Question

What is the angle between these two hybrid orbitals on the same atom? (a) \(s p\) and \(s p\) hybrid orbitals, (b) \(s p^{2}\) and \(s p^{2}\) hybrid orbitals, (c) \(s p^{3}\) and \(s p^{3}\) hybrid orbitals.

Short answer

The bond angle between two sp hybrid orbitals is 180°, two sp2 hybrid orbitals is 120°, and two sp3 hybrid orbitals is 109.5°.

Step-by-step solution

Determine bond angles for sp orbitals

For sp hybrid orbitals, the molecule is arranged in a linear geometry. As there are only two orbitals, they are placed farthest from each other to minimize electron-electron repulsion, hence forming an angle of \(180^\circ\).

Determine bond angles for sp2 orbitals

For sp2 hybrid orbitals, the molecule adopts a trigonal planar geometry. The three hybrid orbitals arrange themselves as far apart as possible in a plane. Hence, the angle between any two orbitals is \(120^\circ\).

Determine bond angles for sp3 orbitals

For sp3 hybrid orbitals, the molecule has a tetrahedral geometry. The four hybrid orbitals are directed towards the corners of a regular tetrahedron in three-dimensional space to minimize electron-electron repulsion. Therefore, the bond angle is \(109.5^\circ\).

Key concepts

Linear Geometry

In the world of chemistry, **linear geometry** arises when atoms form molecules using sp hybrid orbitals. This typically occurs when a central atom is bonded to two other atoms. Linear geometry ensures that the orbitals are positioned as far apart as possible to minimize electron repulsion.

Think of a straight line connecting the atoms, with bond angles of exactly **180°**. This arrangement allows the molecule to have the least resistance due to electron repulsion. Molecules such as carbon dioxide (CO e2) exhibit this linear structural geometry.

Key Points of Linear Geometry:

• Occurs with sp hybridization.
• Bond angle is 180°.
• Commonly seen in diatomic molecules and certain triatomic molecules like CO e2.

Trigonal Planar Geometry

**Trigonal planar geometry** is a fascinating concept that emerges from sp² hybridization. When an atom is surrounded by three groups or atoms, they tend to spread out evenly in a plane. This causes a bond angle of **120°** between the bonds.

In this geometry, the electrons assume a planar triangle configuration to reduce repulsion. This means that all the atoms lie flat, creating a stable structure. Such configurations are prevalent in molecules like boron trifluoride (BF₃).

Key Characteristics of Trigonal Planar Geometry:

• Associated with sp² hybridized orbitals.
• Bond angle is 120°.
• Exemplified in molecules where the central atom is bonded to three peripheral atoms.

Tetrahedral Geometry

The **tetrahedral geometry** is one of the fundamental structures in molecular shapes. It results from sp³ hybridization and involves a central atom bonded to four other atoms or groups.

This tetrahedral arrangement creates bond angles of approximately **109.5°**. The molecule takes on a three-dimensional shape, like a pyramid with a triangular base, maximizing the distance between bonds to minimize repulsion. Methane (CH₄) is a classic example of such a shape.

Essential Aspects of Tetrahedral Geometry:

• Formed by sp³ hybrid orbitals.
• Bond angle is roughly 109.5°.
• Common in molecules with a central atom bonded to four others, offering stability in a 3D space.