Problem 87 - Chemistry Principles and Practice

Question

Draw the molecular orbital diagram, including the electrons, and write the electron configuration of \(\mathrm{Li}_{2}\). Give the bond order and the number of unpaired electrons, if any. Is this a stable species?

Step-by-Step Solution

Answer

The \(\mathrm{Li}_{2}\) molecule is stable with a bond order of 1 and has no unpaired electrons. Its electron configuration is \(\sigma_{1s}^{2}\sigma^{*}_{1s}^{2}\sigma_{2s}^{2}\).

Step 1: Determine the Number of Electrons

Li has an atomic number of 3, meaning each Li atom has 3 electrons. Therefore, in \(\mathrm{Li}_{2}\), there are 6 electrons in total (3 from each Li atom).

Step 2: Construct the Molecular Orbital Diagram

Start by noting the sequence of molecular orbitals for \(\mathrm{Li}_{2}\): \(\sigma_{1s}\), \(\sigma^{*}_{1s}\), \(\sigma_{2s}\), and \(\sigma^{*}_{2s}\). As \(\mathrm{Li}_{2}\) has 6 electrons, we will fill the orbitals in this order, placing two electrons in \(\sigma_{1s}\), two in \(\sigma^{*}_{1s}\), and the remaining two in \(\sigma_{2s}\).

Step 3: Fill the Molecular Orbitals with Electrons

Place the electrons in the molecular orbital diagram: \(\sigma_{1s}^{2}\), \(\sigma^{*}_{1s}^{2}\), \(\sigma_{2s}^{2}\). The \(\sigma^{*}_{2s}\) orbital remains empty because all 6 electrons have been accounted for.

Step 4: Write the Electron Configuration

The electron configuration for \(\mathrm{Li}_{2}\) in terms of molecular orbitals is \(\sigma_{1s}^{2}\sigma^{*}_{1s}^{2}\sigma_{2s}^{2}\).

Step 5: Calculate the Bond Order

Bond order is calculated as \(\text{Bond Order} = \frac{1}{2}( \text{number of bonding electrons} - \text{number of antibonding electrons})\). In this case, it is \(\frac{1}{2}(4 - 2) = 1\).

Step 6: Determine the Number of Unpaired Electrons

All electrons in \(\mathrm{Li}_{2}\) are paired as evident in the molecular orbital diagram. Hence, there are 0 unpaired electrons.

Step 7: Assess the Stability of the Species

\(\mathrm{Li}_{2}\) is stable as it has a positive bond order of 1, indicating a stable bond between the two lithium atoms.

Key Concepts

Li2 molecule

The \( \mathrm{Li}_{2} \) molecule is formed when two lithium atoms bond together through their electrons. Each lithium atom contributes its outermost electrons for bonding, which leads to the formation of molecular orbitals.
In this molecule, we are considering how these electrons are distributed in the available molecular orbitals. Understanding the makeup of these orbitals will help determine the stability and other properties of the molecule.

• Composition: Consists of two lithium (Li) atoms.
• Total Electrons: 6 electrons.

This molecule serves as a simple example of how molecular orbital theory is used to study bond formation in diatomic molecules.

Electron configuration

The electron configuration of a molecule describes how electrons are distributed in molecular orbitals. This configuration provides critical insight into the molecule’s bonding and stability.
For \( \mathrm{Li}_{2} \), the sequence of filling the orbitals follows the order: \( \sigma_{1s} \), \( \sigma^{*}_{1s} \), \( \sigma_{2s} \), and \( \sigma^{*}_{2s} \) based on energy levels.

• Filling Order: Fill from the lowest to highest energy orbital.
• Configuration for \( \mathrm{Li}_{2} \):\( \sigma_{1s}^{2}\sigma^{*}_{1s}^{2}\sigma_{2s}^{2} \).

This configuration shows that each of the \( \sigma_{1s} \) and \( \sigma_{2s} \) orbitals is fully occupied, illustrating how the electrons pair up in stable bonding states.

Bond order

The bond order is a measure of the stability of a chemical bond. It is calculated using the difference between the number of electrons in bonding orbitals and antibonding orbitals, divided by two.
This simple calculation gives us insight into the strength and stability of a chemical bond.For \( \mathrm{Li}_{2} \), the calculation of bond order is:\[ \text{Bond Order} = \frac{1}{2}(\text{number of bonding electrons} - \text{number of antibonding electrons}) \]

• Bonding Electrons in \( \mathrm{Li}_{2} \): 4
• Antibonding Electrons in \( \mathrm{Li}_{2} \): 2
• Resulting Bond Order: \( 1 \)

A positive bond order, such as 1 in \( \mathrm{Li}_{2} \), suggests that the molecule is stable due to the net electron pair in the bonding orbital.

Unpaired electrons

Unpaired electrons are important as they influence the magnetic properties of a molecule. When electrons in orbitals are unpaired, the molecule can exhibit paramagnetism; otherwise, it is diamagnetic.
In the molecular orbital diagram of \( \mathrm{Li}_{2} \), all electrons are paired.

• Number of Unpaired Electrons in \( \mathrm{Li}_{2} \): 0
• Magnetic Property: Diamagnetic, because there are no unpaired electrons.

Thus, the absence of unpaired electrons in \( \mathrm{Li}_{2} \) contributes to its stability and results in it exhibiting no net magnetic field.