Problem 74 - Chemistry The Central Science

Question

Indicate whether each statement is true or false. (a) \(s\) orbitals can only make \(\sigma\) or \(\sigma^{*}\) molecular orbitals. (b) The probability is 100\(\%\) for finding an electron at the nucleus in a \(\pi^{*}\) orbital. (c) Antibonding orbitals are higher in energy than bonding orbitals (if all orbitals are created from the same atomic orbitals). (d) Electrons cannot occupy an antibonding orbital.

Step-by-Step Solution

Answer

(a) True: s orbitals can only form σ and σ* molecular orbitals due to their spherical and symmetric nature around the nucleus. (b) False: The probability of finding an electron at the nucleus in a π* orbital is zero due to the nodal plane passing through the nucleus. (c) True: Antibonding orbitals have higher energy than bonding orbitals when both are created from the same atomic orbitals. (d) False: Electrons can occupy antibonding orbitals, but their presence weakens the overall bond.

Step 1: Statement (a) Analysis

The statement says that s orbitals can only make σ or σ* molecular orbitals. To analyze this statement, let's first recall what σ and σ* orbitals are. σ orbitals are bonding molecular orbitals that are symmetric around the bond axis, while σ* orbitals are antibonding orbitals that are also symmetric around the bond axis. Now we consider s orbitals which are spherical and symmetric around the nucleus. When these s orbitals combine, they can form molecular orbitals that are symmetric around the bond axis, which are σ and σ* orbitals. Therefore, the statement seems to be true.

Step 2: Statement (a) Conclusion

Statement (a) is true, as s orbitals can only form σ and σ* molecular orbitals due to their spherical and symmetric nature around the nucleus.

Step 3: Statement (b) Analysis

The statement says that the probability is 100% for finding an electron at the nucleus in a π* orbital. π* orbitals are antibonding molecular orbitals that arise from the out-of-phase combination of atomic p orbitals. The nature of π* orbitals is such that they have a nodal plane going through the nuclei of the atoms involved in the bond. This means that the probability of finding an electron in the region along the nodal plane, including the nucleus, is zero.

Step 4: Statement (b) Conclusion

Statement (b) is false, as the probability of finding an electron at the nucleus in a π* orbital is zero due to the nodal plane passing through the nucleus.

Step 5: Statement (c) Analysis

The statement says that antibonding orbitals are higher in energy than bonding orbitals if all orbitals are created from the same atomic orbitals. By definition, bonding orbitals result from the constructive interference of atomic orbitals, leading to increased electron density between the nuclei and hence a stabilization of the energy. Antibonding orbitals, on the other hand, result from destructive interference, causing the electron density between the nuclei to decrease and the energy to increase. So, antibonding orbitals should have higher energy than bonding orbitals when created from the same atomic orbitals.

Step 6: Statement (c) Conclusion

Statement (c) is true, as antibonding orbitals have higher energy than bonding orbitals when both are created from the same atomic orbitals.

Step 7: Statement (d) Analysis

The statement says that electrons cannot occupy an antibonding orbital. This statement is not accurate. Electrons can occupy antibonding orbitals, but the more electrons that occupy antibonding orbitals, the weaker the overall bond between the atoms. In molecular orbital theory, we fill up orbitals according to the Aufbau principle, starting with the lowest energy orbitals first. Electrons will fill the bonding orbitals before filling anti-bonding orbitals. However, when filling higher energy orbitals, electrons can and do occupy antibonding orbitals.

Step 8: Statement (d) Conclusion

Statement (d) is false, as electrons can occupy antibonding orbitals, but their presence weakens the overall bond.

Key Concepts

Sigma orbitals

Sigma (\( \sigma \)) orbitals play a central role in molecular orbital theory. They are one of the most significant types of molecular orbitals. These orbitals are characterized by their symmetry around the bond axis, where the electron cloud can freely rotate around the axis without changing its probability distribution. This is why they are termed 'sigma.' Typically, \( s \) orbitals from atoms contribute to forming \( \sigma \) orbitals when they overlap.

When two \( s \) orbitals combine, they create a molecular orbital that is cylindrically symmetric around the internuclear axis, resulting in a \( \sigma \) orbital. This is crucial for the formation of covalent bonds, where electron density between atoms stabilizes the molecular structure. Understanding sigma orbitals helps us grasp the concept of bonding which is necessary to appreciate how atoms stick together to form molecules.

Antibonding orbitals

Antibonding orbitals, often denoted as \( \sigma^* \) or \( \pi^* \), are just as essential as bonding orbitals. They arise when atomic orbitals combine out of phase, creating a region of electron probability where there's a decrease in electron density between nuclei. This leads to an energy increase, making antibonding orbitals higher in energy than their bonding counterparts.

• Antibonding orbitals decrease the probability of electron cloud overlap, reducing the stability of the bond.
• When electrons occupy these orbitals, they exert a destabilizing effect on the molecule by contributing to energy increase.

It's essential to note that electrons can occupy antibonding orbitals, though doing so would weaken the bond. In some molecules, antibonding orbitals are energetically accessible, and their occupation can occur, altering the overall stability significantly.

Bonding orbitals

Bonding orbitals are formed during the constructive interference of atomic orbitals. This results in increased electron density in the region between two nuclei, leading to a stable bond formation. Unlike antibonding orbitals, bonding orbitals decrease the energy of the system, making these structures crucial for maintaining molecular integrity.

For instance, when two hydrogen \( s \) orbitals overlap, they form a low-energy \( \sigma \) bonding orbital. The stabilization is due to the higher electron density between nuclei, which enhances the attractive forces holding the atoms together. The more electrons present in these bonding orbitals, the stronger and more stable the bond becomes. Understanding how bonding orbitals work is pivotal for grasping the basics of molecular stability and the nature of chemical bonds.

Electron probability distribution

In molecular orbital theory, electron probability distribution describes the likelihood of finding an electron in various regions of a molecule. This concept is visualized using molecular orbital diagrams, where orbitals are depicted to show areas of high electron probability.

• In \( \sigma \) and bonding orbitals, electron density is concentrated between atoms which results in a high probability of finding electrons in this area.
• Conversely, in antibonding orbitals like \( \sigma^* \) and \( \pi^* \), electron density is found outside the internuclear region, reflecting in a nodal plane where the electron probability often is zero.

Understanding electron probability distribution helps predict molecular behavior and reactivity. For example, the low probability in antibonding orbitals explains why these are less stable and why occupying these orbitals with electrons weakens bonds. It is an invaluable tool for students learning about chemical bonding and molecular geometry.