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Chapter 9: Problem 1

What are molecular orbitals? How do they compare with atomic orbitals? Can you tell by the shape of the bonding and antibonding orbitals which is lower in energy? Explain.

Short Answer

Expert verified
Molecular orbitals are mathematical functions that describe the probability of finding an electron in a molecule and result from the combination of atomic orbitals when atoms form bonds. Both molecular and atomic orbitals have wave functions ψ; however, molecular orbitals describe the characteristics for the entire molecule. Bonding orbitals, formed from constructive interference, have electron density concentrated between nuclei, leading to lower energy and increased stability. Antibonding orbitals, formed from destructive interference, have electron density away from the region between nuclei, leading to higher energy and decreased stability. In general, bonding orbitals are lower in energy than antibonding orbitals, but other factors should be considered for accurate comparison.

Step by step solution

01

Defining Atomic Orbitals

Atomic orbitals are mathematical functions that describe the probability of finding an electron in a particular region of space around an atom's nucleus. They are represented by the wave function ψ and are related to the energy levels of electrons in an atom. The orbitals have different shapes depending on their energy level and quantum numbers (n, l, and m).
02

Defining Molecular Orbitals

Molecular Orbitals (MO) are mathematical functions that describe the probability of finding an electron in a molecule. These orbitals result from the combination of atomic orbitals when atoms interact and form bonds, leading to a new set of energy levels that belong to the entire molecule rather than individual atoms. Just like atomic orbitals, molecular orbitals are also represented by wave functions ψ.
03

Comparing Molecular and Atomic Orbitals

Both molecular and atomic orbitals describe the probability of finding an electron and are represented by wave functions ψ. However, atomic orbitals are related to the energy levels and spatial distribution of electrons in an atom, while molecular orbitals describe the same characteristics but for the entire molecule. The interaction and combination of atomic orbitals give rise to molecular orbitals, which have their unique energy levels and shapes. Bonding and antibonding orbitals are two types of molecular orbitals that are formed during the interaction between atomic orbitals.
04

Bonding Orbitals

Bonding orbitals result from the constructive interference of atomic orbitals. The electron density between the nuclei increases, leading to a lower potential energy, as the electron cloud gets more attracted to the nuclei. This sort of orbital leads to the formation of a stable bond between the atoms, and it is lower in energy as compared to the parent atomic orbitals.
05

Antibonding Orbitals

Antibonding orbitals arise from the destructive interference between atomic orbitals. The electron density between the nuclei decreases, causing a higher potential energy as the electron cloud is less attracted to the nuclei. Antibonding orbitals lead to higher energy states, and if the electrons in a molecule occupy these orbitals, the bond between the atoms becomes unstable or nonexistent.
06

Energy Levels and Orbital Shapes

Shape alone might not be sufficient to determine the energy level of bonding and antibonding orbitals. However, there are some general trends: Bonding orbitals typically have electron density concentrated between the nuclei, which leads to a lower energy state and increased stability. On the other hand, antibonding orbitals have electron density away from the region between the nuclei, leading to a higher energy state and decreased stability. So, in general, bonding orbitals are lower in energy than antibonding orbitals. However, it is essential to consider other factors, such as the interacting atomic orbitals' energy levels, for a more accurate comparison.

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Most popular questions from this chapter

Describe the bonding in \(\mathrm{NO}^{+}, \mathrm{NO}^{-}\), and NO using both the localized electron and molecular orbital models. Account for any discrepancies between the two models.

Use the MO model to explain the bonding in \(\mathrm{BeH}_{2}\). When constructing the MO energy-level diagram, assume that the Be's \(1 s\) electrons are not involved in bond formation.

As compared with \(\mathrm{CO}\) and \(\mathrm{O}_{2}, \mathrm{CS}\) and \(\mathrm{S}_{2}\) are very unstable molecules. Give an explanation based on the relative abilities of the sulfur and oxygen atoms to form \(\pi\) bonds.

Describe the bonding in the first excited state of \(\mathrm{N}_{2}\) (the one closest in energy to the ground state) using the molecular orbital model. What differences do you expect in the properties of the molecule in the ground state as compared to the first excited state? (An excited state of a molecule corresponds to an electron arrangement other than that giving the lowest possible energy.)

The three most stable oxides of carbon are carbon monoxide (CO), carbon dioxide \(\left(\mathrm{CO}_{2}\right)\), and carbon suboxide \(\left(\mathrm{C}_{3} \mathrm{O}_{2}\right)\). The spacefilling models for these three compounds are For each oxide, draw the Lewis structure, predict the molecular structure, and describe the bonding (in terms of the hybrid orbitals for the carbon atoms).
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