Problem 82 - Chemistry: The Central Science

Question

(a) The nitric oxide molecule, \(\mathrm{NO}\), readily loses one electron to form the \(\mathrm{NO}^{+}\)ion. Which of the following is the best explanation of why this happens: (i) Oxygen is more electronegative than nitrogen, (ii) The highest energy electron in NO lies in a \(\pi_{2 p}^{*}\) molecular orbital, or (iii) The \(\pi_{2 p}^{*} \mathrm{MO}\) in NO is completely filled. (b) Predict the order of the \(\mathrm{N}-\mathrm{O}\) bond strengths in \(\mathrm{NO}^{-} \mathrm{NO}^{+}\), and \(\mathrm{NO}^{-}\), and deseribe the magnetic properties of each. (c) With what neutral homonuclear diatomic molecules are the \(\mathrm{NO}^{+}\)and \(\mathrm{NO}^{-}\)ions isoelectronic (same number of electrons)?

Step-by-Step Solution

Answer

The best explanation for NO losing one electron to form the NO+ ion is because the highest energy electron lies in an anti-bonding molecular orbital (\( \pi_{2 p}^* \)). The N-O bond strengths order is: \( NO^{-} > NO^{+} > NO \). NO and NO+ are paramagnetic while NO- is diamagnetic. NO+ is isoelectronic with \( N_{2} \) and NO- is isoelectronic with \( O_{2} \).

Step 1: (a) Determine the best explanation for electron loss in NO

The best explanation for the nitric oxide molecule losing one electron to form the \(\mathrm{NO}^{+}\) ion is (ii) The highest energy electron in NO lies in a \(\pi_{2 p}^*\) molecular orbital. This is because when the highest-energy electron resides in an anti-bonding molecular orbital (\(\pi_{2 p}^*\)), it weakens the bond. By losing an electron from this orbital, the molecule becomes more stable.

Step 2: (b.1) Predicting N-O bond strengths

To predict the bond strength order of \(\mathrm{NO}^{-}\), \(\mathrm{NO}\), and \(\mathrm{NO}^{+}\), we should look at the bond orders. Bond order refers to the number of bonding interactions between two atoms and can be calculated as the difference between the number of electrons occupying bonding orbitals and anti-bonding orbitals, divided by 2. Higher bond order implies a stronger bond. Using the molecular orbital diagram of NO and filling the electrons as per the rules, we predict the bond order as follows: For \(\mathrm{NO}\): Bond order = \(\frac{1}{2}[(10-2)] = 4\) For \(\mathrm{NO}^{-}\): Bond order = \(\frac{1}{2}[(11-2)] = \frac{9}{2}\) For \(\mathrm{NO}^{+}\): Bond order = \(\frac{1}{2}[(9-2)] = \frac{7}{2}\) The order of the N-O bond strengths is: \(\mathrm{NO}^{-} > \mathrm{NO}^{+} > \mathrm{NO}\)

Step 3: (b.2) Describing magnetic properties

To determine the magnetic properties of each species, we need to find out if they have unpaired electrons in their molecular orbitals. If a molecule has one or more unpaired electrons, it exhibits paramagnetic properties; otherwise, it's diamagnetic (no unpaired electrons). - For \(\mathrm{NO}\), it has one unpaired electron, so it is paramagnetic. - For \(\mathrm{NO}^{-}\), it has no unpaired electrons, so it is diamagnetic. - For \(\mathrm{NO}^{+}\), it has one unpaired electron, so it is paramagnetic.

Step 4: (c) Identifying isoelectronic neutral homonuclear diatomic molecules

The \(\mathrm{NO}^{+}\) ion has a total of 9 electrons (5 from nitrogen and 4 from oxygen). The neutral homonuclear diatomic molecule isoelectronic with \(\mathrm{NO}^{+}\) is \(\mathrm{N}_{2}\), which has 7 electrons from each nitrogen atom, totaling 14 electrons. The \(\mathrm{NO}^{-}\) ion has a total of 11 electrons (5 from nitrogen and 6 from oxygen). The neutral homonuclear diatomic molecule isoelectronic with \(\mathrm{NO}^{-}\) is \(\mathrm{O}_{2}\), which has 8 electrons from each oxygen atom, totaling 16 electrons.

Key Concepts

Bond Order

Bond order is a measure of the strength of a bond between two atoms. It represents the number of bonding electron pairs minus anti-bonding electron pairs, all divided by two. The concept is central in determining the stability and strength of chemical bonds.

• Bond order is calculated using molecular orbital theory, which involves filling electrons into bonding and anti-bonding orbitals.
• A higher bond order indicates a stronger, more stable bond, while a lower bond order indicates a weaker bond.
• For example, the NO molecule is analyzed by determining bond order: \[\text{Bond Order} = \frac{1}{2} \left( \text{Bonding Electrons} - \text{Anti-bonding Electrons} \right)\]
• Commonly, bond order can tell us the relative lengths of bonds; a higher bond order often results in shorter bond lengths.

Understanding bond order is essential when predicting molecular properties like bond length and stability.

Paramagnetism

Paramagnetism is a property of substances that have unpaired electrons and are attracted to magnetic fields. This behavior is explained through molecular orbital theory.

• Unpaired electrons in molecular orbitals lead to paramagnetic behavior.
• For instance, the NO molecule has an odd number of electrons, specifically one unpaired electron that results in its paramagnetism.
• The presence of these unpaired electrons is enough to induce a noticeable magnetic moment.
• Paramagnetic materials will be attracted to a magnet, which can be observed in experiments.

This explains why certain molecules, like NO, respond to magnetic fields due to their electronic structure.

Diamagnetism

Diamagnetism is a property of substances that have all paired electrons and are repelled by a magnetic field. This occurs when all electrons in an atom or molecule are paired, leading to no net magnetic moment.

• Substances with no unpaired electrons exhibit diamagnetism, showing a weak and negative susceptibility to magnetic fields.
• For example, NO^- has all paired electrons, hence it is diamagnetic.
• In general, diamagnetic materials create an induced magnetic field in a direction opposite to the applied magnetic field.
• Unlike paramagnetic substances, diamagnetic materials are slightly pushed away from magnetic fields.

Diamagnetism is a universal property, albeit usually very weak, present in all materials but often overshadowed by stronger effects like paramagnetism.

Isoelectronic Species

Isoelectronic species refer to atoms, molecules, or ions that have the same number of electrons. Despite differences in chemical elements, their identical electron configuration leads to similar chemical properties.

• For example, the NO⁺ ion is isoelectronic with N₂, while the NO^- ion is isoelectronic with O₂.
• Being isoelectronic often leads to comparable chemical behaviors, such as bond lengths and bond energies.
• Isoelectronic species are valuable in comparative chemical studies for predicting the behavior of complex ions or molecules.
• This concept helps in solving problems involving electron arrangements and in predicting molecular structures.

Understanding isoelectronic species aids in anticipating the properties and reactivity of unfamiliar molecules based on known molecules.