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Chapter 11: Problem 58

Show that both the valence-bond method and molecular orbital theory provide an explanation for the existence of the covalent molecule \(\mathrm{Na}_{2}\) in the gaseous state. Would you predict \(\mathrm{Na}_{2}\) by the Lewis theory?

Short Answer

Expert verified
The valence-bond theory and the molecular orbital theory both support the existence of \( \mathrm{Na}_{2} \). The valence-bond theory suggests that overlapping of atomic orbitals forms this molecule. The molecular orbital theory indicates that a bond in \( \mathrm{Na}_{2} \) arises when the two 3s atomic orbitals of the Sodium atoms combine to form a bonding molecular orbital filled by the one valence electron of each Sodium atom. According to the Lewis theory, the existence of \( \mathrm{Na}_{2} \) is not favoured as the formation of \( \mathrm{Na}_{2} \) does not satisfy the octet rule.

Step by step solution

01

Valence-Bond Method

The valence-bond theory suggests that covalent bonds are formed when atomic orbitals on adjacent atoms overlap. For \( \mathrm{Na}_{2} \), each atom of Sodium (Na) has a 3s1 valence-shell electronic configuration. When two sodium atoms collide, the atomic orbitals (3s) of each overlap, leading to the forming of a bond through the sharing of the single electron in each of their 3s orbitals. Consequently, a covalent molecule is formed.
02

Molecular Orbital Theory

The Molecular Orbital (MO) theory discusses the combination of atomic orbitals to lead to the formation of molecular orbitals. The molecular orbital for \( \mathrm{Na}_{2} \) can be constructed by combination of the 3s orbitals of each Sodium atom. The combination leads to two molecular orbitals, a bonding orbital (lower in energy) and an anti-bonding orbital (higher in energy). Both Sodium atoms each contribute one electron (from the 3s orbital) to fill up the bonding molecular orbital, thus leading to the existence of a bond in \( \mathrm{Na}_{2} \), and its existence as a covalent molecule in the gaseous state.
03

Lewis Theory Perspective

The Lewis theory focuses primarily on valence electrons for illustrating chemical bonding. According to Lewis structures, each atom aims for an octet arrangement, i.e., having eight electrons in its outermost shell (except Hydrogen which aims for two). However, in the case of Sodium (Na), the Lewis theory might not predict the formation of \( \mathrm{Na}_{2} \). Each Sodium atom has one valence electron, and sharing of this single electron by each Sodium does lead to a bond. But this doesn't satisfy the octet rule, as each Sodium would then have only 2 electrons in their outermost shell. Thus, it can be predicted that \( \mathrm{Na}_{2} \) might not exist.

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Most popular questions from this chapter

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.

Construct a molecular orbital diagram for \(\mathrm{HF}\), and label the molecular orbitals as bonding, antibonding, or nonbonding.

Explain how it is possible to avoid the concept of resonance by using molecular orbital theory.

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

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.
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