Chemistry 130 Autumn Quarter 2020 ✓ Solved

Chemistry 130 Autumn Quarter 2020name

Complete the molecular orbital diagram for the valence electrons of superoxide anion O2–, label each MO with 2s or 2p, as well as σ or π and an * if needed, fill in the electrons, and calculate the bond order. Determine whether O2– is likely to be stable, and whether it is diamagnetic or paramagnetic. For a given molecular orbital formed from atomic orbitals of CO2, identify its type and number of nodes. Additionally, provide the ideal bond angles and hybridizations for atoms A, B, and C in a molecule, and fill out the number of σ and π bonds, the molecular formula, and molar mass.

Paper For Above Instructions

This assignment encompasses several key aspects of molecular orbital theory, molecular geometry, and hybridization concepts. The primary focus is on analyzing the superoxide ion (O2−), predicting its electronic structure, stability, and magnetic properties. Additionally, the task involves understanding molecular orbitals formed in carbon dioxide and applying knowledge about bond angles, hybridization, and bonding types to determine the geometric and electronic characteristics of the molecules.

Molecular Orbital Diagram of O2−

Constructing the molecular orbital (MO) diagram for superoxide (O2−) requires understanding the electronic configuration of oxygen and how their atomic orbitals combine. Oxygen has an atomic number of 8 with valence electrons in the 2s and 2p orbitals. For the O2 molecule, the MO diagram includes bonding and antibonding orbitals derived from these atomic orbitals. The order of the molecular orbitals for oxygen and similar diatomic molecules in their ground state (up to O2−) generally is:

• σ2s
• σ*2s
• π2p (degenerate)
• σ2p
• π*2p (degenerate)
• σ*2p

In the case of O2−, extra electrons are added—two electrons for the negative charge—distributed into the highest energy orbitals (which are typically the π*2p orbitals). After filling orbitals according to Hund's rule and the Pauli exclusion principle, the electron count and placement determine the bond order and magnetic properties.

Filling electrons in the MO diagram for O2−:

• Bonding orbitals (σ2s, π2p, σ2p):
• Antibonding orbitals (σ2s, π2p, σ*2p):

Based on the total valence electrons (16 electrons for two oxygens plus 2 for the negative charge = 18 electrons), electrons are filled accordingly.

Calculating bond order:

• Bond order = (Number of electrons in bonding MOs – Number of electrons in antibonding MOs)/2

Suppose electrons populate the orbitals as follows (numbers are typical for O2−):

• Bonding orbitals: σ2s (2 electrons), π2p (4 electrons), σ2p (2 electrons)
• Antibonding orbitals: σ2s (2 electrons), π2p (4 electrons), σ*2p (2 electrons)

Counting electrons in bonding orbitals: 2 + 4 + 2 = 8; in antibonding: 2 + 4 + 2= 8; the remaining electrons fill the orbitals accordingly.

Thus, the bond order is:

Bond order = (8 – 4)/2 = 2

Note: This simplified approach assumes proper filling based on energy level considerations. The key is that O2− has a bond order of 2, which correlates with a stable diatomic molecule with a double bond.

Is O2− likely to be stable? Yes, because the bond order is positive and the molecule is predicted to be stable. Additionally, its magnetic property is considered whether it is diamagnetic or paramagnetic.

Magnetic Properties of O2−

The O2 molecule has unpaired electrons in its π*2p orbitals, making it paramagnetic (attracted to magnetic fields). For O2−, with extra electrons filling these orbitals, the electrons tend to pair up, resulting in a diamagnetic species (repelled by magnetic fields). Therefore, O2− is diamagnetic.

Molecular Orbital of Carbon Dioxide (CO2)

The molecular orbital shown is constructed from atomic orbitals of carbon and oxygen atoms forming linear combinations, with phases indicated by shading. The orbital's type can be identified based on symmetry and phase relationships.

Possible orbital types: σ, σ, π, or π. To determine this, observe the phase pattern and nodal structure. Based on typical molecular orbital diagrams for CO2, the bonding orbital shown is usually a σ orbital (sigma), characterized by constructive interference along the internuclear axis with no nodes perpendicular to it.

Number of nodes in this orbital: Since it is a σ orbital often formed from the combination of atomic orbitals, a typical σ orbital has 0 or 1 node depending on the specific orbital. If the diagram shows three nodes, it suggests a higher-energy σ orbital with three points where the wave function crosses zero.

Ideal Bond Angles and Hybridizations

In CO2, the molecule adopts a linear geometry with a bond angle of 180°, consistent with sp hybridization of the carbon atom, which involves an s orbital and one p orbital hybridizing to linear geometry (180° bond angle). Atoms A, B, and C could correspond to the central carbon and terminal oxygens, which are sp hybridized for maximum symmetry and minimal repulsion.

Additional Molecular Parameters

Number of σ bonds: 2 (double bonds involve one σ bond each)

Number of π bonds: 2 (each double bond contains one π bond, total of two for the molecule)

Molecular formula: CO2

Molar mass: 44.01 g/mol (carbon: 12.01, oxygen: 16.00 × 2)

Summary and Conclusions

This assignment integrates key concepts of molecular orbital theory, bonding, and molecular geometry. The analysis of O2− indicates a stable, diamagnetic species with a bond order of 2, reflecting the double bond character of the molecule. The orbital analysis for CO2 underscores the importance of hybridization and symmetry in determining molecular structure and bonding patterns. Understanding these principles is crucial for predicting the behavior and properties of molecules in chemistry.

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