Question

How many atomic orbitals form a set of \(s p^{3}\) hybrid orbitals? A set of \(s p^{2}\) hybrid orbitals? A set of \(s p\) hybrid orbitals? What is the relationship between these numbers and the number of electron groups around the central atom?

Short answer

4 sp3 hybrid orbitals, 3 sp2 hybrid orbitals, and 2 sp hybrid orbitals are formed. The number of hybrid orbitals corresponds to the number of electron groups around the central atom.

Step-by-step solution

Understanding Hybrid Orbitals

Hybridization is a concept where atomic orbitals mix to form new, identical hybrid orbitals. An 's' orbital can mix with 'p' orbitals to form different sets of hybrid orbitals. The number of hybrid orbitals formed is equal to the number of atomic orbitals that combine.

Determining the Number of Orbitals in Sp3

For the set of sp3 hybrid orbitals, one 's' orbital mixes with three 'p' orbitals (px, py, and pz). Since there are 1 s orbital and 3 p orbitals, a total of 1 + 3 = 4 orbitals mix together. Thus, 4 sp3 hybrid orbitals are formed.

Determining the Number of Orbitals in Sp2

In the case of sp2 hybrid orbitals, one 's' orbital mixes with two 'p' orbitals (px and py, for instance). Since there are 1 s orbital and 2 p orbitals, a total of 1 + 2 = 3 orbitals mix together. This results in 3 sp2 hybrid orbitals.

Determining the Number of Orbitals in Sp

For sp hybrid orbitals, one 's' orbital mixes with one 'p' orbital (px, for example). So, there are 1 s orbital and 1 p orbitals, hence 1 + 1 = 2 orbitals combine. This process will create 2 sp hybrid orbitals.

Understanding the Relationship with Electron Groups

The number of hybrid orbitals corresponds to the number of electron groups around the central atom. This includes bonding pairs and lone pairs. For example, 4 sp3 hybrid orbitals accommodate 4 electron groups, 3 sp2 orbitals for 3 electron groups, and 2 sp orbitals for 2 electron groups around the central atom.

Key concepts

Atomic Orbitals

In chemistry, atomic orbitals are the regions in an atom where there is a high probability of finding electrons. These orbitals are classified into different shapes and energies, primarily known as 's', 'p', 'd', and 'f' orbitals. The 's' orbital has a spherical shape and can contain up to two electrons, while 'p' orbitals have a dumbbell shape and can hold up to six electrons, divided across three spatially oriented lobes labeled px, py, and pz.

Each orbital type represents a specific energy level and electron cloud shape. For example, within the energy level known as the second shell, there is one 's' orbital and three 'p' orbitals; each with the capacity to accommodate two electrons. When these atomic orbitals combine, such as during the formation of covalent bonds, they can create hybrid orbitals which are crucial in understanding molecular shapes and bonding properties.

Hybridization Chemistry

Hybridization chemistry is a model that describes the bonding in molecules that cannot be represented adequately by a single Lewis structure. It's a mixing of atomic orbitals to form a set of equivalent hybrid orbitals, each of which will form a sigma bond or carry a lone pair of electrons. This concept is based on the mixing of different types of orbitals available to an atom (like one s orbital with one or more p orbitals) to generate new orbitals that can better explain the electron distribution around an atom in a molecule.

For instance, when a carbon atom forms four single bonds, as in methane (CH4), its one s orbital and three p orbitals hybridize to create four equivalent sp3 hybrid orbitals. Each carries a single electron and points towards the vertices of a tetrahedron, resulting in a tetrahedral molecular geometry. Every step up from a simple s orbital to sp3 is a reflection of the atom's increasing complexity in binding capacity and molecular intricacy.

Electron Group Geometry

Electron group geometry refers to the three-dimensional arrangement of electron groups (bonds and lone pairs) around a central atom. This geometry determines the molecular shape, which ultimately influences the molecule's properties and reactivity. Electron groups repel each other and adopt an arrangement in space to minimize this repulsion, a principle known as VSEPR (Valence Shell Electron Pair Repulsion) theory.

When evaluating the electron group geometry, both the bonding electron pairs and lone pairs are considered. For example, a central atom with 4 electron groups, such as in sp3 hybridization, will adopt a tetrahedral geometry. However, variations can occur; for example, if there are 4 electron groups and one is a lone pair, as seen in ammonia (NH3), the molecular geometry becomes trigonal pyramidal. Understanding electron group geometry is fundamental to predicting the shape and behavior of molecules.