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Chapter 9

Covalent Bonding: Orbitals

Shaun Williams, PhD

Hybridization and the Localized Electron Model

Exercise 1

Draw the Lewis structure for methane, \(\chem{CH_4}\).

A central carbon atom singly bonded to four neighboring hydrogen atoms.

Hybridization and the Localized Electron Model

Exercise 1 - Answer

Draw the Lewis structure for methane, \(\chem{CH_4}\).

A central carbon atom singly bonded to four neighboring hydrogen atoms.

Concept Check 1

What is the valence electron configuration of a carbon atom?

$$ \phantom{s^2p^2} $$

Why can't the bonding orbitals for methane be formed by an overlap of atomic orbitals?

Concept Check 1 - Answer

What is the valence electron configuration of a carbon atom?

$$ s^2p^2 $$

Why can't the bonding orbitals for methane be formed by an overlap of atomic orbitals?

Because this would lead to two different types of C-H bonds and we know that methane has four identical C-H bonds that are 109.5° apart from each other (not 90° from each other).

Bonding in Methane

Hybridization

\(sp^3\) Hybridization

An Energy-Level Diagram Showing the Formation of Four \(sp^3\) Orbitals

The one 2s and the three 2p orbitals mix together to make four sp3 hybrid orbitals.

The Formation of \(sp^3\) Hybrid Orbitals

A graphical representation of the one 2s and the three 2p orbitals mix together to make four sp3 hybrid orbitals.

A graphical representation of the set of sp3 hybrid orbitals showing their tetrahedral arrangement.

Exercise 2

Draw the Lewis structure for \(\chem{C_2H_4}\) (ethylene)?

Two carbon atoms doubly bonded to each other. Each carbon atom is songly bonded to two hydrogen atoms.

Exercise 2 - Answer

Draw the Lewis structure for \(\chem{C_2H_4}\) (ethylene)?

Two carbon atoms doubly bonded to each other. Each carbon atom is songly bonded to two hydrogen atoms.

\(sp^2\) Hybridization

Sigma (\(\Sigma\)) Bond

Pi (\(\Pi\)) Bond

An Orbital Energy-Level Diagram for \(sp^2\) Hybridization

The one 2s and the two 2p orbitals mix together to make three sp2 hybrid orbitals. There is also a left over unhybridized 2p orbital.

The Hybridization of the \(s\), \(p_x\), and \(p_y\) Atomic Orbitals

A graphical representation of the one 2s and the two 2p orbitals mix together to make three sp2 hybrid orbitals and a left over 2p orbital.

\(sp\) Hybridization

The Orbital Energy-Level Diagram for the Formation of \(sp\) Hybrid Orbitals on Carbon

The one 2s and the one 2p orbitals mix together to make two sp hybrid orbitals. There are also two left over unhybridized 2p orbitals.

When One \(s\) Orbital and One \(p\) Orbital are Hybridized, a Set of Two \(sp\) Orbitals Oriented at \(180^\circ\) Results

A graphical representation of the one 2s and one 2p orbitals mix together to make two sp hybrid orbitals and two left over 2p orbitals.

The Orbitals for \(\chem{CO_2}\)

A graphical representation carbon dioxide with the central carbon atom forming a sigma bond with each oxygen atom and a pi bond with each of the oxygen atoms.

Exercise 3

Draw the Lewis structure for \(\chem{PCl_5}\)?

A central phosphorus atom singly bonded to five chlorine atoms. Each chlorine atom has three lone pairs of electrons.

Exercise 3 - Answer

Draw the Lewis structure for \(\chem{PCl_5}\)?

A central phosphorus atom singly bonded to five chlorine atoms. Each chlorine atom has three lone pairs of electrons.

\(dsp^3\) Hybridization

The Orbitals Used to Form the Bonds in \(\chem{PCl_5}\)

A graphical representation phosphorus pentachloride with the central phosphorus atom forming a sigma bond with each chlorine atom.

Exercise 3

Draw the Lewis structure for \(\chem{XeF_4}\)?

A central xenon atom with two lone electron pairs is singly bonded to four fluorine atoms. Each fluorine atom has three lone pairs of electrons.

Exercise 3 - Answer

Draw the Lewis structure for \(\chem{XeF_4}\)?

A central xenon atom with two lone electron pairs is singly bonded to four fluorine atoms. Each fluorine atom has three lone pairs of electrons.

\(d^2sp^3\) Hybridization

How is the Xenon Atom in \(\chem{XeF_4}\) Hybridized

A graphical representation of the two d orbitals, one 2s and the three 2p orbitals mix together to make four sp3 hybrid orbitals.

Using the Localized Electron Model

The Molecular Orbital Model

Combination of Hydrogen 1s Atomic Orbitals to form MOs

A graphical representation of subtracting the 1s orbitals on the two atoms to form the antibonding MO (called MO1) and adding the two 1s orbitals to form the bonding MO (MO2). The antibonding MO has a node between the atoms while the bonding MO does not.

Relative Stabilities

MO Energy-Level Diagram for the \(\chem{H_2}\) Molecule

A graphical representation of the relative energies of the bonding and antibonding orbitals showing the bonding MO at a lower energy than the antibonding orbital.

Description of Bonding

Bond Order

Example: \(\chem{H_2}\)

In the H2 molecule, two electrons are in the lower energy bonding orbital and the higher energy antibonding orbital is empty.

$$ \text{Bond order}=\frac{2-0}{2} = 1 $$

Example: \(\chem{H_2^-}\)

In the H2 negative 1 ion, two electrons are in the lower energy bonding orbital and one electron is in the higher energy antibonding orbital.

$$ \text{Bond order}=\frac{2-1}{2} = \frac{1}{2} $$

Bonding on Homonuclear Diatomic Molecules

Homonuclear Diatomic Molecules

Paramagnetism

Apparatus Used to Measure the Paramagnetism of a Sample

The pan of a balance is connected to a hanging sample tube which is houses in glass tubing. The sample tube is suspended between the poles of an electromagnet.

Molecular Orbital Summary of Second Row Diatomic Molecules

A summary of the molecular orbital diagrams for B2, C2, N2, O2, and F2.

Bonding in Heteronuclear Diatomic Molecules

Heteronuclear Diatomic Molecules

Heteronuclear Diatomic Molecule: \(\chem{HF}\)

Orbital Energy-Level Diagram for the \(\chem{HF}\) Molecule

In the HF molecule, two electrons are in the lower energy bonding orbital and the higher energy antibonding orbital is empty.

Heteronuclear Diatomic Molecule: HF (cont.)

Combining the Localized Electron and Molecular Orbital Models

Delocalization

Resonance in Benzene

The two resonance structures of the benzene molecule with alternating single/double bonds around the ring of six carbon atoms.

The Sigma System for Benzene

There is a sigma bond between each neighboring carbon atoms in the six membered carbon atom ring. There is also sigma bonds to the hydrogen atoms.

The Pi System for Benzene

There are p orbitals above and below the plane of the ring on each carbon atom. These p orbitals bond to form a ringed pi system.

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