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Chapter 23: Problem 14

What is the electron configuration corresponding to \(\mathrm{O}_{2}, \mathrm{O}_{2}^{-},\) and \(\mathrm{O}_{2}^{+} ?\) What do you expect the relative order of bond strength to be for these species? Which, if any, have unpaired electrons?

Short Answer

Expert verified
The electron configurations of the species O鈧�, O鈧傗伝, and O鈧傗伜 are: - O鈧�: \[[(\sigma(1s))^{2}(\sigma^{*}(1s))^{2}(\sigma(2s))^{2}(\sigma^{*}(2s))^{2}]\sigma(2p)^{2}\pi(2p)^{4}\pi^{*}(2p)^{2}\] - O鈧傗伝: \[[(\sigma(1s))^{2}(\sigma^{*}(1s))^{2}(\sigma(2s))^{2}(\sigma^{*}(2s))^{2}]\sigma(2p)^{2}\pi(2p)^{4}\pi^{*}(2p)^{3}\] - O鈧傗伜: \[[(\sigma(1s))^{2}(\sigma^{*}(1s))^{2}(\sigma(2s))^{2}(\sigma^{*}(2s))^{2}]\sigma(2p)^{2}\pi(2p)^{4}\pi^{*}(2p)^{1}\] The relative order of bond strength is: O鈧傗伜 > O鈧� > O鈧傗伝. All three species have unpaired electrons: O鈧� has two, while O鈧傗伝 and O鈧傗伜 have one each.

Step by step solution

01

Finding the atomic electron configuration of oxygen

The first thing we need to do is find the electron configuration of an oxygen atom. Oxygen has 8 electrons, and its electron configuration is: \[1s^{2}2s^{2}2p^{4}\]
02

Determine molecular orbitals for O2

For diatomic molecules like O2, we can use the molecular orbital theory to find the electron configuration of the entire molecule. In this theory, atomic orbitals of the same energy combine to form molecular orbitals. For oxygen, the molecular orbitals in order of increasing energy are: 蟽(1s), 蟽*(1s), 蟽(2s), 蟽*(2s), 蟽(2p), 蟺(2p), 蟺*(2p), and 蟽*(2p). Now we can fill these orbitals with the electrons from two oxygen atoms combined (2 x 8 = 16 electrons). The resulting molecular electron configuration is: \[[(\sigma(1s))^{2}(\sigma^{*}(1s))^{2}(\sigma(2s))^{2}(\sigma^{*}(2s))^{2}]\sigma(2p)^{2}\pi(2p)^{4}\pi^{*}(2p)^{2}\]
03

Determine electron configurations for O鈧傗伝 and O鈧傗伜

Now we can find the electron configurations of O鈧傗伝 and O鈧傗伜 by adding or removing electrons from the molecular orbitals of O鈧� determined in step 2. - For O鈧傗伝 (17 electrons): \[[(\sigma(1s))^{2}(\sigma^{*}(1s))^{2}(\sigma(2s))^{2}(\sigma^{*}(2s))^{2}]\sigma(2p)^{2}\pi(2p)^{4}\pi^{*}(2p)^{3}\] - For O鈧傗伜 (15 electrons): \[[(\sigma(1s))^{2}(\sigma^{*}(1s))^{2}(\sigma(2s))^{2}(\sigma^{*}(2s))^{2}]\sigma(2p)^{2}\pi(2p)^{4}\pi^{*}(2p)^{1}\]
04

Compare bond strengths

To determine the relative bond strengths of O鈧�, O鈧傗伝, and O鈧傗伜, we can compare the number of bonding electrons minus the number of anti-bonding electrons in their molecular electron configurations. - For O鈧�: 10 bonding electrons - 6 anti-bonding electrons = 4 - For O鈧傗伝: 10 bonding electrons - 7 anti-bonding electrons = 3 - For O鈧傗伜: 10 bonding electrons - 5 anti-bonding electrons = 5 Bond strength is directly related to the number calculated above, so the order of bond strength is: O鈧傗伜 > O鈧� > O鈧傗伝
05

Identify unpaired electrons

Finally, we will identify any unpaired electrons in each species by examining their molecular electron configurations: - O鈧� has two unpaired electrons in the 蟺*(2p) orbital. - O鈧傗伝 has one unpaired electron in the 蟺*(2p) orbital. - O鈧傗伜 has one unpaired electron in the 蟺*(2p) orbital. All three species have unpaired electrons.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Electron Configuration
In Molecular Orbital Theory, electron configuration helps us understand how electrons are distributed in a molecule. For diatomic molecules like oxygen (\(\text{O}_2\)), molecular orbitals are established by combining atomic orbitals of similar energies. Oxygen atoms have an electron configuration of \(1s^{2}2s^{2}2p^{4}\). This means that each oxygen atom has 8 electrons, and when two oxygen atoms come together, as in \(\text{O}_2\), a total of 16 electrons must be allocated to molecular orbitals.
  • The sequence for oxygen's molecular orbitals is: \(sigma(1s), sigma^*(1s), sigma(2s), sigma^*(2s), sigma(2p), \pi(2p), \pi^*(2p), sigma^*(2p)\).
  • The \(\text{O}_2\) molecule is filled with electrons as: \([(sigma(1s))^2(sigma^*(1s))^2(sigma(2s))^2(sigma^*(2s))^2](sigma(2p))^2(\pi(2p))^4(\pi^*(2p))^2\).

For the ions \(\text{O}_2^-\) and \(\text{O}_2^+\), electron configuration differs based on whether electrons are added or removed.
  • \(\text{O}_2^-\) has one extra electron: \([(sigma(1s))^2(sigma^*(1s))^2(sigma(2s))^2(sigma^*(2s))^2](sigma(2p))^2(\pi(2p))^4(\pi^*(2p))^3\).
  • \(\text{O}_2^+\) has one less electron: \([(sigma(1s))^2(sigma^*(1s))^2(sigma(2s))^2(sigma^*(2s))^2](sigma(2p))^2(\pi(2p))^4(\pi^*(2p))^1\).
This electron distribution impacts each species' chemical properties and reactivity.
Bond Strength
The bond strength in molecules can be determined by comparing bonding and anti-bonding electrons in their molecular electron configuration. In molecular orbital notation, bonding orbitals hold electrons that stabilize the molecule, while anti-bonding orbitals, indicated with an asterisk (*), have the opposite effect.
  • Bond order provides a numerical representation of bond strength by subtracting the number of electrons in anti-bonding orbitals from the number of electrons in bonding orbitals, and then dividing by two.
  • For \(\text{O}_2\): There are 10 electrons in bonding orbitals and 6 in anti-bonding, leading to a bond order of \((10-6)/2 = 2\).
  • For \(\text{O}_2^-\): 10 electrons are in bonding and 7 in anti-bonding orbitals, yielding a bond order of \((10-7)/2 = 1.5\).
  • For \(\text{O}_2^+\): With 10 in bonding and only 5 in anti-bonding orbitals, the bond order is \((10-5)/2 = 2.5\).

Thus, the order of bond strength is \(\text{O}_2^+ > \text{O}_2 > \text{O}_2^-\), indicating \(\text{O}_2^+\) has the strongest bond and \(\text{O}_2^-\) the weakest.
Unpaired Electrons
The presence of unpaired electrons in a molecule affects its magnetic properties and reactivity. Unpaired electrons make a molecule paramagnetic, causing it to be attracted to a magnetic field. For oxygen and its ions, we examine the highest energy molecular orbitals, specifically the \(\pi^*(2p)\) orbitals, to determine the unpaired electrons.
  • In \(\text{O}_2\), there are two electrons in the \(\pi^*(2p)\) orbitals, both unpaired, making it paramagnetic with two unpaired electrons.
  • For \(\text{O}_2^-\), the additional electron leads to three electrons in \(\pi^*(2p)\), with one unpaired electron.
  • For \(\text{O}_2^+\), the removal of one electron results in only one unpaired electron in the \(\pi^*(2p)\) orbital.

Consequently, all three species \(\text{O}_2\,\text{O}_2^-\,\text{and}\,\text{O}_2^+\) have unpaired electrons, contributing to their paramagnetic nature.

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Most popular questions from this chapter

The ionization energy of \(\mathrm{CO}\) is greater than that of NO. Explain this difference based on the electron configuration of these two molecules.

The overlap integral for \(\psi_{g}\) and \(\psi_{u}\) as defined in Section 23.3 is given by \\[S_{a b}=e^{-\zeta R / a_{0}}\left(1+\zeta \frac{R}{a_{0}}+\frac{1}{3} \zeta^{2} \frac{R^{2}}{a_{0}^{2}}\right)\\] Plot \(S_{a b}\) as a function of \(R / a_{0}\) for \(\zeta=0.8,1.0,\) and 1.2 Estimate the value of \(R / a_{0}\) for which \(S_{a b}=0.4\) for each of these values of \(\zeta\).

Calculate the dipole moment of HF for the bonding \(\mathrm{MO}\) in Equation \((23.33) .\) Use the method outlined in Section 23.8 to calculate the charge on each atom. The bond length in HF is \(91.7 \mathrm{pm}\). The experimentally determined dipole moment of ground-state HF is 1.91 debye, where 1 debye \(=3.33 \times 10^{-30} \mathrm{C} \mathrm{m} .\) Compare your result with this value. Does the simple theory give a reliable prediction of the dipole moment?

Evaluate the energy for the two MOs generated by combining a H1s and a \(\mathrm{F} 2 p\) AO. Use Equation (23.12) and carry out the calculation for \(S_{H F}=0.075,0.18,\) and 0.40 to mimic the effect of increasing the atomic separation in the molecule. Use the parameters \(H_{11}=-13.6 \mathrm{eV}\) \\[H_{22}=-18.6 \mathrm{eV}, \text { and } H_{12}=-1.75 S_{12} \sqrt{H_{11} H_{22}}\\] Explain the trend that you observe in the results.

Predict the bond order in the following species: a. \(N_{2}^{+}\) b. \(\mathrm{Li}_{2}^{+}\) \(\mathbf{c} . \mathrm{O}_{2}^{-}\) d. \(\mathrm{H}_{2}\) \(\mathbf{e}_{*} C_{2}^{+}\)
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