Chapter 4: Problem 18
Which of the following molecules/ions does not contain unpaired electrons? (a) \(\mathrm{O}_{2}^{2-}\) (b) \(\mathrm{B}_{2}\) (c) \(\mathrm{N}_{2}^{+}\) (d) \(\mathrm{O}_{2}\)
Short Answer
Expert verified
\(\mathrm{O}_{2}^{2-}\) does not contain unpaired electrons.
Step by step solution
01
Identify Electron Configuration
First, determine the electron configuration for each molecule/ion. Use molecular orbital theory to assess whether there are unpaired electrons. This involves identifying the total number of electrons and filling molecular orbitals accordingly.
02
Calculate Electrons for Each Option
(a) \(\mathrm{O}_{2}^{2-}\) has 18 electrons.(b) \(\mathrm{B}_{2}\) has 10 electrons.(c) \(\mathrm{N}_{2}^{+}\) has 13 electrons.(d) \(\mathrm{O}_{2}\) has 16 electrons.
03
Molecular Orbital Diagram Analysis for \(\mathrm{O}_{2}^{2-}\)
With 18 electrons, \(\mathrm{O}_{2}^{2-}\) fills all bonding orbitals, including the \(\pi^*_{2p}\) antibonding orbitals, resulting in no unpaired electrons.
04
Molecular Orbital Diagram Analysis for \(\mathrm{B}_{2}\)
With 10 electrons, \(\mathrm{B}_{2}\) fills up through the \(\sigma_{2p}\) bonding orbital, resulting in unpaired electrons in the \(\pi_{2p}\) orbitals.
05
Molecular Orbital Diagram Analysis for \(\mathrm{N}_{2}^{+}\)
With 13 electrons, \(\mathrm{N}_{2}^{+}\) fills orbitals up through the \(\pi_{2p}\) antibonding orbitals, resulting in at least one unpaired electron.
06
Molecular Orbital Diagram Analysis for \(\mathrm{O}_{2}\)
With 16 electrons, \(\mathrm{O}_{2}\) places its electrons in the \(\pi^*_{2p}\) antibonding orbitals, which leaves it with unpaired electrons.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Electron Configuration
Electron configuration is a fundamental concept in chemistry that dictates how electrons are distributed in an atom or molecule. When determining the electron configuration for a molecule or ion, you need to identify the total number of electrons and then place them in the appropriate molecular orbitals following the principles of the Aufbau principle, the Pauli exclusion principle, and Hund’s rule.
For example, - In the case of \(\mathrm{O}_{2}^{2-}\), the total number of electrons is 18. These electrons need to be filled into molecular orbitals from the lowest to the highest energy level.- Comparatively, \(\mathrm{B}_{2}\) is made up of 10 electrons, which must be assigned to various molecular orbitals according to stability and availability.- \(\mathrm{N}_{2}^{+}\) with its 13 electrons and \(\mathrm{O}_{2}\) with 16 electrons, would be similarly analyzed to understand their respective electron configurations.
Understanding electron configurations is important for predicting chemical behavior and magnetic properties of molecules, as electron configuration directly influences whether a molecule is diamagnetic or paramagnetic.
For example, - In the case of \(\mathrm{O}_{2}^{2-}\), the total number of electrons is 18. These electrons need to be filled into molecular orbitals from the lowest to the highest energy level.- Comparatively, \(\mathrm{B}_{2}\) is made up of 10 electrons, which must be assigned to various molecular orbitals according to stability and availability.- \(\mathrm{N}_{2}^{+}\) with its 13 electrons and \(\mathrm{O}_{2}\) with 16 electrons, would be similarly analyzed to understand their respective electron configurations.
Understanding electron configurations is important for predicting chemical behavior and magnetic properties of molecules, as electron configuration directly influences whether a molecule is diamagnetic or paramagnetic.
Unpaired Electrons
Unpaired electrons in a molecule or ion emerge when some electrons are not paired in their respective orbitals. The presence of unpaired electrons leads to specific magnetic properties, primarily making a molecule paramagnetic, which means it is attracted by an external magnetic field.
For example, in - \(\mathrm{O}_{2}\) with its unpaired electrons in the \(\pi^*_{2p}\) antibonding orbitals, it exhibits paramagnetic characteristics. - \(\mathrm{B}_{2}\), exhibiting unpaired electrons in the \(\pi_{2p}\) orbitals, also has paramagnetic properties.
Contrastingly, - \(\mathrm{O}_{2}^{2-}\) does not have unpaired electrons, as all its electrons are paired even after filling its antibonding orbitals, making it diamagnetic. - Understanding the concept of unpaired electrons is crucial for predicting the magnetic properties of molecules, as seen practically where diamagnetic substances are repelled by a magnetic field while paramagnetic substances are attracted.
For example, in - \(\mathrm{O}_{2}\) with its unpaired electrons in the \(\pi^*_{2p}\) antibonding orbitals, it exhibits paramagnetic characteristics. - \(\mathrm{B}_{2}\), exhibiting unpaired electrons in the \(\pi_{2p}\) orbitals, also has paramagnetic properties.
Contrastingly, - \(\mathrm{O}_{2}^{2-}\) does not have unpaired electrons, as all its electrons are paired even after filling its antibonding orbitals, making it diamagnetic. - Understanding the concept of unpaired electrons is crucial for predicting the magnetic properties of molecules, as seen practically where diamagnetic substances are repelled by a magnetic field while paramagnetic substances are attracted.
Molecular Orbital Theory
Molecular Orbital Theory provides a detailed and accurate picture of electron distribution among atoms within a molecule, offering an understanding of bonding and antibonding interactions.
According to this theory, molecular orbitals are formed by the combination of atomic orbitals from bonded atoms, which can be occupied by electrons that determine the nature and strength of the bond between the atoms. - Bonding molecular orbitals, such as \(\sigma\) and \(\pi\), stabilize the molecule and are usually lower in energy compared to the original atomic orbitals.
- Antibonding molecular orbitals, like \(\sigma^*\) and \(\pi^*\), destabilize and are higher in energy.
In the analysis of these orbitals for molecules like - \(\mathrm{O}_{2}^{2-}\), where all electrons are paired despite the filling of antibonding orbitals, the molecule remains stable and does not exhibit magnetism.- \(\mathrm{O}_{2}\) and \(\mathrm{B}_{2}\), the presence of electrons in these antibonding orbitals results in unpaired electrons leading to the paramagnetic nature of the molecules.
This theory not only describes the bonding in simple molecules but also is crucial in explaining the electronic structure of more complex molecules and the features resulting from them.
According to this theory, molecular orbitals are formed by the combination of atomic orbitals from bonded atoms, which can be occupied by electrons that determine the nature and strength of the bond between the atoms. - Bonding molecular orbitals, such as \(\sigma\) and \(\pi\), stabilize the molecule and are usually lower in energy compared to the original atomic orbitals.
- Antibonding molecular orbitals, like \(\sigma^*\) and \(\pi^*\), destabilize and are higher in energy.
In the analysis of these orbitals for molecules like - \(\mathrm{O}_{2}^{2-}\), where all electrons are paired despite the filling of antibonding orbitals, the molecule remains stable and does not exhibit magnetism.- \(\mathrm{O}_{2}\) and \(\mathrm{B}_{2}\), the presence of electrons in these antibonding orbitals results in unpaired electrons leading to the paramagnetic nature of the molecules.
This theory not only describes the bonding in simple molecules but also is crucial in explaining the electronic structure of more complex molecules and the features resulting from them.
