Question

Which of the following molecules are linear: \(\mathrm{ICl}_{2}^{-}, \mathrm{IF}_{2}^{+},\) \(\mathrm{OF}_{2}, \mathrm{SnI}_{2}, \mathrm{CdBr}_{2} ?\)

Short answer

Linear molecules: \( \text{ICl}_2^- \), \( \text{SnI}_2 \), \( \text{CdBr}_2 \).

Step-by-step solution

Understand Molecular Geometry

The linear molecular geometry typically arises when there are two bonded atoms and no or an even number of lone pairs on the central atom. It can be seen in molecules that follow the formula AX2, where A is the central atom and X represents terminal atoms.

Analyze \( \text{ICl}_2^- \)

\( \text{ICl}_2^- \) ion has iodine (I) as the central atom with three lone pairs and two chlorine (Cl) atoms bonded to it. It follows the VSEPR arrangement AX2E3, resulting in a linear geometry.

Analyze \( \text{IF}_2^+ \)

\( \text{IF}_2^+ \) ion has iodine (I) as the central atom with two lone pairs. This results in an AX2E2 arrangement according to VSEPR theory, making the structure bent, therefore, it is not linear.

Analyze \( \text{OF}_2 \)

\( \text{OF}_2 \) has oxygen (O) as the central atom with two lone pairs and two fluorine (F) atoms, giving it an AX2E2 configuration. This bent shape leads to a non-linear structure.

Analyze \( \text{SnI}_2 \)

\( \text{SnI}_2 \) consists of tin (Sn) as the central atom with no lone pairs and it is bound to two iodine (I) atoms. It follows the AX2 formula, resulting in a linear geometry.

Analyze \( \text{CdBr}_2 \)

\( \text{CdBr}_2 \) has cadmium (Cd) as the central atom and it forms single bonds with two bromine (Br) atoms and has no lone pairs. Also following an AX2 configuration, the geometry is linear.

Conclusion: List Linear Molecules

The linear molecules among the given options are \( \text{ICl}_2^- \), \( \text{SnI}_2 \), and \( \text{CdBr}_2 \).

Key concepts

Linear Molecules

Linear molecules are those with a specific arrangement in which all the atoms are aligned in a straight line. This linear structure typically arises when there are two atoms bonded to a central atom, with no or an even number of lone pairs affecting the geometry.

• In a linear molecule, the bond angle between the bonded atoms is 180 degrees.
• The molecule's shape is described by the general formula AX2, where A represents the central atom and X represents the atoms bonded to it.
• If lone pairs are present, they must not hinder the linear geometry, leading to formations like AX2E3, where E represents lone pairs.

For instance, in the molecule \( \text{ICl}_2^- \), iodine (I) is the central atom. It forms bonds with two chlorine (Cl) atoms and has three lone pairs, which results in a linear structure because the lone pairs do not disturb the direct arrangement of the terminal atoms. Similarly, \( \text{SnI}_2 \) and \( \text{CdBr}_2 \) are linear because their central atoms, tin (Sn) and cadmium (Cd) respectively, have two bonded atoms each with no lone pairs, maintaining the 180-degree bond angle.

VSEPR Theory

The Valence Shell Electron Pair Repulsion (VSEPR) Theory is fundamental in understanding and predicting the shapes of molecules. This theory is based on the idea that electron pairs surrounding a central atom will arrange themselves as far apart as possible to minimize repulsion.

• Electron pairs include both bonding pairs that hold atoms together and lone pairs that do not participate in bonding.
• The arrangement minimizes repulsion and dictates the geometry of the molecule.

For example, in the molecule \( \text{IF}_2^+ \), iodine is the central atom surrounded by two fluorine atoms and two lone pairs. According to VSEPR theory, this gives an AX2E2 configuration, leading to a bent shape rather than a linear one because the lone pairs create additional repulsion that modifies the geometry. VSEPR theory helps predict not only linear molecular shapes but various other geometries by considering all electron pairs.

Bent Molecular Shape

A bent molecular shape occurs when the central atom of a molecule has two bonded atoms and one or more lone pairs, causing the bonded atoms to be pushed closer together than they would be in a linear configuration.

• Typically, bent molecules have an AX2E or AX2E2 configuration according to VSEPR theory.
• The lone pairs exert greater repulsive forces than bonded pairs, adjusting the bond angle to less than 180 degrees.

In the molecule \( \text{OF}_2 \), the central oxygen atom is bonded to two fluorine atoms and has two lone pairs, resulting in a bent shape. The lone pairs create repulsion that decreases the bond angle from 180 degrees to around 104.5 degrees, similar to the bent shape of a water molecule \( \text{H}_2\text{O} \). Understanding the bent shape is crucial because it affects the molecule’s polarity and chemical properties.