Question

Using the molecular orbital model, write electron configurations for the following diatomic species and calculate the bond orders. Which ones are paramagnetic? a. \(\mathrm{Li}_{2}\) b. \(\mathrm{C}_{2}\) c. \(\mathrm{S}_{2}\)

Short answer

The bond orders for \(\mathrm{Li}_{2}\), \(\mathrm{C}_{2}\), and \(\mathrm{S}_{2}\) are 1, 2, and 0, respectively. Out of the given diatomic species, only \(\mathrm{C}_{2}\) is paramagnetic.

Step-by-step solution

Write the electron configuration for each species

Based on the periodic table, we have the atomic number for Li, C, and S as 3, 6, and 16 respectively. Hence, the number of electrons in their diatomic species will be 6, 12, and 32 respectively. a. \(\mathrm{Li}_{2}\) has 6 electrons: Electron configuration: \(\mathrm{1}\sigma_{g}^{2}\) \(\mathrm{1}\sigma_{u}^{2}\) \(\mathrm{2}\sigma_{g}^{2}\) b. \(\mathrm{C}_{2}\) has 12 electrons: Electron configuration: \(\mathrm{1}\sigma_{g}^{2}\) \(\mathrm{1}\sigma_{u}^{2}\) \(\mathrm{2}\sigma_{g}^{2}\) \(\mathrm{2}\sigma_{u}^{2}\) \(\mathrm{1}\pi_{u}^{4}\) \(\mathrm{1}\pi_{g}^{2}\) c. \(\mathrm{S}_{2}\) has 32 electrons: Electron configuration: \(\mathrm{1}\sigma_{g}^{2}\) \(\mathrm{1}\sigma_{u}^{2}\) \(\mathrm{2}\sigma_{g}^{2}\) \(\mathrm{2}\sigma_{u}^{2}\) \(\mathrm{1}\pi_{u}^{4}\) \(\mathrm{1}\pi_{g}^{4}\) \(\mathrm{3}\sigma_{g}^{2}\) \(\mathrm{1}\pi_{u}^{4}\) \(\mathrm{3}\sigma_{u}^{2}\) \(\mathrm{1}\pi_{g}^{4}\) \(\mathrm{2}\pi_{u}^{2}\)

Calculate the bond order for each species

The bond order is given by the following formula: Bond order = (number of electrons in bonding MOs - number of electrons in antibonding MOs)/2 a. Bond order of \(\mathrm{Li}_{2}\): Bond order = (4 - 2) / 2 = 1 b. Bond order of \(\mathrm{C}_{2}\): Bond order = (8 - 4) / 2 = 2 c. Bond order of \(\mathrm{S}_{2}\): Bond order = (16 - 16) / 2 = 0

Determine which species are paramagnetic

A species is paramagnetic if it has unpaired electrons in its molecular orbitals. a. \(\mathrm{Li}_{2}\): No unpaired electrons in its molecular orbitals (all paired). Therefore, it is diamagnetic. b. \(\mathrm{C}_{2}\): Two unpaired electrons in the \(\pi_{*}\) molecular orbitals. Therefore, it is paramagnetic. c. \(\mathrm{S}_{2}\): No unpaired electrons in its molecular orbitals (all paired). Therefore, it is diamagnetic. In conclusion, the bond orders for \(\mathrm{Li}_{2}\), \(\mathrm{C}_{2}\), and \(\mathrm{S}_{2}\) are 1, 2, and 0, respectively. Out of the given diatomic species, only \(\mathrm{C}_{2}\) is paramagnetic.

Key concepts

Electron Configuration

Electron configuration is a way of distributing electrons among different atomic or molecular orbitals. In molecular orbital theory, electrons are filled in a sequence of energy levels called molecular orbitals (MOs).
Each MO can hold a specific number of electrons based on its type (sigma or pi) and its symmetry (gerade or ungerade).

• For a diatomic molecule like \( \mathrm{Li}_{2} \), the electrons fill the orbitals based on energy levels: \( \mathrm{1}\sigma_{g}^{2}\), \( \mathrm{1}\sigma_{u}^{2}\), \( \mathrm{2}\sigma_{g}^{2}\). These designations specify the energy levels and type of MOs occupied by electrons.
• Each electron occupies the lowest available energy level first in a specific filling order determined by the Pauli exclusion principle and Hund's rule.
• The superscript number indicates the number of electrons occupying that particular molecular orbital.

Understanding electron configuration will help predict physical properties such as magnetism and reactivity in molecules.

Bond Order

Bond order is an indicator of the strength and stability of a bond within a molecule. It helps determine how securely atoms are held together. To calculate bond order in a molecule, use the simple formula:
\[\text{Bond order} = \frac{\text{number of electrons in bonding MOs} - \text{number of electrons in antibonding MOs}}{2}.\]For example, the bond order of \( \mathrm{C}_{2} \) is calculated as \((8 - 4) / 2 = 2\), indicating a strong double bond between the carbon atoms.

• A higher bond order signifies a stronger bond, such as the triple bond in a nitrogen molecule with a bond order of 3.
• A lower or zero bond order suggests weaker or non-existent bonds, like in \( \mathrm{S}_{2} \) with a bond order of 0.
• While bond order can predict bond length and stability, it doesn't cover all aspects of chemical reactivity on its own.

Bond order, combined with electron configuration, gives a complete picture of molecular interactions and stability.

Paramagnetism

Paramagnetism occurs in molecules that have unpaired electrons in their molecular orbitals. This property makes the substance attracted to magnetic fields.

• A molecule like \( \mathrm{C}_{2} \), which has unpaired electrons in its \( \pi_{*} \) molecular orbitals, will exhibit paramagnetism.
• Paramagnetic substances are typically characterized by one or more unpaired electrons because these electrons cause the individual magnetic moments to align parallel to an external magnetic field.
• In contrast, molecules like \( \mathrm{Li}_{2} \) and \( \mathrm{S}_{2} \) are diamagnetic, as all their electrons are paired, resulting in no net magnetic moment.

Whether a species is paramagnetic or diamagnetic gives clues about its electronic structure and potential reactions under magnetic influence. Understanding these concepts is critical for applications in chemistry and materials science.