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Chapter 11: Problem 28

Describe the bond order of diatomic carbon, \(\mathrm{C}_{2},\) with Lewis theory and molecular orbital theory, and explain why the results are different.

Short Answer

Expert verified
The bond order of diatomic carbon, \(\mathrm{C}_{2}\), is 1 according to Lewis theory and 2 according to molecular orbital theory. The difference is because Lewis theory only recognizes single bonds, while molecular orbital theory accounts for delocalization of electrons in atomic orbitals.

Step by step solution

01

Understanding Theories

Lewis theory is focused mainly on electron pairs and creating stable by sharing pairs of electrons, while the molecular orbital theory considers the wave properties of electrons and creates molecular orbitals that are spread over the entire molecule.
02

Using Lewis theory

Each carbon in diatomic carbon, \(\mathrm{C}_{2}\), has 4 electrons in its outer shell. According to Lewis theory, a carbon-carbon bond is created when each carbon atom shares one of its electrons to form a covalent bond. Thus, the bond order according to Lewis theory is 1, meaning there is a single bond between the two carbon atoms.
03

Using Molecular Orbital Theory

In molecular orbital theory, we combine atomic orbitals to form molecular orbitals, which can be bonding, anti-bonding, or non-bonding. For carbon, we fill the molecular orbitals starting with the lower energy orbitals. We have a total of 8 electrons (4 from each carbon). These electrons will fill the \(\sigma_{1s}\), \(\sigma_{1s}*\), \(\sigma_{2s}\),\(\sigma_{2s}*\), and \(\pi_{2p}\) orbitals, each pair cancelling each other out except in the \(\pi_{2p}\) orbital. The bond order is then \(\frac{1}{2} (4- 0)\) = 2.
04

Comparing Results and Explaining the Difference

The bond order obtained using Lewis theory is 1 while that obtained using Molecular Orbital theory is 2. This discrepancy is due to the count of \(\pi_{2p}\) electrons in molecular orbital theory. While Lewis theory only recognizes single bonds, molecular orbital theory accounts for delocalization of electrons in atomic orbitals, therefore considering \(\pi_{2p}\) electrons which creates a double bond.

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Most popular questions from this chapter

In what type of material is the energy gap between the valence band and the conduction band greatest: metal, semiconductor, or insulator? Explain.

Of the following, the species with a bond order of 1 is (a) \(\mathrm{H}_{2}^{+} ;\) (b) \(\mathrm{Li}_{2} ;\) (c) \(\mathrm{He}_{2} ;\) (d) \(\mathrm{H}_{2}^{-}\)

Lewis theory is satisfactory to explain bonding in the ionic compound \(\mathrm{K}_{2} \mathrm{O},\) but it does not readily explain formation of the ionic compounds potassium superoxide, \(\mathrm{KO}_{2}\), and potassium peroxide, \(\mathrm{K}_{2} \mathrm{O}_{2}\) (a) Show that molecular orbital theory can provide this explanation. (b) Write Lewis structures consistent with the molecular orbital explanation.

Describe the molecular geometry of \(\mathrm{H}_{2} \mathrm{O}\) suggested by each of the following methods: (a) Lewis theory; (b) valence-bond method using simple atomic orbitals; (c) VSEPR theory; (d) valence-bond method using hybridized atomic orbitals.

In which of the following molecules would you expect to find delocalized molecular orbitals: (a) \(\mathrm{C}_{2} \mathrm{H}_{4}\) (b) \(\mathrm{SO}_{2} ;\) (c) \(\mathrm{H}_{2} \mathrm{CO}\) ? Explain.
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