Question

The reaction \(\mathrm{S}_{8}(\mathrm{~g}) \longrightarrow 4 \mathrm{~S}_{2}(\mathrm{~g})\) has \(\Delta H^{\circ}=+237 \mathrm{k}\) ) (a) The \(\mathrm{S}_{8}\) molecule has eight sulfur atoms arranged in a ring. What is the hybridization and geometry around each sulfur atom in \(\mathrm{S}_{8}\) ? (b) The average \(\mathrm{S}-\mathrm{S}\) bond dissociation energy is \(225 \mathrm{~kJ} / \mathrm{mol}\). Using the value of \(\Delta H^{\circ}\) given above, what is the \(\mathrm{S}=\mathrm{S}\) double bond energy in \(\mathrm{S}_{2}(g)\) ? (c) Assuming that the bonding in \(\mathrm{S}_{2}\) is similar to the bonding in \(\mathrm{O}_{2}\), give a molecular orbital description of the bonding in \(\mathrm{S}_{2}\). Is \(S_{2}\) likely to be paramagnetic or diamagnetic?

Short answer

(a) sp3; bent geometry. (b) 509.25 kJ/mol. (c) Paramagnetic; similar to O2, with unpaired electrons.

Step-by-step solution

Determine hybridization and geometry in S8

Each sulfur atom in the S8 molecule forms two bonds and has no lone pairs. The hybridization of each sulfur atom is sp3. The geometry around each sulfur atom due to its ring structure results in a bent or slightly distorted tetrahedral shape.

Calculate S=S bond energy

Use the given enthalpy change (\(\Delta H^{\circ} = +237 \ \mathrm{kJ}\), which represents the energy change for the process). The reaction involves breaking 4 S-S single bonds in S8 and forming 4 S=S double bonds in S2:\[S_8 \rightarrow 4 S_2\]Energy required to break bonds in \(S_8\):\[8 \times 225 \ \mathrm{kJ/mol} = 1800 \ \mathrm{kJ/mol}\]Change in energy for forming 4 S=S bonds:\(4 \times x\). Given that breaking bonds costs more than forming them, we find the bond energy for double bonds:\[x = \frac{1800 + 237}{4} = 509.25 \ \mathrm{kJ/mol}.\] Thus, the energy of one \(S=S\) double bond is approximately 509.25 kJ/mol.

Molecular orbital description of S2

The S2 molecule is similar to O2 in its electron configuration. The bonding involves three bonding (\(\sigma_{2s}, \sigma_{2p_z}, \pi_{2p_x}, \pi_{2p_y}\)) and two antibonding orbitals (\(\pi^*_{2p_x}, \pi^*_{2p_y}\)). Since it has two unpaired electrons, S2 is paramagnetic, meaning it is attracted by an external magnetic field due to these unpaired electrons.

Key concepts

Hybridization

In chemistry, hybridization refers to the merging of atomic orbitals to form new hybrid orbitals, which can help explain molecular geometry and bonding properties. For the sulfur atoms in the \( \text{S}_8 \) molecule, each sulfur atom is surrounded by other sulfur atoms forming a ring.

Each sulfur atom in \( \text{S}_8 \) forms two sigma bonds, resulting in an \( \text{sp}^3 \) hybridization. This type of hybridization involves the mixing of one s orbital and three p orbitals from the sulfur atom. Such a configuration generally leads to a tetrahedral geometry. However, in the \( \text{S}_8 \) ring, this geometry is somewhat bent or distorted, due to the circular arrangement of the atoms.

To visualize this, imagine a crown-like or cyclic ring where each sulfur atom contributes to the bending of the overall shape. This structure allows the ring to maintain stability while accommodating the ring's configuration.

Molecular Orbital Theory

Molecular Orbital (MO) Theory is a robust model used to describe the electronic structure of molecules by considering electrons in terms of molecular orbitals that are distributed over the entire molecule.

For molecules like \( \text{S}_2 \), which is comparable to the more familiar \( \text{O}_2 \), the electron configuration can be understood through MO diagrams. \( \text{S}_2 \) has electrons filling into several orbitals: bonding orbitals, such as \( \sigma_{2s} \) and \( \sigma_{2p_z} \), as well as \( \pi_{2p_x} \) and \( \pi_{2p_y} \) orbitals, and antibonding orbitals such as \( \pi^*_{2p_x} \) and \( \pi^*_{2p_y} \).

The filled \( \pi_{2p_x} \) and \( \pi_{2p_y} \) orbitals contribute to the molecule's total bond order, helping to account for the stability and properties of \( \text{S}_2 \). MO Theory allows chemists to predict and confirm that due to the presence of unpaired electrons in these molecular orbitals, \( \text{S}_2 \) displays paramagnetism.

Bond Dissociation Energy

Bond Dissociation Energy (BDE) measures the strength of a chemical bond, defined as the energy required to break a bond in a molecule to form separate atoms. It provides insight into the stability of the molecule.

In the conversion from \( \text{S}_8 \) to \( \text{S}_2 \), BDE becomes critical for determining the energy involved in breaking and forming bonds. Each \( \text{S-S} \) single bond in \( \text{S}_8 \) requires approximately 225 kJ/mol to break.
When we calculate for the double bonds, using the enthalpy change \( \Delta H^{\circ} \), we find that each \( \text{S=S} \) double bond in \( \text{S}_2 \) has a dissociation energy of approximately 509.25 kJ/mol. This distinction between the single and double bond energies illustrates just how much more robust double bonds are, contributing to the considerable differences in molecular behavior and stability.

Paramagnetism

Paramagnetism is a form of magnetism that occurs when a material is attracted to an external magnetic field. This property is often due to the presence of unpaired electrons within the molecule.

In molecular terms, \( \text{S}_2 \) serves as a classic example of a paramagnetic molecule. According to Molecular Orbital Theory, \( \text{S}_2 \) has two unpaired electrons occupying antibonding \( \pi^* \) orbitals.

The unpaired electrons in these orbitals result in magnetic moments that do not cancel each other out, causing an attraction to magnetic fields. This is in contrast to diamagnetic materials, where all electrons are paired, and the net magnetic moment is zero, leading to a slight repulsion from magnetic fields.

Understanding paramagnetism helps chemists predict magnetic properties of unknown molecules or verify experimental observations.