 electrons to fill: \(\mathrm{1\sigma_{g}}\)(2), \(\mathrm{1\sigma_{u}^{*}}\)(0), \(\mathrm{2\sigma_{g}}\)(2), \(\mathrm{2\sigma_{u}^{*}}\)(0), \(\mathrm{3\sigma_{g}}\)(2), \(\mathrm{3\sigma_{u}^{*}}\)(0), \(\mathrm{1\pi_{u}}\)(6), \(\mathrm{1\pi_{g}^{*}}\)(2), \(\mathrm{4\sigma_{g}}\)(0), and \(\mathrm{4\sigma_{u}^{*}}\)(0). For \(\mathrm{N}_{2}^{+}\), we have 13 electrons to fill: \(\mathrm{1\sigma_{g}}\)(2), \(\mathrm{1\sigma_{u}^{*}}\)(0), \(\mathrm{2\sigma_{g}}\)(2), \(\mathrm{2\sigma_{u}^{*}}\)(0), \(\mathrm{3\sigma_{g}}\)(2), \(\mathrm{3\sigma_{u}^{*}}\)(0), \(\mathrm{1\pi_{u}}\)(5), \(\mathrm{1\pi_{g}^{*}}\)(0), \(\mathrm{4\sigma_{g}}\)(0), and \(\mathrm{4\sigma_{u}^{*}}\)(0). For \(\mathrm{N}_{2}^{-}\), we have 15 electrons to fill: \(\mathrm{1\sigma_{g}}\)(2), \(\mathrm{1\sigma_{u}^{*}}\)(0), \(\mathrm{2\sigma_{g}}\)(2), \(\mathrm{2\sigma_{u}^{*}}\)(0), \(\mathrm{3\sigma_{g}}\)(2), \(\mathrm{3\sigma_{u}^{*}}\)(0), \(\mathrm{1\pi_{u}}\)(6), \(\mathrm{1\pi_{g}^{*}}\)(3), \(\mathrm{4\sigma_{g}}\)(0), and \(\mathrm{4\sigma_{u}^{*}}\)(0). Step 3: Complete the table

Fill in the table with the molecular orbital electron configurations

| MO | \(\mathrm{N}_{2}\) | \(\mathrm{N}_{2}^{+}\) | \(\mathrm{N}_{2}^{-}\) | |------------|--------|-------------|-------------| | \(\mathrm{1\sigma_{g}}\) | 2 | 2 | 2 | | \(\mathrm{1\sigma_{u}^{*}}\) | 0 | 0 | 0 | | \(\mathrm{2\sigma_{g}}\) | 2 | 2 | 2 | | \(\mathrm{2\sigma_{u}^{*}}\) | 0 | 0 | 0 | | \(\mathrm{3\sigma_{g}}\) | 2 | 2 | 2 | | \(\mathrm{3\sigma_{u}^{*}}\) | 0 | 0 | 0 | | \(\mathrm{1\pi_{u}}\) | 6 | 5 | 6 | | \(\mathrm{1\pi_{g}^{*}}\) | 2 | 0 | 3 | | \(\mathrm{4\sigma_{g}}\) | 0 | 0 | 0 | | \(\mathrm{4\sigma_{u}^{*}}\) | 0 | 0 | 0 |

Key concepts

Electron Configuration

Electron configuration is a way to represent how electrons are distributed in an atom or molecule. In general, electrons fill lower energy levels first before moving to higher ones. This concept is crucial in understanding chemical bonding and the formation of compounds.

• Electrons fill orbitals in a specific order: starting from the lowest available energy levels.
• Each type of orbital (s, p, d, f) can hold a certain number of electrons (2, 6, 10, 14 respectively).
• For diatomic molecules like nitrogen ( _2), molecular orbitals are formed by combining atomic orbitals.

Representing electron configuration in molecular orbitals helps us understand the bond formation and stability in molecules. It also reveals information about the bond order and magnetic properties of the molecule.

Nitrogen Molecules

Nitrogen molecules ( _2) are composed of two nitrogen atoms sharing electrons to achieve a stable electron configuration. They are one of the most basic examples used to study molecular orbital theory. Each nitrogen atom contributes seven electrons, leading to a total of 14 electrons for the _2 molecule.

• The _2 molecule is diatomic, meaning it consists of two atoms.
• In its natural state, nitrogen is a colorless and odorless diatomic gas.
• Nitrogen molecules are very stable due to the triple bond formed between two nitrogen atoms.

This bond is the result of overlapping atomic orbitals to create molecular orbitals, allowing the molecule to achieve a lower energy and more stable state. Understanding the distribution of electrons in the molecular orbitals helps explain this stability and the overall properties of the nitrogen molecule.

Molecular Orbital Theory

Molecular orbital (MO) theory is a method for describing the electronic structure of molecules. Unlike atomic orbital theory, which focuses on individual atoms, MO theory treats electrons as being spread across a molecule. This allows for better insight into the bonding and properties of molecules.

• In MO theory, atomic orbitals combine to form molecular orbitals that can extend over the whole molecule.
• MOs are classified as bonding or antibonding, influencing the stability of the molecule.
• Electrons filled in bonding MOs stabilize the molecule, while those in antibonding MOs can destabilize it.

In nitrogen molecules, the molecular orbitals are filled following the principle of filling from the lowest to highest energy levels. By using MO theory, it is possible to determine characteristics like bond order, magnetic properties, and reactivity of the molecule.

Chemical Bonding

Chemical bonding involves the interaction between atoms to form molecules or compounds. The focus is to achieve stable electron configurations, often resembling the noble gases. Molecular orbitals play a major role in chemical bonding by determining how electrons are shared or transferred between atoms.

• Covalent bonds involve the sharing of electrons between atoms, as seen in nitrogen molecules.
• Ionic bonds involve the transfer of electrons from one atom to another, forming charged ions.
• Molecular orbitals influence the strength and type of bonding in a molecule.

In nitrogen, the triple bond formed is notably strong due to the significant overlap of p-orbitals, creating a high bond order. This makes nitrogen gas very stable under normal conditions. By exploring molecular orbital configurations, chemists can predict how molecules will behave chemically.