Question

The number of \(p\)-molecular orbitals completely filled in the ground state of benzene is (A) 3 (B) 1 (C) 6 (D) None

Short answer

In the ground state of benzene, there are six \(2p\) electrons from the six carbon atoms participating in the formation of \( \pi \) molecular orbitals. These electrons fill the three bonding orbitals, each with two electrons. Therefore, there are 3 completely filled \(p\)-molecular orbitals in the ground state of benzene. The correct answer is (A) 3.

Step-by-step solution

Understanding Benzene Structure

The structure of benzene consists of six carbon atoms arranged in a hexagonal ring, with one hydrogen atom attached to each carbon atom. Each carbon atom utilizes three electrons for \(\sigma\) bonds with two neighbouring carbon atoms and a hydrogen atom. The fourth electron is found in a \(2p\) orbital perpendicular to the plane of benzene, it partakes in \(\pi\) bonding. Hence six electrons participate in forming \( \pi \) molecular orbitals.

Formation of \( \pi \) Molecular Orbitals

The six \(2p\) electrons from each carbon atom form six molecular \( \pi \) orbitals. Three of these orbitals have bonding character and are lower in energy, the other three orbitals have antibonding character and are higher in energy. Since we are talking about the ground state of benzene, electrons will fill the lower energy orbitals first.

Filling of \( \pi \) Molecular Orbitals

According to the Aufbau principle, electrons fill the lower energy orbitals first before filling the higher energy ones. Hence, in the ground state, all six electrons reside in the three bonding orbitals which means that each of these orbitals is fully filled with two electrons. The higher energy antibonding \( \pi \) orbitals remain unoccupied.

Conclusion

In conclusion, completely filled \(p\)-molecular orbitals in the ground state of benzene molecule are only the three bonding orbitals (considering the Aufbau Principle). Hence, the correct answer is (A) 3.

Key concepts

Chemical Bonding

Chemical bonding refers to the interaction between atoms that allows the formation of chemical substances. In benzene, this bonding includes both sigma (\(\sigma\)) and pi (\(\pi\)) bonds. Benzene is a unique compound, made up of six carbon atoms arranged in a hexagonal ring with hydrogen atoms attached to each carbon. Each carbon atom in benzene forms three \(\sigma\) bonds with its neighbors: two with adjacent carbon atoms and one with a hydrogen atom.
However, it's not just about \(\sigma\) bonds. Each carbon in benzene has an extra electron in a \(2p\) orbital, which is perpendicular to the plane of the carbon atoms. These electrons engage in \(\pi\) bonding, creating a complex, delocalized \(\pi\) electron cloud above and below the benzene ring. This \(\pi\) bond system greatly contributes to the stability of benzene, as these electrons are free to move across the ring, providing extra bonding strength through resonance.

Molecular Orbital Theory

Molecular Orbital (MO) Theory provides a framework for understanding the electronic structure of molecules by considering electrons in terms of molecular orbitals, which are spread over the entire molecule rather than localized between individual atom pairs. In benzene, Molecular Orbital Theory can explain the presence of \(\pi\) molecular orbitals that arise from the carbon \(2p\) electrons.
These \(\pi\) molecular orbitals in benzene are divided into bonding and antibonding types. There are six in total, created from the interaction of the six \(2p\) electrons, where three are bonding and three are antibonding. The bonding orbitals have lower energy and their electron density is concentrated between the nuclei of the carbon atoms, stabilizing the molecule. Electrons fill these in the ground state following the principles defined by the Aufbau Principle.

• Bonding orbitals = Lower energy
• Antibonding orbitals = Higher energy and typically unoccupied in stable forms
• Benzene's highly stable nature is further confirmed by its equal distribution of electrons across the bonding molecular orbitals.

Aufbau Principle

The Aufbau Principle is a concept in chemistry that electrons fill atomic and molecular orbitals from the lowest energy level upwards. This principle also governs how benzene's \(\pi\) molecular orbitals are filled in its ground state. In benzene, the six \(\pi\) electrons will initially fill the three lower energy bonding orbitals:

• This ensures that these orbitals are completely filled first before any electron occupies the higher energy antibonding orbitals, which remain empty in the ground state.
• The principle is fundamental in determining the electronic structure, predicting the stability and chemical behavior of molecules like benzene.

By adhering to the Aufbau Principle, benzene achieves a stable configuration that is reflected in its chemical properties like lower reactivity and extraordinary stability.