Problem 16 - Chemistry: Introducing Inorganic, Organic and Physical Chemistry

Question

Construct a labelled molecular orbital energy level diagram for Si \(_{2}\), stating any assumptions you have made. Measurements suggest that \(\mathrm{Si}_{2}\) is diamagnetic in the gas phase. Is this consistent with your diagram? If not, what changes could be made to the order of the molecular orbitals? How could these be justified? (Section 4.11).

Step-by-Step Solution

Answer

The constructed molecular orbital diagram is consistent with Si\(_{2}\)'s diamagnetic nature. Therefore, no changes are needed to the order of orbitals.

Step 1: Understand Silicon Atom's Electron Configuration

Silicon (Si) has an atomic number of 14. Its electron configuration in the ground state is \(1s^2 2s^2 2p^6 3s^2 3p^2\). For Si\(_{2}\), we consider the valence electrons located in the \(3s\) and \(3p\) orbitals of each Si atom.

Step 2: Determine Total Valence Electrons in Si\(_{2}\)

Each Si atom contributes 4 valence electrons from the \(3s\) and \(3p\) orbitals. Therefore, Si\(_{2}\) has a total of 8 valence electrons (4 electrons per Si atom \(\times\) 2 Si atoms).

Step 3: Construct Molecular Orbital Energy Level Diagram

Begin with the \(\sigma_{3s}\) and \(\sigma_{3s}^*\) orbitals, followed by \(\sigma_{3p}\) and \(\sigma_{3p}^*\). Assume \(\pi_{3p}\) orbitals are lower in energy than \(\sigma_{3p}\). Fill the molecular orbitals according to the Aufbau principle with these 8 valence electrons.

Step 4: Fill Molecular Orbitals According to Rules

The molecular orbitals are filled in order of increasing energy: \(\sigma_{3s}\) (2 electrons), \(\sigma_{3s}^*\) (0 electrons as it's higher energy), \(\pi_{3p}\) (4 electrons, two in each degenerate \(\pi\) orbital), and \(\sigma_{3p}\) (2 electrons). The next higher energy orbitals \(\pi_{3p}^*\) and \(\sigma_{3p}^*\) remain empty.

Step 5: Analyze Magnetism Consistent with Diagram

According to our diagram, all electrons are paired within the molecular orbitals, reflecting diamagnetic behavior as observed. This is consistent with the measurement that Si\(_{2}\) is diamagnetic. If a different ordering was required, one would evaluate electronic configurations and empirical data to assess whether any exceptions or different electron pairing were possible.

Key Concepts

Electron Configuration

Electron configuration is a fundamental idea in chemistry that describes the distribution of electrons in an atom. Silicon (Si) has 14 electrons, distributed as \(1s^2 2s^2 2p^6 3s^2 3p^2\). This configuration tells us that the electrons fill the orbitals starting from the lowest energy level moving upwards, according to the Aufbau principle.

• Ground State: The default, lowest energy arrangement of electrons in an atom.
• Aufbau Principle: States that electrons will fill orbitals in order of increasing energy.

Understanding electron configuration helps to predict how an atom will interact or bond with others. For Si\(_{2}\), we focus on the valence electrons, which are responsible for bonding.

Diamagnetism

Diamagnetism is a property observed in materials with all paired electrons. When subjected to a magnetic field, diamagnetic substances create an opposing magnetic field. This means they will be gently repelled by a magnet rather than attracted.
Si\(_{2}\) is diamagnetic because the molecular orbital (MO) configuration results in all electrons being paired. Unpaired electrons would create a magnetic moment and result in paramagnetism instead.

• Paired Electrons: In diamagnetic materials, all electrons are paired, minimizing magnetic interaction.
• Magnetic Response: Diamagnetic substances are slightly repelled by a strong magnetic field.

Therefore, the diamagnetic nature of Si\(_{2}\) aligns with the MO diagram where electron pairing in orbitals minimizes magnetic effects.

Valence Electrons

Valence electrons are the outermost electrons of an atom that are available for bonding. For silicon, these are located in the \(3s\) and \(3p\) orbitals. Each silicon atom contributes 4 valence electrons, making a total of 8 for the Si\(_{2}\) molecule.
Valence electrons determine how atoms can bond with one another. They are key to predicting the behavior of molecules in chemical reactions. In Si\(_{2}\), the valence electrons are used to form molecular orbitals which ultimately determine the chemical properties of the molecule.

• Bonding Electrons: These electrons participate in forming chemical bonds.
• Orbital Participation: The arrangement of valence electrons in molecular orbitals affects molecular structure and stability.

Comprehending the role of valence electrons is crucial for constructing accurate molecular orbital diagrams.

Molecular Orbital Diagram

A molecular orbital diagram is a visual representation of how atomic orbitals combine to form molecular orbitals. The key is to follow the rules of filling these orbitals, reflecting the molecule's energy levels and electron pairings.
For Si\(_{2}\), the molecular orbitals start with \(\sigma_{3s}\) (filled by 2 electrons), followed by \(\pi_{3p}\) (4 electrons, spread across two orbitals). The order assumes \(\pi_{3p}\) is lower in energy than \(\sigma_{3p}\), as per our chosen assumptions.

• Energy Level Filling: Determined by increasing energy, governed by the Aufbau principle.
• Electron Pairing: Electrons enter orbitals within a level singly before pairing due to Hund's rule.
• Diagram Analysis: Helps visualize the magnetic and chemical properties predicted by electron configurations.

Constructing a molecular orbital diagram requires careful consideration of energy order and electron assignments to predict molecular properties accurately.