Question

You can think of the bonding in the \(\mathrm{Cl}_{2}\) molecule in several ways. For example, you can picturethe 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 Cl atom? (c) What kind of orbital overlap, in this view, makes the \(\mathrm{Cl}-\mathrm{Cl}\) 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

The Lewis structure of the \(\mathrm{Cl}_{2}\) molecule is Cl - Cl, with each chlorine atom having three lone pairs. Each Cl atom is sp3 hybridized, and the orbital overlap is sp3-sp3. To distinguish between atomic and hybrid orbital models, measure the positions of lone pairs in \(\mathrm{Cl}_{2}\) and compare the bond angles to the predicted angles in each model. To determine if the molecular orbital (MO) theory provides the best representation, experimentally measure bond lengths, bond energies, and light absorption properties of ionized species, then compare these results with the MO theory's predictions.

Step-by-step solution

(a) Draw the Lewis structure of the \(\mathrm{Cl}_{2}\) molecule.

To draw the Lewis structure, we need to count the total number of valence electrons available, arrange the atoms, and distribute the electrons to create bonds and fill the octet rule. 1. Count the valence electrons: Chlorine has 7 valence electrons, and since there are 2 chlorine atoms in the molecule, we have a total of 14 valence electrons. 2. Arrange the atoms: The two chlorine atoms will be bonded together, and each atom will have 3 lone pairs of electrons. 3. Distribute the electrons: The two chlorines bond by sharing one electron each, forming a single bond. Each chlorine atom has 6 remaining electrons, which are distributed as 3 lone pairs around each atom. The Lewis structure of \(\mathrm{Cl}_{2}\) is: Cl - Cl

(b) What is the hybridization of each Cl atom?

The hybridization of an atom depends on the number of electron regions around the atom (regions of electron density). In the case of \(\mathrm{Cl}_{2}\), each chlorine atom has 4 electron regions: one single bond and three lone pairs. Using the hybridization scheme: - 2 electron regions: \(sp\) - 3 electron regions: \(sp^2\) - 4 electron regions: \(sp^3\) The hybridization of each Cl atom in \(\mathrm{Cl}_{2}\) is \(sp^3\).

(c) What kind of orbital overlap, in this view, makes the \(\mathrm{Cl}-\mathrm{Cl}\) bond?

In the hybrid orbital model, the \(sp^3\) hybrid orbitals of each chlorine atom overlap to form the single bond. The orbital overlap in this model is an \(sp^3 - sp^3\) overlap.

(d) How would you distinguish between the atomic orbital and hybrid orbital models of bonding using the position of lone pairs of electrons in \(\mathrm{Cl}_{2}\)?

In the atomic orbital model, the valence electrons are located in pure \(3p\) orbitals, while in the hybrid model, the electrons are in \(sp^3\) orbitals. We can distinguish between these models by measuring the angles and distances between the lone pairs of electrons in the \(\mathrm{Cl}_{2}\) molecule. In the hybrid orbital model (\(sp^3\)), the lone pairs and the bond should arrange themselves tetrahedrally, leading to an ideal bond angle of \(109.5^\circ\). In the atomic orbital model (\(3p\)), the bond angle is expected to be \(90^\circ\) between the lone pairs in the \(p\) orbitals. So if we could measure the positions of the lone pairs of electrons in \(\mathrm{Cl}_{2}\), we would look for whether the bond angles match the predicted angles for the hybrid or atomic orbital model.

(e) Design an experiment that could tell you if the MO picture of \(\mathrm{Cl}_{2}\) is the best one

An experiment to test the molecular orbital (MO) theory for \(\mathrm{Cl}_{2}\) would involve measuring bond lengths, bond energies, and light absorption properties for ionized species, then comparing the experimental results against the predictions from the MO theory. 1. Measure bond lengths and bond energies: Using X-ray diffraction or other techniques, determine the \(\mathrm{Cl}-\mathrm{Cl}\) bond length in the molecule and compare it with the predicted values from the MO theory. Similarly, measure the bond dissociation energy (energy needed to break the \(\mathrm{Cl}-\mathrm{Cl}\) bond) and compare it with MO predictions. 2. Measure light absorption properties: Using spectroscopy techniques, determine the absorption spectrum of \(\mathrm{Cl}_{2}\) and its ionized species. The observed spectrum should match the energy level diagram predicted by the MO theory. 3. Compare results with MO predictions: If the experimental measurements are consistent with the MO theory's predictions, the MO picture of \(\mathrm{Cl}_{2}\) would be considered the best representation for the bonding in the molecule. If the measurements deviate significantly from the predictions, further investigation may be needed to refine the understanding of \(\mathrm{Cl}_{2}\) bonding.

Key concepts

Lewis structure

Lewis structures are a valuable visual representation in chemistry for showing how atoms connect in a molecule. They are often the first step in analyzing a compound's electron configuration and bond structure. To construct a Lewis structure, we begin by counting the total number of valence electrons available from all participating atoms. For chlorine ( Cl_2 ), each chlorine atom has 7 valence electrons, summing up to 14 for the molecule.

If we arrange the chlorine atoms side by side, a single bond is formed by sharing one electron each. The Lewis structure thus appears as: Cl - Cl , with each chlorine atom having three lone pairs of electrons. This structure fulfills the octet rule, ensuring that each chlorine atom is surrounded by eight electrons (counting the shared pair).

This graphical illustration helps us to predict reactivity and locate electrons available for bonding or interactions, which is fundamental when progressing to other theories like hybridization or molecular orbital theory.

hybridization

Hybridization is a concept used to explain the observed geometry of molecules in terms of the mixing of atomic orbitals to form new hybrid orbitals. In the case of an individual chlorine atom in Cl_2 , it exhibits sp^3 hybridization. This means that the s orbital mixes with three p orbitals to form four equivalent sp^3 hybrid orbitals.

Each chlorine atom has one sp^3 hybrid orbital engaged in bonding with the other chlorine, while the remaining three are filled with lone pairs. The hybridization perfectly accounts for the existing four regions of electron density around each chlorine atom, categorized as one bond and three lone pairs of electrons.

Understanding hybridization allows chemists to grasp the arrangement of electrons in space, which influences molecular shape, bond angles, and the overall stability of the molecule.

orbital overlap

Orbital overlap is an essential concept to describe covalent bond formation between atoms. In Cl_2 , when one lone pair-bearing chlorine atom approaches another, their outer sp^3 orbitals overlap. This overlap results in the sharing of one electron from each chlorine atom, forming a covalent bond.

The type of overlap in this case is referred to as sigma ( σ ) overlap, where the bond forms by the head-to-head interaction of two sp^3 orbitals. Sigma bonds are characterized by their ability to rotate around the bond axis and are typically the strongest type of covalent bond.

Bond formation through orbital overlap provides insight into how molecules achieve their stability and spatial arrangements, and an understanding of these interactions is important when delving deeper into chemical bonding theories.

molecular orbital theory

Molecular Orbital (MO) theory provides a more detailed and advanced way of understanding bonding in molecules, particularly for complex systems. Unlike the Lewis and hybridization models, which focus on individual atoms, MO theory examines the molecule as a whole.

In Cl_2 , the 3p atomic orbitals of each chlorine atom combine to form molecular orbitals that extend over the entire molecule. These orbitals are filled according to their energy levels. The resulting bond order, determined by the difference in occupancy of bonding versus antibonding molecular orbitals, can indicate the strength and stability of the bond.

Testing MO theory predictions involves experiments such as examining bond lengths, energies, and spectroscopic measurements. If experimental results match MO forecasts, it affirms the accuracy of the theory in portraying the molecule's real nature. MO theory, therefore, provides a comprehensive picture of bonding, capturing nuances that simpler models may miss.