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Chapter 11: Problem 85

Borazine, \(\mathrm{B}_{3} \mathrm{N}_{3} \mathrm{H}_{6}\) is often referred to as inorganic benzene because of its similar structure. Like benzene, borazine has a delocalized \(\pi\) system. Describe the molecular orbitals of the \(\pi\) system. Identify the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). How many nodes does the LUMO possess?

Short Answer

Expert verified
The HOMO for Borazine is a non-bonding molecular orbital and LUMO is an antibonding molecular orbital. The LUMO possesses one node.

Step by step solution

01

Analysing π system

Start by understanding that a π system is formed by the overlap of p orbitals above and below the plane of the molecule. In Borazine(\(\mathrm{B}_{3} \mathrm{N}_{3} \mathrm{H}_{6}\)), boron and nitrogen atoms contribute to the π system. Each boron atom donates one electron and each nitrogen atom donates two electrons to the π system, making a total of 6 π electrons.
02

Describing the Molecular Orbitals

With six electrons in the π system, we can build molecular orbitals similar to benzene. The six molecular orbitals of the π system can be arranged in increasing energy levels, and filled with the 6 electrons. The two lowest energy molecular orbitals are bonding, followed by two non-bonding, and two anti-bonding molecular orbitals.
03

Identifying HOMO and LUMO

The HOMO (Highest Occupied Molecular Orbital) is the molecular orbital that has the highest energy and is filled with electrons. In borazine, the HOMO is one of the nonbonding molecular orbitals. The LUMO (Lowest Unoccupied Molecular Orbital) is the molecular orbital with the lowest energy that does not contain electrons. In borazine, the LUMO is one of the antibonding molecular orbitals.
04

Finding the Number of Nodes in LUMO

A node in a molecular orbital is a region where there is zero probability of finding an electron. As we go up in energy level, the number of nodes increases. Since our LUMO is the first antibonding molecular orbital, it has one node.

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Most popular questions from this chapter

Methyl nitrate, \(\mathrm{CH}_{3} \mathrm{NO}_{3}\), is used as a rocket propellant. The skeletal structure of the molecule is \(\mathrm{CH}_{3} \mathrm{ONO}_{2}\). The N and three O atoms all lie in the same plane, but the \(\mathrm{CH}_{3}\) group is not in the same plane as the \(\mathrm{NO}_{3}\) group. The bond angle \(\mathrm{C}-\mathrm{O}-\mathrm{N}\) is \(105^{\circ},\) and the bond angle \(\mathrm{O}-\mathrm{N}-\mathrm{O}\) is \(125^{\circ} .\) One nitrogen-to-oxygen bond length is \(136 \mathrm{pm},\) and the other two are \(126 \mathrm{pm}\) (a) Draw a sketch of the molecule showing its geometric shape. (b) Label all the bonds in the molecule as \(\sigma\) or \(\pi\), and indicate the probable orbital overlaps involved. (c) Explain why all three nitrogen-to-oxygen bond lengths are not the same.

Which of the following factors are especially important in determining whether a substance has metallic properties: (a) atomic number; (b) atomic mass; (c) number of valence electrons; (d) number of vacant atomic orbitals; (e) total number of electronic shells in the atom? Explain.

Explain why the electrical conductivity of a semiconductor is significantly increased if trace amounts of either donor or acceptor atoms are present, but is unchanged if both are present in equal number.

Construct a concept map that describes the interconnection between valence- bond theory and molecular orbital theory in the description of resonance structures.

The bond angle in \(\mathrm{H}_{2} \mathrm{Se}\) is best described as (a) between \(109^{\circ}\) and \(120^{\circ} ;\) (b) less than in \(\mathrm{H}_{2} \mathrm{S} ;\) (c) less than in \(\mathrm{H}_{2} \mathrm{S},\) but not less than \(90^{\circ} ;(\mathrm{d})\) less than \(90^{\circ}\)
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