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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 蠄; 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 蠄 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 蠄.
03

Comparing Molecular and Atomic Orbitals

Both molecular and atomic orbitals describe the probability of finding an electron and are represented by wave functions 蠄. 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

Which is the more correct statement: "The methane molecule \(\left(\mathrm{CH}_{4}\right)\) is a tetrahedral molecule because it is \(s p^{3}\) hybridized" or "The methane molecule \(\left(\mathrm{CH}_{4}\right)\) is \(s p^{3}\) hybridized because it is a tetrahedral molecule"? What, if anything, is the difference between these two statements?

An unusual category of acids known as superacids, which are defined as any acid stronger than \(100 \%\) sulfuric acid, can be prepared by seemingly simple reactions similar to the one below. In this example, the reaction of anhydrous HF with \(\mathrm{SbF}_{5}\) produces the superacid \(\left[\mathrm{H}_{2} \mathrm{~F}\right]^{+}\left[\mathrm{SbF}_{6}\right]^{-}\) : $$ 2 \mathrm{HF}(l)+\mathrm{SbF}_{5}(l) \longrightarrow\left[\mathrm{H}_{2} \mathrm{~F}\right]^{+}\left[\mathrm{SbF}_{6}\right]^{-}(l) $$ a. What are the molecular structures of all species in this reaction? What are the hybridizations of the central atoms in each species? b. What mass of \(\left[\mathrm{H}_{2} \mathrm{~F}\right]^{+}\left[\mathrm{SbF}_{6}\right]^{-}\) can be prepared when \(2.93 \mathrm{~mL}\) anhydrous HF (density \(=0.975 \mathrm{~g} / \mathrm{mL}\) ) and \(10.0 \mathrm{~mL} \mathrm{SbF}_{5}\) (density \(=3.10 \mathrm{~g} / \mathrm{mL}\) ) are allowed to react?

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Cyanamide \(\left(\mathrm{H}_{2} \mathrm{NCN}\right)\), an important industrial chemical, is produced by the following steps: $$ \begin{aligned} \mathrm{CaC}_{2}+\mathrm{N}_{2} & \longrightarrow \mathrm{CaNCN}+\mathrm{C} \\\ \mathrm{CaNCN} & \stackrel{\text { Acid }}{\longrightarrow} \mathrm{H}_{2} \mathrm{NCN} \end{aligned} $$ Cyanamid Calcium cyanamide (CaNCN) is used as a direct-application fertilizer, weed killer, and cotton defoliant. It is also used to make cyanamide, dicyandiamide, and melamine plastics: a. Write Lewis structures for \(\mathrm{NCN}^{2-}, \mathrm{H}_{2} \mathrm{NCN}\), dicyandiamide, and melamine, including resonance structures where appropriate. b. Give the hybridization of the \(\mathrm{C}\) and \(\mathrm{N}\) atoms in each species. c. How many \(\sigma\) bonds and how many \(\pi\) bonds are in each species? d. Is the ring in melamine planar? e. There are three different \(\mathrm{C}-\mathrm{N}\) bond distances in dicyandiamide, \(\mathrm{NCNC}\left(\mathrm{NH}_{2}\right)_{2}\), and the molecule is nonlinear. Of all the resonance structures you drew for this molecule, predict which should be the most important.

Compare and contrast bonding molecular orbitals with antibonding molecular orbitals.
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