Problem 74 - Chemistry: The Central Science in SI Units, Global Edition

Question

Indicate whether each statement is true or false. (a) \(p\) orbitals can only make \(\sigma\) or \(\sigma^{*}\) molecular orbitals. (b) The probability is always \(0 \%\) for finding an electron in an antibonding orbital. (c) Molecules containing electrons that occupy antibonding orbitals must be unstable. (d) Electrons cannot occupy a nonbonding orbital.

Step-by-Step Solution

Answer

a) False. \(p\) orbitals can also make \(\pi\) or \(\pi^{*}\) molecular orbitals. b) False. Electrons can occupy antibonding orbitals, with a non-zero probability of being found there. c) Partially true, molecules with electrons in antibonding orbitals are not necessarily unstable, but they tend to be less stable compared to molecules without electrons in antibonding orbitals. d) False, electrons can occupy nonbonding orbitals.

Step 1: a) \(p\) orbitals can only make \(\sigma\) or \(\sigma^{*}\) molecular orbitals.

The statement is false. Although \(p\) orbitals can form \(\sigma\) and \(\sigma^{*}\) molecular orbitals, they can also form other types of molecular orbitals, such as \(\pi\) and \(\pi^{*}\) molecular orbitals. In the formation of a molecular orbital, \(p\) orbitals may align along the axis and overlap end-to-end, which results in the formation of a \(\sigma\) or \(\sigma^{*}\) molecular orbital. Besides this, they can also interact side-by-side and form \(\pi\) or \(\pi^{*}\) molecular orbitals.

Step 2: b) The probability is always \(0 \%\) for finding an electron in an antibonding orbital.

The statement is false. Antibonding orbitals are characterized by their higher energy compared to bonding orbitals and are generally less stable. However, electrons can and do occupy antibonding orbitals. The probability of finding an electron in an antibonding orbital is not 0. The key is the number of electrons in a given molecule – if there are more electrons than can be accommodated by the bonding orbitals, some electrons will be forced into antibonding orbitals.

Step 3: c) Molecules containing electrons that occupy antibonding orbitals must be unstable.

The statement is partially true. While it is true that having electrons in antibonding orbitals can make a molecule less stable compared to a molecule with no electrons in antibonding orbitals, the presence of electrons in antibonding orbitals doesn't necessarily make the molecule unstable. A molecule's stability is affected by many factors, not only the occupancy of antibonding orbitals. In some cases, the overall bonding situation of a molecule might be stable despite the presence of electrons in antibonding orbitals.

Step 4: d) Electrons cannot occupy a nonbonding orbital.

The statement is false. Nonbonding orbitals are orbitals that do not participate in bonding within a molecule, but they can still be occupied by electrons. These orbitals are generally at an energy level between bonding and antibonding orbitals, so they do not contribute to the overall bonding or antibonding properties of the molecule. However, their occupancy is still essential in determining the overall electron configuration and molecular properties. After analyzing all the statements, we find that: a) False. \(p\) orbitals can also make \(\pi\) or \(\pi^{*}\) molecular orbitals. b) False. Electrons can occupy antibonding orbitals, with a non-zero probability of being found there. c) Partially true, molecules with electrons in antibonding orbitals are not necessarily unstable, but they tend to be less stable compared to molecules without electrons in antibonding orbitals. d) False, electrons can occupy nonbonding orbitals.

Key Concepts

Antibonding Orbitals

Antibonding orbitals play a crucial role in the stability of molecules. They are formed when atomic orbitals combine in a way that results in a higher energy molecular orbital. This is often due to destructive interference. Because of this high energy level, electrons in antibonding orbitals can destabilize a molecule. The name "antibonding" refers to the fact that the presence of electrons in these orbitals counteracts the bonding effects of electrons in bonding orbitals. Despite the negative impact on stability, antibonding orbitals can indeed be occupied by electrons.

• Electrons fill antibonding orbitals when there are more electrons than can be accommodated by the bonding orbitals of a molecule.
• Although antibonding orbitals lead to less stability, their presence does not automatically render a molecule unstable.

This means that it's still possible for a molecule to hold together, even if it contains electrons in antibonding orbitals. Other factors, such as overall molecular structure and environment, contribute to overall stability.

Nonbonding Orbitals

Nonbonding orbitals are intriguing since they neither contribute to nor detract from a molecule's bonding interactions. These orbitals often arise from lone pairs of electrons that do not engage in bonding. Unlike bonding or antibonding orbitals, nonbonding orbitals are neutral, sitting at an energy level between the two. Yet, the electrons occupying these orbitals can influence molecular shape and reactivity.

• Nonbonding orbitals are often filled with electrons in atoms that have filled or partially filled valence shells.
• Their presence affects the electron configuration without altering the bonding stability.
• Electrons in nonbonding orbitals can influence the polar nature of molecules.

Therefore, even though they don't participate directly in bonding, nonbonding orbitals play a significant role in defining a molecule's characteristics.

Electron Configuration

The electron configuration of a molecule provides vital insight into its chemical nature. By understanding how electrons are distributed across different orbitals, we can predict a molecule's reactivity and stability. Typically, electrons will fill the lowest energy orbitals first, following the Aufbau principle. This means electrons occupy bonding orbitals before moving onto higher-energy nonbonding or antibonding orbitals.

• Electron configuration helps determine the overall magnetic properties of a molecule.
• Knowing which orbitals are filled allows chemists to predict whether a molecule will react with other species.
• An electron configuration can illustrate whether a molecule will be stable or likely participate in further reactions.

In essence, the electron configuration acts as a roadmap for understanding and predicting molecular behavior, guiding us in the study of chemistry.