Question

Describe the bond angles to be found in each of the follow- ing molecular structures: (a) trigonal planar, \((\mathbf{b})\) tetrahedral, (c) octahedral, (d) linear.

Short answer

The bond angles for each molecular structure are: (a) Trigonal planar: \(120^{\circ}\) (b) Tetrahedral: \(109.5^{\circ}\) (c) Octahedral: \(90^{\circ}\) and \(180^{\circ}\) (d) Linear: \(180^{\circ}\)

Step-by-step solution

Analyze Trigonal Planar Structure

A trigonal planar structure has three atoms bonded to the central atom, with all of them placing in one plane and the electron pairs arranging themselves as far apart as possible. In this structure, the bond angles are equal.

Calculate Bond Angle for Trigonal Planar Structure

As there are 3 atoms bonded to the central atom in a trigonal planar structure, and they are all in the same plane, the bond angle between them is \(120^{\circ}\).

Analyze Tetrahedral Structure

A tetrahedral structure has four atoms bonded to the central atom. The electron pairs arrange themselves as far apart as possible, creating a three-dimensional structure.

Calculate Bond Angle for Tetrahedral Structure

In a tetrahedral structure, the bond angle between the atoms is approximately \(109.5^{\circ}\).

Analyze Octahedral Structure

An octahedral structure has six atoms bonded to the central atom. The electron pairs arrange themselves as far apart as possible to minimize repulsion, resulting in a regular three-dimensional structure.

Calculate Bond Angle for Octahedral Structure

In an octahedral structure, there are two possible bond angles: 1. The angle between two atoms that are adjacent to each other, which is \(90^{\circ}\). 2. The angle between two atoms opposite each other (linear arrangement), which is \(180^{\circ}\).

Analyze Linear Structure

A linear structure has two atoms bonded to the central atom. The electron pairs arrange themselves as far apart as possible, resulting in a linear arrangement.

Calculate Bond Angle for Linear Structure

In a linear structure, the bond angle between the atoms is \(180^{\circ}\) as they are in a straight line. To summarize, the bond angles for each molecular structure are as follows: (a) Trigonal planar: \(120^{\circ}\) (b) Tetrahedral: \(109.5^{\circ}\) (c) Octahedral: \(90^{\circ}\) and \(180^{\circ}\) (d) Linear: \(180^{\circ}\)

Key concepts

Bond Angles

In molecular geometry, bond angles are the angles formed between adjacent lines representing bonds. These angles are crucial to understanding the shapes of molecules as they indicate how the atoms are oriented in space. The distribution of these angles is determined by the electron cloud's repulsion forces that exist between bonded atoms. For instance, in a trigonal planar molecule, the bond angle is always exactly \(120^{\circ}\), because the atoms and electron pairs will equally repel each other to maintain this separation. Similarly, the bond angle in other molecular shapes define how the structure appears in three-dimensional space, dictating the geometry that minimizes repulsion forces.

Trigonal Planar

A trigonal planar molecular geometry features a central atom bonded to three peripheral atoms. These atoms are placed at the corners of an equilateral triangle, all lying in one plane. This configuration appears commonly in molecules where the central atom has three areas of electron density. These regions strive to maintain equal distance from one another, leading to bond angles of \(120^{\circ}\). This angle helps stabilize the molecule's structure by reducing electron pair repulsion. Imagine any three points on a flat surface that are all equally spaced from one another; that's your foundation for visualizing a trigonal planar shape.

Tetrahedral Structure

In a tetrahedral structure, a central atom is connected to four surrounding atoms, forming a three-dimensional arrangement that resembles a pyramid with a triangular base. This shape is crucial in numerous organic compounds. The symmetric distribution of the atoms around the central point means that each bond angle in a tetrahedral structure is approximately \(109.5^{\circ}\). This arrangement ensures that the repulsion between electron pairs is minimized. By picturing a regular four-sided die, you can visualize how the atoms are symmetrically placed in three-dimensional space. The tetrahedral geometry is prevalent, due to its ability to allow for four atoms to be as far apart from each other as possible.

Octahedral Structure

An octahedral structure involves a central atom surrounded by six atoms or groups, positioned at the vertices of an octahedron. This formation results in a highly symmetrical, three-dimensional shape. The distinctive bond angles in an octahedral molecular geometry are primarily \(90^{\circ}\), formed between any two adjacent bonds. Additionally, there's a \(180^{\circ}\) bond angle between opposite bonds in this structure. This geometry allows for maximizing the distance between bonded pairs, minimizing electron repulsion. When trying to think of an octahedral shape, consider a die, but with eight equal triangular faces instead of six square ones. It's a common configuration in coordination compounds where stability requires the maximum separation of bonds.