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Chapter 9: Problem 49

Using the molecular orbital model, write electron configurations for the following diatomic species and calculate the bond orders. Which ones are paramagnetic? $$ \text {a} \mathrm{Li}_{2} \quad \text { b. } \mathrm{C}_{2} \quad \text { c. } \mathrm{S}_{2} $$

Short Answer

Expert verified
The electron configurations and bond orders for the diatomic species are as follows: Li₂: \(1\sigma_{g}^{2}\), Bond Order = 1 (diamagnetic) C₂: \(1\sigma_{g}^{2} \, 1\sigma_{u}^{2} \, 2\sigma_{g}^{2} \, 2\sigma_{u}^{2} \, 3\sigma_{g}^{2}\), Bond Order = 2 (paramagnetic) S₂: \(1\sigma_{g}^{2} \, 1\sigma_{u}^{2} \, 2\sigma_{g}^{2} \, 2\sigma_{u}^{2} \, 3\sigma_{g}^{2} \, 1\pi_{u}^{4} \, 1\pi_{g}^{2}\), Bond Order = 3 (diamagnetic)

Step by step solution

01

Determine the total number of valence electrons

Li₂ (2 valence electrons), C₂ (8 valence electrons), S₂ (12 valence electrons).
02

Write Molecular Orbital (MO) configurations

For Li₂: \(1\sigma_{g}^{2}\) For C₂: \(1\sigma_{g}^{2} \, 1\sigma_{u}^{2} \, 2\sigma_{g}^{2} \, 2\sigma_{u}^{2} \, 3\sigma_{g}^{2}\) For S₂: \(1\sigma_{g}^{2} \, 1\sigma_{u}^{2} \, 2\sigma_{g}^{2} \, 2\sigma_{u}^{2} \, 3\sigma_{g}^{2} \, 1\pi_{u}^{4} \, 1\pi_{g}^{2}\)
03

Calculate the bond orders

Bond Order = (No. of electrons in bonding MOs - No. of electrons in antibonding MOs) / 2 For Li₂: Bond Order = (2 - 0) / 2 = 1 For C₂: Bond Order = (8 - 4) / 2 = 2 For S₂: Bond Order = (12 - 6) / 2 = 3
04

Identify the paramagnetic species

A molecule is paramagnetic if it has unpaired electrons in any of its molecular orbitals. For Li₂: There are no unpaired electrons, so it is diamagnetic. For C₂: There is a pair of unpaired electrons in the \(3\sigma_{g}\) orbital, so it is paramagnetic. For S₂: There are no unpaired electrons, so it is diamagnetic.
05

Summary:

Li₂: Bond Order = 1 (diamagnetic) C₂: Bond Order = 2 (paramagnetic) S₂: Bond Order = 3 (diamagnetic)

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Most popular questions from this chapter

The three most stable oxides of carbon are carbon monoxide \((\mathrm{CO}),\) carbon dioxide \(\left(\mathrm{CO}_{2}\right),\) and carbon suboxide \(\left(\mathrm{C}_{3} \mathrm{O}_{2}\right) .\) The space-filling models for these three compounds are For each oxide, draw the Lewis structure, predict the molecular structure, and describe the bonding (in terms of the hybrid orbitals for the carbon atoms).

Consider three molecules: A, \(\mathrm{B},\) and \(\mathrm{C}\) . Molecule \(\mathrm{A}\) has a hybridization of \(s p^{3} .\) Molecule \(\mathrm{B}\) has two more effective pairs (electron pairs around the central atom) than molecule A. Molecule C consists of two \(\sigma\) bonds and two \(\pi\) bonds. Give the molecular structure, hybridization, bond angles, and an example for each molecule.

Describe the bonding in the \(\mathrm{O}_{3}\) molecule and the \(\mathrm{NO}_{2}^{-}\) ion using the localized electron model. How would the molecular orbital model describe the \(\pi\) bonding in these two species?

Show how two 2\(p\) atomic orbitals can combine to form a \(\sigma\) or a \(\pi\) molecular orbital.

Draw the Lewis structures for $\mathrm{TeCl}_{4}, \mathrm{ICl}_{5}, \mathrm{PCl}_{5}, \mathrm{KrCl}_{4},\( and \)\mathrm{XeCl}_{2}$ . Which of the compounds exhibit at least one bond angle that is approximately $120^{\circ} ?\( Which of the compounds exhibit \)d^{2} s p^{3}$ hybridization? Which of the compounds have a square planar molecular structure? Which of the compounds are polar?
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