Question

You can think of the bonding in the \(\mathrm{Cl}_{2}\) molecule in several ways. For example, you can picture the Cl- -Cl bond containing two electrons that each come from the \(3 p\) orbitals of a \(\mathrm{Cl}\) atom that are pointing in the appropriate direction. However, you can also think about hybrid orbitals. (a) Draw the Lewis structure of the \(\mathrm{Cl}_{2}\) molecule. (b) What is the hybridization of each \(\mathrm{Cl}\) atom? (c) What kind of orbital overlap, in this view, makes the Cl- -Cl bond? (d) Imagine if you could measure the positions of the lone pairs of electrons in \(\mathrm{Cl}_{2}\). How would you distinguish between the atomic orbital and hybrid orbital models of bonding using that knowledge? (e) You can also treat \(\mathrm{Cl}_{2}\) using molecular orbital theory to obtain an energy level diagram similar to that for \(\mathrm{F}_{2}\). Design an experiment that could tell you if the MO picture of \(\mathrm{Cl}_{2}\) is the best one, assuming you could easily measure bond lengths, bond energies, and the light absorption properties for any ionized species.

Short answer

(a) The Lewis structure of Cl2 is :Cl - Cl: with single bond between two chlorine atoms and three lone pairs around each chlorine atom. (b) Each Cl atom in Cl2 has sp³ hybridization. (c) The Cl-Cl bond is formed through σ bond overlap of their 3sp³ orbitals. (d) To distinguish between atomic orbital and hybrid orbital models, measure the positions of the lone pairs to observe tetrahedron geometry consistent with sp³ hybridization or 90° angles consistent with atomic 3p orbitals. (e) Design an experiment to compare measured bond lengths, bond energies, and light absorption properties of ionized species with the molecular orbital theory's predictions to determine if MO theory best describes Cl2.

Step-by-step solution

(a) Drawing Lewis structure of Cl2

To draw the Lewis structure of Cl2, first, we need to determine the number of valence electrons each chlorine atom has. Chlorine (Cl) belongs to Group 17 of the periodic table and has 7 valence electrons. Since there are two chlorine atoms in Cl2, we have 14 valence electrons in total. Place two chlorine atoms next to each other and form a single bond between them by sharing one electron from each chlorine atom. Distribute the remaining 12 electrons as 3 lone pairs (6 electrons) around each chlorine atom. The Lewis structure of Cl2 molecule then looks like this: :Cl - Cl:

(b) Determining the hybridization of each Cl atom

To determine the hybridization of each chlorine atom in Cl2, we need to look at the total number of electron groups (bonds and lone pairs) around each chlorine atom. Since there is one single bond and three lone pairs around each chlorine atom, there are 4 electron groups in total. Hence, the hybridization of each chlorine atom is sp³.

(c) Identifying the type of orbital overlap

In the hybrid orbital model, the bond between the two chlorine atoms is formed through the overlap of their half-filled 3sp³ orbitals. This overlap forms a sigma bond (σ bond) between the chlorine atoms.

(d) Distinguishing between atomic orbital and hybrid orbital models

To distinguish between atomic orbital and hybrid orbital models, we need to measure the positions of the lone pairs of electrons in Cl2. If the measurements are consistent with a tetrahedron geometry around each chlorine atom, this confirms the hybrid orbital model (sp³ hybridization). However, if the measurements correspond to the position of atomic 3p orbitals (90° angles between the electron pairs), this would indicate the atomic orbital model.

(e) Designing an experiment for the molecular orbital theory

To design an experiment that could help determine if the molecular orbital (MO) picture of Cl2 provides the best model, we can consider the following: 1. Measure the bond length and bond energy of Cl2. 2. Ionize Cl2 and measure the light absorption properties of the resulting ionized species. 3. Compare these results to the predictions made by the MO theory. If both the bond length and bond energy of Cl2 match the MO theory's predictions, and if the light absorption properties correspond to the MO energy diagrams, it indicates that the molecular orbital theory provides an accurate and better description of the Cl2 molecule.

Key concepts

Lewis Structure

In chemistry, a Lewis structure is a simple yet powerful way to represent molecules and visualize their bonding arrangements. To draw the Lewis structure for a \(\mathrm{Cl}_2\) molecule, we first identify the number of valence electrons each chlorine atom possesses. Since chlorine is in Group 17 of the periodic table, it has 7 valence electrons. There are two chlorine atoms in \(\mathrm{Cl}_2\), making a total of 14 valence electrons shared between them.

Place the two chlorine atoms next to each other and form a single bond by sharing one electron from each atom. This bond accounts for 2 of the 14 valence electrons, leaving 12 valence electrons.

Distribute these remaining electrons as lone pairs around each chlorine atom, ensuring that each atom has a complete octet. The resulting Lewis structure for \(\mathrm{Cl}_2\) is displayed as :Cl - Cl:, where each chlorine atom has three lone pairs of electrons completing their octet. This visualization is crucial for understanding the arrangement of electrons and predicting molecular shape and reactivity.

Hybridization

Hybridization is a concept that explains the mixing of atomic orbitals to form new hybrid orbitals. These hybrid orbitals are used in forming chemical bonds in molecules.

For each chlorine atom in \(\mathrm{Cl}_2\), there are four electron groups: one single bond and three lone pairs. This requires an \(sp^3\) hybridization as it allows each chlorine to accommodate the lone pairs and the bond.

Here's how hybridization occurs in \(\mathrm{Cl}_2\):

• One 3s orbital and three 3p orbitals from each chlorine mix to form four \(sp^3\) hybrid orbitals.
• The hybrid orbitals arrange themselves in a tetrahedral geometry to minimize repulsion.
• Only one of the \(sp^3\) orbitals from each chlorine makes a sigma bond.
• The remaining three are occupied by lone pairs.

Understanding hybridization helps determine the geometry of molecules and the types of bonds they can form.

Orbital Overlap

When two atomic orbitals overlap, they form a chemical bond. In \(\mathrm{Cl}_2\), the bond between the chlorine atoms results from the overlap of their \(sp^3\) hybrid orbitals.

Each chlorine uses one of its hybrid orbitals to overlap with the hybrid orbital of the neighboring chlorine, forming a sigma (\(\sigma\)) bond. This type of bond involves head-on overlap which is symmetrical along the axis joining the two atoms.

This sharing of electrons in the form of a \(\sigma\) bond results in the stable diatomic \(\mathrm{Cl}_2\) molecule. The remaining three hybrid orbitals surrounding each chlorine atom contain lone electron pairs, showing that their primary interaction is not with each other but within each atom. This concept of orbital overlap is fundamental in understanding not only the formation of bonds but also the concept of bond strength and molecular geometry.

Molecular Orbital Theory

Molecular Orbital (MO) Theory provides an alternative viewing approach to Valence Bond Theory, using quantum mechanics to describe the electronic structure of molecules.

In the context of \(\mathrm{Cl}_2\), MO theory involves combining the atomic orbitals of each chlorine atom to form molecular orbitals. These orbitals belong to the molecule as a whole:

• Atomic orbitals combine to produce bonding and antibonding molecular orbitals.
• The bonding molecular orbital contains electron density that stabilizes the molecule.
• The antibonding orbital, which is higher in energy, is typically unoccupied for stable molecules.

To evaluate the validity of this theory for \(\mathrm{Cl}_2\), experiments can be set up to measure bond length, bond energies, and the light absorption properties of the molecule.

Comparing empirical results to MO predictions enhances our understanding of whether MO theory provides a more accurate description than other bonding models. This theory enhances comprehension of electron distribution over a molecule, providing insights into bond strengths and the overall stability of chemical structures.