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Magazine Chapter 9: Problem 106
Which of the following molecular ions have electrons in \(\pi\) antibonding orbitals? (a) \(\mathrm{O}_{2}^{-} ;\) (b) \(\mathrm{O}_{2}^{2-} ;\) (c) \(\mathrm{N}_{2}^{2-} ;\) (d) \(\mathrm{F}_{2}^{+}\) (e) \(\mathrm{N}_{2}^{+} ;\) (f) \(\mathrm{O}_{2}^{+} ;(\mathrm{g}) \mathrm{C}_{2}^{2+} ;\) (h) \(\mathrm{Br}_{2}^{2+}\)
Short Answer
Expert verified
Answer: \(\mathrm{O}_{2}^{-}\), \(\mathrm{O}_{2}^{2-}\), and \(\mathrm{O}_{2}^{+}\).
Step by step solution
01
Identify 蟺 antibonding orbitals
Use a molecular orbital diagram for diatomic molecules to find which orbitals are 蟺 antibonding orbitals. For this exercise, 蟺 antibonding orbitals generally refer to \(\pi _{\mathrm{u}}^{\star}\) and \(\pi _{\mathrm{g}}^{\star}\) orbitals but may slightly depend on the atoms involved.
02
Determine electron configurations for each molecular ion
Using the molecular orbital diagrams as guides and counting the total electrons in each ion, find the electron configuration for each molecular ion in the list: \(\mathrm{O}_{2}^{-}\), \(\mathrm{O}_{2}^{2-}\), \(\mathrm{N}_{2}^{2-}\), \(\mathrm{F}_{2}^{+}\), \(\mathrm{N}_{2}^{+}\), \(\mathrm{O}_{2}^{+}\), \(\mathrm{C}_{2}^{2+}\), and \(\mathrm{Br}_{2}^{2+}\).
03
Identify molecular ions with electrons in 蟺 antibonding orbitals
Check if any of the highest-energy occupied molecular orbitals are 蟺 antibonding orbitals for each molecular ion. If a 蟺 antibonding orbital is among occupied orbitals, then the molecular ion in question has electrons in 蟺 antibonding orbitals.
Now, let's work through the steps to identify which molecular ions have electrons in 蟺 antibonding orbitals:
(a) \(\mathrm{O}_{2}^{-}\):
Electron configuration: \(\sigma_{\mathrm{g}}^2 \, \mathrm{2}\sigma_{\mathrm{u}}^2 \, \mathrm{1}\pi_{\mathrm{g}}^4 \, \mathrm{1}\pi_{\mathrm{u}}^3 \, \mathrm{1}\sigma_{\mathrm{u}}^2\); the highest-energy occupied MO is \(\mathrm{1}\pi_{\mathrm{u}}\) which is a 蟺 antibonding orbital.
(b) \(\mathrm{O}_{2}^{2-}\):
Electron configuration: \(\sigma_{\mathrm{g}}^2 \, \mathrm{2}\sigma_{\mathrm{u}}^2 \, \mathrm{1}\pi_{\mathrm{g}}^4 \, \mathrm{1}\pi_{\mathrm{u}}^4 \, \mathrm{1}\sigma_{\mathrm{u}}^2\); the highest-energy occupied MO is \(\mathrm{1}\pi_{\mathrm{u}}\) which is a 蟺 antibonding orbital.
(c) \(\mathrm{N}_{2}^{2-}\):
Electron configuration: \(\sigma_{\mathrm{g}}^2 \, \mathrm{2}\sigma_{\mathrm{u}}^2 \, \mathrm{1}\pi_{\mathrm{g}}^6 \, \mathrm{1}\sigma_{\mathrm{g}}^2\pi _{\mathrm{u}}^{\star}\); the highest-energy occupied MO is \(\mathrm{1}\sigma_{\mathrm{g}}\) which is not a 蟺 antibonding orbital.
(d) \(\mathrm{F}_{2}^{+}\):
Electron configuration: \(\sigma_{\mathrm{g}}^2 \, \mathrm{2}\sigma_{\mathrm{u}}^2 \, \mathrm{1}\pi_{\mathrm{g}}^4 \, \mathrm{1}\pi_{\mathrm{u}}^0 \, \mathrm{1}\sigma_{\mathrm{u}}^2\); the highest-energy occupied MO is \(\mathrm{1}\pi_{\mathrm{g}}\) which is not a 蟺 antibonding orbital.
(e) \(\mathrm{N}_{2}^{+}\):
Electron configuration: \(\sigma_{\mathrm{g}}^2 \, \mathrm{2}\sigma_{\mathrm{u}}^2 \, \mathrm{1}\pi_{\mathrm{g}}^4 \, \mathrm{1}\sigma_{\mathrm{g}}^2\pi _{\mathrm{u}}^{\star}\); the highest-energy occupied MO is \(\mathrm{1}\sigma_{\mathrm{g}}\) which is not a 蟺 antibonding orbital.
(f) \(\mathrm{O}_{2}^{+}\):
Electron configuration: \(\sigma_{\mathrm{g}}^2 \, \mathrm{2}\sigma_{\mathrm{u}}^2 \, \mathrm{1}\pi_{\mathrm{g}}^4 \, \mathrm{1}\pi_{\mathrm{u}}^2 \, \mathrm{1}\sigma_{\mathrm{u}}^2\); the highest-energy occupied MO is \(\mathrm{1}\pi_{\mathrm{u}}\) which is a 蟺 antibonding orbital.
(g) \(\mathrm{C}_{2}^{2+}\):
Electron configuration: \(\sigma_{\mathrm{g}}^2 \, \mathrm{2}\sigma_{\mathrm{u}}^2 \, \mathrm{1}\pi_{\mathrm{g}}^2 \, \mathrm{1}\sigma_{\mathrm{g}}^{\star 2}\pi _{\mathrm{u}}^{\star}\); the highest-energy occupied MO is \(\mathrm{1}\pi_{\mathrm{g}}\) which is not a 蟺 antibonding orbital.
(h) \(\mathrm{Br}_{2}^{2+}\):
Electron configuration: \(\sigma_{\mathrm{g}}^2 \, \mathrm{2}\sigma_{\mathrm{u}}^2 \, \mathrm{1}\pi_{\mathrm{g}}^4 \, \mathrm{1}\pi_{\mathrm{u}}^0 \, \mathrm{1}\sigma_{\mathrm{u}}^2\); the highest-energy occupied MO is \(\mathrm{1}\pi_{\mathrm{g}}\) which is not a 蟺 antibonding orbital.
Therefore, the molecular ions with electrons in 蟺 antibonding orbitals are: \(\mathrm{O}_{2}^{-}\), \(\mathrm{O}_{2}^{2-}\), and \(\mathrm{O}_{2}^{+}\).
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Molecular Orbital Theory
Molecular Orbital (MO) Theory is a fundamental concept in chemistry that allows us to explain the bonding in molecules. It is based on combining atomic orbitals to form molecular orbitals, which are spread over the entire molecule rather than localized around individual atoms.
When two atomic orbitals combine, they form two molecular orbitals: one is a bonding orbital, which is lower in energy and favors the stability of the molecule, and the other is an antibonding orbital, with higher energy and less stability. The electrons in a molecule fill these orbitals according to the Pauli exclusion principle and Hund's rule, similar to the way electrons fill atomic orbitals.
The concept of 蟺 antibonding orbitals is especially important in the context of diatomic molecules. These orbitals are denoted as (蟺_{mathrm{u}}^{star}) or (蟺_{mathrm{g}}^{star}), reflective of their higher energy level and the fact that electrons in these orbitals can actually weaken the bond between the two atoms. Identifying whether electrons reside in these orbitals is crucial for understanding the bonding properties of the molecule, such as bond length and strength, as well as its chemical reactivity.
When two atomic orbitals combine, they form two molecular orbitals: one is a bonding orbital, which is lower in energy and favors the stability of the molecule, and the other is an antibonding orbital, with higher energy and less stability. The electrons in a molecule fill these orbitals according to the Pauli exclusion principle and Hund's rule, similar to the way electrons fill atomic orbitals.
The concept of 蟺 antibonding orbitals is especially important in the context of diatomic molecules. These orbitals are denoted as (蟺_{mathrm{u}}^{star}) or (蟺_{mathrm{g}}^{star}), reflective of their higher energy level and the fact that electrons in these orbitals can actually weaken the bond between the two atoms. Identifying whether electrons reside in these orbitals is crucial for understanding the bonding properties of the molecule, such as bond length and strength, as well as its chemical reactivity.
Electron Configuration
Understanding electron configuration is key to predicting the chemical properties of molecules. In simple terms, electron configuration refers to the distribution of electrons in the orbitals of an atom or molecule.
For molecules, especially molecular ions, the electron configuration is determined based on molecular orbital theory. Electrons are placed into molecular orbitals in order of increasing energy; first filling the lower-energy (bonding) orbitals before the higher-energy (antibonding) ones. When determining the electron configuration of molecular ions like (mathrm{O}_{2}^{-}), it is important to keep in mind the overall charge of the ion, as it indicates the loss or gain of electrons.
In our exercise, we follow a systematic approach to arrive at the correct configurations. For example, the electron configuration of (mathrm{O}_{2}^{-}) is written as (蟽_{mathrm{g}}^2 2蟽_{mathrm{u}}^2 1蟺_{mathrm{g}}^4 1蟺_{mathrm{u}}^3 1蟽_{mathrm{u}}^2), showing that it has an extra electron in a 蟺 antibonding orbital compared to the neutral O2 molecule. This systematic approach allows students to visualize which orbitals the electrons occupy, which is crucial for understanding molecular behavior and reactivity.
For molecules, especially molecular ions, the electron configuration is determined based on molecular orbital theory. Electrons are placed into molecular orbitals in order of increasing energy; first filling the lower-energy (bonding) orbitals before the higher-energy (antibonding) ones. When determining the electron configuration of molecular ions like (mathrm{O}_{2}^{-}), it is important to keep in mind the overall charge of the ion, as it indicates the loss or gain of electrons.
In our exercise, we follow a systematic approach to arrive at the correct configurations. For example, the electron configuration of (mathrm{O}_{2}^{-}) is written as (蟽_{mathrm{g}}^2 2蟽_{mathrm{u}}^2 1蟺_{mathrm{g}}^4 1蟺_{mathrm{u}}^3 1蟽_{mathrm{u}}^2), showing that it has an extra electron in a 蟺 antibonding orbital compared to the neutral O2 molecule. This systematic approach allows students to visualize which orbitals the electrons occupy, which is crucial for understanding molecular behavior and reactivity.
Molecular Ions
A molecular ion is a molecule that has gained or lost one or more electrons, resulting in a net positive or negative charge. These charged molecules have distinct properties compared to their neutral counterparts and are highly relevant in various chemical reactions.
In the context of our exercise, recognizing how to determine the presence of electrons in 蟺 antibonding orbitals in molecular ions like (mathrm{O}_{2}^{+}) or (mathrm{N}_{2}^{2-}) is essential. The added or removed electrons due to the ionization change the electron configuration and directly influence the molecule's stability and reactivity. For instance, placing an electron in a 蟺 antibonding orbital can weaken the bond between atoms, thereby affecting the bond order.
The challenge with molecular ions is that their behavior can significantly vary even with a small change in their electron configuration. For instance, the addition of one electron to a molecule can make it more reactive or more stable, depending on whether that electron enters a bonding or antibonding orbital. This exercise not only helps students understand the specifics of molecular ions but also emphasizes the importance of electron configurations in dictating the properties of ions.
In the context of our exercise, recognizing how to determine the presence of electrons in 蟺 antibonding orbitals in molecular ions like (mathrm{O}_{2}^{+}) or (mathrm{N}_{2}^{2-}) is essential. The added or removed electrons due to the ionization change the electron configuration and directly influence the molecule's stability and reactivity. For instance, placing an electron in a 蟺 antibonding orbital can weaken the bond between atoms, thereby affecting the bond order.
The challenge with molecular ions is that their behavior can significantly vary even with a small change in their electron configuration. For instance, the addition of one electron to a molecule can make it more reactive or more stable, depending on whether that electron enters a bonding or antibonding orbital. This exercise not only helps students understand the specifics of molecular ions but also emphasizes the importance of electron configurations in dictating the properties of ions.
