Question

The ionosphere lies about \(100 \mathrm{~km}\) above Earth's surface. This layer of the atmosphere consists mostly of \(\mathrm{NO}, \mathrm{O}_{2},\) and \(\mathrm{N}_{2}\), and photoionization creates \(\mathrm{NO}^{+}, \mathrm{O}_{2}^{+},\) and \(\mathrm{N}_{2}^{+}\). (a) Use MO theory to compare the bond orders of the molecules and ions. (b) Does the magnetic behavior of each species change when its ion forms?

Short answer

Bond orders: NO=2.5, NO+=3.0, O2=2.0, O2+=2.5, N2=3.0, N2+=2.5. Magnetic behavior changes: NO (paramagnetic to diamagnetic), O2 (remains paramagnetic), N2 (diamagnetic to paramagnetic).

Step-by-step solution

- Understanding Molecular Orbital Theory

Molecular Orbital (MO) theory helps determine the bond order in molecules. To use MO theory, obtain the molecular orbital diagram for each species and count the number of electrons in bonding and antibonding orbitals.

- Molecular Orbital Diagram for \(\text{NO}\)

NO has 11 valence electrons:\[\sigma(1s)^2 \ \sigma^*(1s)^2 \ \sigma(2s)^2 \ \sigma^*(2s)^2 \ (\pi(2p_x)=\pi(2p_y))^4 \ \sigma(2p_z)^1\]Bond order is calculated as:\[\text{Bond Order} = \frac{1}{2}(\text{Number of Bonding Electrons} - \text{Number of Antibonding Electrons}) \]For NO: \[\text{Bond Order} = \frac{1}{2}(8 - 3) = 2.5\]

- Molecular Orbital Diagram for \(\text{NO}^+\)

NO\(^+\) has 10 valence electrons:\[\sigma(1s)^2 \sigma^*(1s)^2 \sigma(2s)^2 \sigma^*(2s)^2 (\pi(2p_x)=\pi(2p_y))^4\]For NO\(^+\): \[\text{Bond Order} = \frac{1}{2}(8 - 2) = 3.0\]

- Molecular Orbital Diagrams for \(\text{O}_2\) and \(\text{O}_2^+\)

O\(_2\) has 12 valence electrons:\[\sigma(1s)^2 \sigma^*(1s)^2 \sigma(2s)^2 \sigma^*(2s)^2 (\pi(2p_x)=\pi(2p_y))^4 \pi^*(2p_x)^2 \pi^*(2p_y)^2\]For O\(_2\): \[\text{Bond Order} = \frac{1}{2}(8 - 4) = 2.0\]O\(_2^+\) has 11 valence electrons:\[\sigma(1s)^2 \sigma^*(1s)^2 \sigma(2s)^2 \sigma^*(2s)^2 (\pi(2p_x)=\pi(2p_y))^4 \pi^*(2p_x)^2 \pi^*(2p_y)^1\]For O\(_2^+\): \[\text{Bond Order} = \frac{1}{2}(8 - 3) = 2.5\]

- Molecular Orbital Diagrams for \(\text{N}_2\) and \(\text{N}_2^+\)

N\(_2\) has 10 valence electrons:\[\sigma(1s)^2 \sigma^*(1s)^2 \sigma(2s)^2 \sigma^*(2s)^2 \pi(2p_x)^2 \pi(2p_y)^2 \sigma(2p_z)^2\]For N\(_2\): \[\text{Bond Order} = \frac{1}{2}(8 - 2) = 3.0\]N\(_2^+\) has 9 valence electrons:\[\sigma(1s)^2 \sigma^*(1s)^2 \sigma(2s)^2 \sigma^*(2s)^2 \pi(2p_x)^2 \pi(2p_y)^2 \sigma(2p_z)^1\]For N\(_2^+\): \[\text{Bond Order} = \frac{1}{2}(7 - 2) = 2.5\]

- Determining Magnetic Behavior

To determine magnetic behavior, check for the presence of unpaired electrons. If unpaired electrons are present, the molecule is paramagnetic; otherwise, it is diamagnetic.NO: 1 unpaired electron (Paramagnetic)NO\(^+\): No unpaired electrons (Diamagnetic)O\(_2\): 2 unpaired electrons (Paramagnetic)O\(_2^+\): 1 unpaired electron (Paramagnetic)N\(_2\): No unpaired electrons (Diamagnetic)N\(_2^+\): 1 unpaired electron (Paramagnetic)

Key concepts

Bond Order

Molecular Orbital (MO) Theory is a powerful tool used to determine the bond order in molecules and ions. Bond order tells us about the stability of a molecule. Generally, a higher bond order means a more stable molecule. To find the bond order, we use molecular orbital diagrams, which show the placement of electrons in a molecule's bonding and antibonding orbitals. For example:

NO has a molecular orbital configuration of \(\sigma(1s)^2 \ \sigma^*(1s)^2 \ \sigma(2s)^2 \ \sigma^*(2s)^2 \ (\pi(2p_x)=\pi(2p_y))^4 \ \sigma(2p_z)^1\). Using MO theory, the bond order of NO is calculated as: \[ \text{Bond Order} = \frac{1}{2}(8 - 3) = 2.5 \].

When NO is ionized to form NO+ (ten electrons), the configuration is \(\sigma(1s)^2 \sigma^*(1s)^2 \sigma(2s)^2 \sigma^*(2s)^2 (\pi(2p_x)=\pi(2p_y))^4\), and the bond order is \[ \text{Bond Order} = \frac{1}{2}(8 - 2) = 3.0 \].

Studying other molecules like O_2 and N_2 in their neutral and ionized forms follows a similar process. By counting bonding and antibonding electrons, we can compute their bond orders and understand their relative stabilities.

Paramagnetism

Paramagnetism refers to the presence of unpaired electrons in a molecule. Molecules and ions with unpaired electrons are attracted to magnetic fields. To determine if a species is paramagnetic, look for unpaired electrons in its molecular orbital diagram.

When comparing NO and NO+, NO has one unpaired electron, making it paramagnetic. NO+, on the other hand, has all paired electrons and is diamagnetic. For O_2, its configuration reveals two unpaired electrons, making it paramagnetic, while O_2+ has one unpaired electron, which also makes it paramagnetic.

Finally, consider N_2's configuration, which has no unpaired electrons and is diamagnetic. When it is ionized to form N_2+, it has one unpaired electron, rendering it paramagnetic.

Diamagnetism

Diamagnetism occurs in molecules that have all their electrons paired. Diamagnetic substances are repelled by magnetic fields. Unlike paramagnetic substances, diamagnetic ones do not have unpaired electrons.

Take NO+ as an example; its molecular orbital configuration has no unpaired electrons, making it diamagnetic. This is a key difference from NO, which has an unpaired electron and is paramagnetic.

Using MO theory, we can determine that O_2 is paramagnetic, but if O_2 loses an electron to form O_2+, it still has one unpaired electron, leaving it paramagnetic. Conversely, N_2, with its paired electrons, is diamagnetic, and when it becomes N_2+, it gains an unpaired electron, thus becoming paramagnetic.

This clear distinction between paramagnetic and diamagnetic substances shows us the critical role of electron pairing in determining a molecule's magnetic properties.