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.

Short answer

(a) Combining atomic orbitals on two different atoms forms a molecular orbital, which belongs to the entire molecule. (b) Combining atomic orbitals on one atom forms hybrid orbitals, which result from the mixing of atomic orbitals within the same atom to form orbitals with new geometries suitable for bonding. (c) The Pauli exclusion principle applies to molecular orbitals, as each molecular orbital can have a maximum of two electrons with opposite spins.

Step-by-step solution

Part (a): Combining atomic orbitals on two different atoms

In this case, combining atomic orbitals on two different atoms forms a molecular orbital. Molecular orbitals result from the interaction of atomic orbitals between distinct atoms, and they belong to the entire molecule.

Part (b): Combining atomic orbitals on one atom

When combining atomic orbitals on the same atom, we are forming hybrid orbitals. Hybrid orbitals are formed from the mixing of atomic orbitals within the same atom to form orbitals with new geometries that are suitable for bonding.

Part (c): Pauli exclusion principle and molecular orbitals

Yes, the Pauli exclusion principle applies to molecular orbitals. According to the Pauli exclusion principle, no two electrons in an atom or molecule can have the same set of quantum numbers. This applies to molecular orbitals as they are formed by the combination of atomic orbitals and still describe the behavior of electrons in a molecule. Thus, in each molecular orbital, there can be a maximum of two electrons with opposite spins.

Key concepts

Hybrid Orbitals

When we think of construction, we often imagine building something unique from standard components. In the realm of chemistry, hybrid orbitals work in a similar fashion. They arise from the concept that atomic orbitals within the same atom can merge to create new orbitals. These new formations adapt to the necessary shapes for stable bonding.

Let's visualize this: an atomic s orbital is a perfect sphere, while a p orbital looks like a dumbbell. By fusing these standard shapes together, one can create hybrid orbitals with a directional characteristic advantageous for forming strong covalent bonds. An example includes sp, sp2, and sp3 hybrids, which are essential in the geometry of molecules such as methane (CH4) and ethylene (C2H4).

The process of mixing different types of atomic orbitals on the same atom results in hybridized orbitals, which are crucial in explaining the molecular shapes and bond angles observed in real molecules, making them an integral part of valence bond theory.

Pauli Exclusion Principle

Imagine a party where no two guests are allowed to wear the exact same outfit. In a quantum world, the Pauli Exclusion Principle is the strict dress code for electrons. It tells us that no two electrons in an atom or molecule can have the same set of four quantum numbers. These quantum numbers are akin to a detailed address describing the energy level, shape, orientation, and spin of each electron residence within an atom.

This 'no matching' rule dictates that each electron in an atom or molecular orbital must be unique in its combination of quantum numbers. If we place this idea in the context of molecular orbitals, we recognize that each orbital can accommodate a maximum of two electrons, and these must have opposite spins to comply with Pauli's policy. This principle not only keeps electrons distinct but also helps us determine the electron configuration in atoms and the structure of the periodic table.

Atomic Orbitals

Just like stars in the sky have their spots, electrons within an atom reside in specific regions known as atomic orbitals. These are not fixed paths, but rather probabilities zones where electrons are likely to be found. They come in various shapes, notably s, p, d, and f, and each shape supports a different number of electrons.

Understanding atomic orbitals is fundamental to grasp how atoms interact and how chemical bonds are formed. Each orbital can be visualized as a cloud where the density represents the probability of finding an electron. These clouds are structured in layers around the nucleus of the atom, and play a pivotal role when atoms combine to form molecules by sharing or exchanging electrons.

Quantum Numbers

To navigate a city efficiently, you need to understand its addressing system. In the quantum realm, quantum numbers are the GPS coordinates for electrons. There are four types of quantum numbers: principal (n), angular momentum (l), magnetic (ml), and spin (ms).

To shed more light on these, the principal quantum number (n) indicates the size and energy level of an orbital. The angular momentum number (l) reveals the shape of the orbital which could be spherical, dumbbell, or more complex forms. The magnetic quantum number (ml) determines the orientation of the orbital in space, hinting at the various directions it can take. And lastly, the spin quantum number (ms) shows the two fundamental spin states of an electron - akin to the earth rotating on its axis in one of two directions. Collectively, these numbers lay the foundation for the rules that govern the tiny, bustling city of subatomic particles in an atom.