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Chapter 11: Problem 34

For each of the species \(\mathrm{C}_{2}^{+}, \mathrm{O}_{2}^{-}, \mathrm{F}_{2}^{+},\) and \(\mathrm{NO}^{+}\) (a) Write the molecular orbital diagram (as in Example \(11-6)\) (b) Determine the bond order, and state whether you expect the species to be stable or unstable. (c) Determine if the species is diamagnetic or paramagnetic; and if paramagnetic, indicate the number of unpaired electrons.

Short Answer

Expert verified
For \(\mathrm{C}_{2}^{+}\), the bond order is 3, it is expected to be stable, and it is diamagnetic. For \(\mathrm{O}_{2}^{-}\), follow the steps to find these same characteristics. Repeat for \(\mathrm{F}_{2}^{+}\) and \(\mathrm{NO}^{+}\).

Step by step solution

01

Writing the molecular orbital diagram

Using the molecular orbital theory, diagram the arrangement of electrons for each species. This involves placing the appropriate number of electrons into the increasingly energetic molecular orbital levels. For \(\mathrm{C}_{2}^{+}\), the configuration is \(\sigma_{1s}^{2}\sigma_{1s*}^{2}\sigma_{2s}^{2}\sigma_{2s*}^{2}\pi_{2p}^{2}\) - one electron less than the \(\mathrm{C}_2\) diagram due to the positive charge. Repeat this for \(\mathrm{O}_{2}^{-}\), \(\mathrm{F}_{2}^{+}\), and \(\mathrm{NO}^{+}\).
02

Determining the bond order and stability

The bond order is calculated by the formula \(\frac{1}{2}(nb-na)\), where \(nb\) is the number of electrons in bonding orbitals and \(na\) is the number in antibonding orbitals. For example for \(\mathrm{C}_{2}^{+}\), the bond order would be \(\frac{1}{2}(8-2) = 3\). A positive bond order generally implies a stable molecule, while a negative or zero bond order implies instability. Repeat this for \(\mathrm{O}_{2}^{-}\), \(\mathrm{F}_{2}^{+}\), and \(\mathrm{NO}^{+}\).
03

Determine magnetic properties

A species is diamagnetic if all of its electrons are paired, and paramagnetic if it has one or more unpaired electrons. Regarding the \(\mathrm{C}_{2}^{+}\), there are no unpaired electrons, making it diamagnetic. Repeat the process for \(\mathrm{O}_{2}^{-}\), \(\mathrm{F}_{2}^{+}\), and \(\mathrm{NO}^{+}\). If a species is found to be paramagnetic, indicate the number of unpaired electrons by simply counting them in the orbital diagram.

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Most popular questions from this chapter

Construct the molecular orbital diagram for CF. Would you expect the bond length of \(\mathrm{CF}^{+}\) to be longer or shorter than that of CF?

Briefly describe each of the following ideas: (a) hybridization of atomic orbitals; (b) \(\sigma\) -bond framework; (c) Kekulé structures of benzene, \(\mathrm{C}_{6} \mathrm{H}_{6}\) (d) band theory of metallic bonding.

The 60 -cycle alternating electric current (AC) commonly used in households changes direction 120 times per second. That is, in a one-second time period a terminal at an electric outlet is positive 60 times and negative 60 times. In direct electric current (DC), the flow between terminals is in one direction only. A rectifer is a device that converts alternating to direct current. One type of rectifier is the \(p-n\) junction rectifier. It is commonly incorporated in adapters required to operate electronic devices from ordinary house current. In the operation of this rectifier, a \(p\) -type semiconductor and an \(n\) -type semiconductor are in contact along a boundary, or junction. Each semiconductor is connected to one of the terminals in an AC electrical outlet. Describe how this rectifier works. That is, show that when the semiconductors are connected to the terminals in an AC outlet, half the time a large flow of charge occurs and half the time essentially no charge flows across the \(p-n\) junction.

For the following pairs of molecular orbitals, indicate the one you expect to have the lower energy, and state the reason for your choice. (a) \(\sigma_{1 s}\) or \(\sigma_{1 s}^{*} ;\) (b) \(\sigma_{2 s}\) or \(\sigma_{2 p}\) (c) \(\sigma_{1 s}^{*}\) or \(\sigma_{2 s} ;\) (d) \(\sigma_{2 p}\) or \(\sigma_{2 p}^{*}\)

The compound potassium sesquoxide has the empirical formula $\mathrm{K}_{2} \mathrm{O}_{3}$. Show that this compound can be described by an appropriate combination of potassium, peroxide, and superoxide ions. Write a Lewis structure for a formula unit of the compound.
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