Problem 70 - Chemistry The Central Science In Si Units

Question

(a) If you combine two atomic orbitals on two different atoms to make a new orbital, is this a hybrid orbital or a molecular orbital? (b) If you combine two atomic orbitals on one atom to make a new orbital, is this a hybrid orbital or a molecular orbital? (c) Does the Pauli exclusion principle (Section 6.7 ) apply to MOs? Explain.

Step-by-Step Solution

Answer

(a) Molecular orbital. (b) Hybrid orbital. (c) Yes, the Pauli exclusion principle applies to molecular orbitals.

Step 1: Understanding Atomic and Molecular Orbitals

Atomic orbitals are regions around an atom's nucleus where the probability of finding an electron is the highest. When these orbitals combine, they form either molecular orbitals or hybrid orbitals, depending on whether they are shared between different atoms or belong to the same atom.

Step 2: Determine the Type of Orbital for Part (a)

When atomic orbitals from two different atoms combine, they form molecular orbitals. These orbitals are delocalized over the entire molecule and account for covalent bonding where electrons are shared between atoms.

Step 3: Determine the Type of Orbital for Part (b)

When atomic orbitals within the same atom combine, they form hybrid orbitals. These are used to describe the electron geometry around that atom and help explain bond angles and molecular shapes in covalent compounds.

Step 4: Applying the Pauli Exclusion Principle

The Pauli exclusion principle states that no two electrons in a system can have the same set of quantum numbers. This principle applies to molecular orbitals as well, meaning that each molecular orbital can hold a maximum of two electrons with opposite spins.

Key Concepts

Atomic Orbitals

Atomic orbitals are fundamental concepts in chemistry that describe the regions around an atom's nucleus where electrons are most likely to be found. Think of them as invisible clouds that indicate where an electron might be at any given time.
These orbitals are defined by three quantum numbers which influence their shape and orientation:

• The principal quantum number, which tells us about the size and energy level of the orbital.
• The azimuthal quantum number, which gives the shape of the orbital (s, p, d, f).
• The magnetic quantum number, which describes the orientation of the orbital in space.

Imagine these orbitals as spherical or dumbbell-shaped regions extending from the nucleus. They provide essential information that helps chemists predict chemical bonding patterns and molecular geometry.

Hybrid Orbitals

Hybrid orbitals are unique formations that occur when atomic orbitals within a single atom mix to create new orbitals. These new orbitals are essential for explaining how atoms bond in molecules.
Hybridization occurs primarily in covalently bonded atoms. For instance:

• In ethene (C₂H₄), carbon atoms utilize sp8 hybrid orbitals for forming sigma bonds.
• These sp8 hybrid orbitals allow for specific geometrical arrangements, like the linear or trigonal planar shapes, that we observe in real molecules.
• Hybrid orbitals help explain experimental bond angles and are usually larger than typical atomic orbitals, allowing them to overlap more effectively with adjacent atoms.

Understanding these hybrid formations is key in predicting molecular shapes and explaining chemical reactivity.

Pauli Exclusion Principle

The Pauli exclusion principle is a core idea in quantum mechanics that has significant implications for molecular orbitals. It dictates that within a given system, no two electrons can have the same set of four quantum numbers.
But how does this apply to molecular orbitals (MOs)?

• MOs can be seen as a bridge between the atomic orbitals of two or more atoms, sharing electrons across atoms in a molecule.
• The principle ensures that each molecular orbital can hold a maximum of two electrons, and these must have opposite spins. This means one electron spins "up" while the other spins "down," adhering to the requirement of unique quantum states.
• This rule helps maintain the stability of electron configurations and influences the chemical properties of molecules.

Through this principle, chemists can predict how electrons will populate molecular orbitals resulting in the stability and reactivity of molecules.