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Ch.9 - Molecular Geometry and Bonding Theories
Chapter 9, Problem 104a

One of the molecular orbitals of the H2βˆ’ ion can be sketched as follows:
a. Is the molecular orbital a 𝜎 or πœ‹ MO? Is it bonding or antibonding?

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1
Identify the type of molecular orbital (MO) by observing the symmetry of the electron cloud distribution around the internuclear axis. If the electron cloud is cylindrically symmetric around the axis, it is a sigma (𝜎) MO. If the electron cloud is oriented perpendicular to the axis, it is a pi (πœ‹) MO.
Determine if the MO is bonding or antibonding by looking at the phase of the wave functions. Bonding orbitals have constructive interference (same phase) between atomic orbitals, leading to an increase in electron density between the nuclei. Antibonding orbitals have destructive interference (opposite phase), leading to a decrease in electron density between the nuclei.
Examine any nodal planes (regions of zero electron density) present in the MO. Bonding orbitals typically have fewer nodal planes than the corresponding antibonding orbitals.
Consider the energy level of the MO. Bonding orbitals are generally lower in energy compared to the atomic orbitals from which they form, while antibonding orbitals are higher in energy.
Use the molecular orbital theory to predict the stability of the molecule or ion. A molecule with more electrons in bonding orbitals than in antibonding orbitals is generally more stable.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Molecular Orbitals

Molecular orbitals (MOs) are formed by the combination of atomic orbitals when atoms bond together. They can be classified as bonding or antibonding. Bonding MOs lower the energy of the system and stabilize the molecule, while antibonding MOs increase energy and destabilize it. Understanding the type of molecular orbital is crucial for predicting the stability and properties of the molecule.
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Sigma (𝜎) and Pi (πœ‹) Bonds

Sigma (𝜎) and pi (πœ‹) bonds are types of covalent bonds that arise from the overlap of atomic orbitals. A sigma bond is formed by the head-on overlap of orbitals, allowing for free rotation, while a pi bond results from the side-to-side overlap, restricting rotation. In molecular orbital theory, 𝜎 MOs are typically lower in energy than πœ‹ MOs, influencing the overall bonding characteristics of the molecule.
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Bonding vs. Antibonding Orbitals

Bonding orbitals are formed when atomic orbitals combine constructively, leading to increased electron density between the nuclei, which stabilizes the molecule. Antibonding orbitals, on the other hand, result from destructive interference, creating a node between the nuclei and leading to decreased electron density in that region. The presence of electrons in antibonding orbitals can weaken or negate the bond formed by bonding orbitals.
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Related Practice
Textbook Question

The structure of borazine, B3N3H6, is a six-membered ring of alternating B and N atoms. There is one H atom bonded to each B and to each N atom. The molecule is planar. (a) Write a Lewis structure for borazine in which the formal charge on every atom is zero.

Textbook Question

The structure of borazine, B3N3H6, is a six-membered ring of alternating B and N atoms. There is one H atom bonded to each B and to each N atom. The molecule is planar. (e) What are the hybridizations at the B and N atoms in the Lewis structures from parts (a) and (b)? Would you expect the molecule to be planar for both Lewis structures? Would you expect the molecule to be planar for both Lewis structures?

Textbook Question

The highest occupied molecular orbital of a molecule is abbreviated as the HOMO. The lowest unoccupied molecular orbital in a molecule is called the LUMO. Experimentally, one can measure the difference in energy between the HOMO and LUMO by taking the electronic absorption (UV-visible) spectrum of the molecule. Peaks in the electronic absorption spectrum can be labeled as Ο€2p-Ο€2p*, Οƒs-Οƒ2s*, and so on, corresponding to electrons being promoted from one orbital to another. The HOMO-LUMO transition corresponds to molecules going from their ground state to their first excited state. (c) The electronic absorption spectrum of the N2 molecule has the lowest energy peak at 170 nm. To what orbital transition does this correspond?

Textbook Question

One of the molecular orbitals of the H2βˆ’ ion can be sketched as follows:

d. Compared to the Hβ€”H bond in H2, the Hβ€”H bond in H2βˆ’ is expected to be which of the following?

i. shorter and stronger

ii. longer and stronger

iii. shorter and weaker

iv. longer and weaker or

v. the same length and strength

Textbook Question

Place the following molecules and ions in order from smallest to largest bond order: H2+,B2,N2+,F2+, and Ne2.

Textbook Question

Azo dyes are organic dyes that are used for many applications, such as the coloring of fabrics. Many azo dyes are derivatives of the organic substance azobenzene, C12H10N2. A closely related substance is hydrazobenzene, C12H12N2. The Lewis structures of these two substances are

(Recall the shorthand notation used for benzene.) (b) How many unhybridized atomic orbitals are there on the N and the C atoms in each of the substances? How many unhybridized atomic orbitals are there on the N and the C atoms in hydrazobenzene?