Problem 70 - Chemistry The Central Science

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) Combining two atomic orbitals on different atoms forms a molecular orbital, which occurs due to the overlap of atomic orbitals from different atoms. (b) Combining two atomic orbitals on the same atom forms a hybrid orbital, created by mixing atomic orbitals of the same atom to create new orbitals with new geometries and energy levels. (c) Yes, the Pauli Exclusion Principle applies to molecular orbitals, meaning that each molecular orbital can be occupied by a maximum of two electrons with opposite spins.

Step 1: Answer to Question (a)

When two atomic orbitals on different atoms combine to form a new orbital, it results in a molecular orbital. Molecular orbitals are formed due to the overlap of atomic orbitals from different atoms getting close enough to each other, leading to a new bonding or antibonding molecular orbital.

Step 2: Answer to Question (b)

When two atomic orbitals on the same atom combine to make a new orbital, it creates a hybrid orbital. Hybrid orbitals are formed by mixing atomic orbitals of the same atom to create new orbitals with new geometries and energy levels. Hybridization is essential for understanding the bonding properties and molecular geometry of many molecules.

Step 3: Answer to Question (c)

Yes, the Pauli Exclusion Principle applies to molecular orbitals. The Pauli Exclusion Principle states that no two electrons within an atom or molecule can have the same set of quantum numbers. In the context of molecular orbitals, it means that each molecular orbital can be occupied by a maximum of two electrons with opposite spins, represented by their magnetic quantum numbers (+1/2 and -1/2). Molecular orbitals are the result of the overlap and interaction of atomic orbitals; thus, all principles applying to atomic orbitals, including the Pauli Exclusion Principle, apply to molecular orbitals as well.

Key Concepts

Atomic Orbitals

Atomic orbitals are the basic building blocks of chemical bonding. They are regions in space where there is a high probability of finding an electron. These orbitals are defined by a set of quantum numbers: the principal quantum number (), the angular momentum quantum number (), the magnetic quantum number (), and the spin quantum number (). The shape of an atomic orbital is determined by its , which can be s (spherical), p (dumbbell), d (cloverleaf), or f (complex).

Understanding atomic orbitals is fundamental to grasping concepts such as the formation of chemical bonds and the arrangement of electrons around an atom. For instance, the carbon atom has one s orbital and three p orbitals that can combine in different ways to form bonds with other atoms.

Hybrid Orbitals

Hybrid orbitals are created when atomic orbitals within the same atom mix to accommodate bonding with other atoms. They are a conceptual blend of s, p, and sometimes d orbitals that result in new orbitals with different orientations and shapes suitable for forming bonds. A quintessential example is the sp3 hybridization seen in methane (CH4), where one s and three p orbitals combine to form four equivalent sp3 hybrid orbitals pointing towards the corners of a tetrahedron.

This hybridization explains the molecular geometry of many molecules. It is not an actual physical process but a model that provides a close approximation to the behavior of electron orbitals during chemical bonding.

Pauli Exclusion Principle

The Pauli Exclusion Principle is a quantum mechanical principle which states that no two electrons in an atom or molecule can have the same set of four quantum numbers. This principle dictates electron configuration and is crucial for understanding the structure of the periodic table. In the context of molecular orbitals, it ensures that electrons will fill the available space in a way that no two have identical energy states.

As a direct implication, any given molecular orbital can hold only two electrons, and they must have opposite spins. This is evidenced by the magnetic quantum number, which can be either +1/2 or -1/2, representing the two possible spins of an electron.

Quantum Numbers

Quantum numbers are the numerical values that describe the unique quantum state of an electron. There are four types: the principal quantum number (), which indicates the energy level and size of the orbital; the angular momentum quantum number (), which indicates the shape of the orbital; the magnetic quantum number (), which indicates the orientation of the orbital; and the spin quantum number (), which indicates the direction of the electron's spin.

These numbers obey the rules set by the Pauli Exclusion Principle and are essential in determining the electron configuration of an atom, which in turn dictates the atom’s reactivity and properties.

Molecular Geometry

Molecular geometry is the three-dimensional arrangement of atoms within a molecule. It is determined by the spatial distributions of the electrons and can significantly affect the physical and chemical properties of a compound. Hybridizing atomic orbitals provide a framework for predicting molecular geometry through models like the Valence Shell Electron Pair Repulsion (VSEPR) theory and molecular orbital theory.

Common geometries include linear, bent, trigonal planar, tetrahedral, trigonal bipyramidal, and octahedral. These shapes are predicted by considering the repulsive forces between electron pairs and the resulting angles and distances between adjacent atoms.

Bonding and Antibonding Orbitals

Bonding and antibonding orbitals arise from the interaction between atomic orbitals when atoms approach each other to form a molecule. Bonding orbitals are lower in energy and result from the constructive interference of atomic orbital wave functions, which leads to an increased electron density between nuclei, stabilizing the molecule. Antibonding orbitals, on the other hand, are the result of destructive interference and have higher energy, leading to a decrease in electron density between nuclei and, thus, they destabilize the molecule.

Only bonding orbitals are occupied in a stable molecule under normal conditions, whereas antibonding orbitals are typically unoccupied. However, these can play a role in excited states of molecules and in the understanding of chemical reactivity.