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Chapter 10: Problem 52

Arrange the following species in order of increasing stability: \(\mathrm{Li}_{2}, \mathrm{Li}_{2}^{+}, \mathrm{Li}_{2}^{-}\). Justify your choice with a molecular orbital energy level diagram.

Short Answer

Expert verified
The correct order of increasing stability for the given species is Li2+ < Li2- < Li2. This is based on the quantity of unpaired electrons and electrons in bonding molecular orbitals for each species.

Step by step solution

01

Understand Molecular Orbital Theory

The concepts related to molecular orbital (MO) theory are essential for solving this exercise. According to MO theory, atomic orbitals (AOs) merge to form molecular orbitals when atoms combine to form molecules. These molecular orbitals can be bonding, non-bonding, or anti-bonding. The stability of a molecule is related to how these orbitals are filled.
02

Illustrate the Molecular Orbital Diagram for Lithium

Lithium atom has an electronic configuration of 1s² 2s¹. Once two Lithium atoms combine to form Li2, they would have a total of 6 electrons to distribute among the molecular orbitals. This is the molecular orbital energy diagram: \[ \begin{align*} &\text{Li2: }\sigma_{1s}^{2}\sigma_{1s*}^{2}\sigma_{2s}^{2}\ &\text{Li2+ : }\sigma_{1s}^{2}\sigma_{1s*}^{2}\sigma_{2s}^{1}\ &\text{Li2- : }\sigma_{1s}^{2}\sigma_{1s*}^{2}\sigma_{2s}^{3} \end{align*} \]
03

Analyze Molecular Orbital Diagram and Arrange Species

The molecule or ion with less number of unpaired electrons and more number of electrons in bonding orbitals will have a higher stability. Therefore, referring to the MO diagrams: \[ \begin{align*} &1. \text{Li2+ : }\text{Has 1 unpaired electron and 5 electrons in bonding MOs.}\ &2. \text{Li2- : }\text{Has 1 unpaired electron and 6 electrons in bonding MOs.}\ &3. \text{Li2: }\text{Has no unpaired electron and 6 electrons in bonding MOs.} \end{align*} \] So, the correct sequence of stability is: Li2+ < Li2- < Li2

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Most popular questions from this chapter

Draw the Lewis structure for the \(\mathrm{BeCl}_{4}^{2-}\) ion. Predict its geometry and describe the hybridization state of the Be atom.

Predict the geometry of the following molecules and ion using the VSEPR model: (a) \(\mathrm{CBr}_{4},\) (b) \(\mathrm{BCl}_{3}\) (c) \(\mathrm{NF}_{3}\), (d) \(\mathrm{H}_{2} \mathrm{Se},\) (e) \(\mathrm{NO}_{2}^{-}\).

Consider the reaction $$ \mathrm{BF}_{3}+\mathrm{NH}_{3} \longrightarrow \mathrm{F}_{3} \mathrm{~B}-\mathrm{NH}_{3} $$ Describe the changes in hybridization (if any) of the \(\mathrm{B}\) and \(\mathrm{N}\) atoms as a result of this reaction.

How is the geometry of a molecule defined and why is the study of molecular geometry important?

What are the hybrid orbitals of the carbon atoms in the following molecules? (a) \(\mathrm{H}_{3} \mathrm{C}-\mathrm{CH}_{3}\) (b) \(\mathrm{H}_{3} \mathrm{C}-\mathrm{CH}=\mathrm{CH}_{2}\) (c) \(\mathrm{CH}_{3}-\mathrm{C} \equiv \mathrm{C}-\mathrm{CH}_{2} \mathrm{OH}\) (d) \(\mathrm{CH}_{3} \mathrm{CH}=\mathrm{O}\) (e) \(\mathrm{CH}_{3} \mathrm{COOH}\)
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