Question

Arrange the following compounds in the increasing order of F-Xe-F bond angle : \(\mathrm{XeF}_{2}, \mathrm{XeF}_{4}, \mathrm{XeF}_{5}^{-}\) (1) \(\mathrm{XeF}_{2}<\mathrm{XeF}_{4}<\mathrm{XeF}_{5}^{-}\) (2) \(\mathrm{XeF}_{5}^{-}<\mathrm{XeF}_{4}<\mathrm{XeF}_{2}\) (3) \(\mathrm{XeF}_{2}<\mathrm{XeF}_{5}^{-}<\mathrm{XeF}_{4}\) (4) \(\mathrm{XeF}_{2}=\mathrm{XeF}_{4}=\mathrm{XeF}_{5}^{-}\)

Short answer

3) \(\mathrm{XeF}_{2} < \mathrm{XeF}_{5}^{-} < \mathrm{XeF}_{4}\)

Step-by-step solution

- Determine the structure of each compound

To arrange the compounds in increasing order of F-Xe-F bond angle, first identify the molecular geometry of \(\mathrm{XeF}_{2}\), \(\mathrm{XeF}_{4}\), and \(\mathrm{XeF}_{5}^{-}\).

- Molecular Geometry of \(\mathrm{XeF}_{2}\)

The molecular geometry of \(\mathrm{XeF}_{2}\) is linear with the bond angle of 180°. It has a total of 5 electron pairs (2 bonding pairs and 3 lone pairs) around xenon.

- Molecular Geometry of \(\mathrm{XeF}_{4}\)

The molecular geometry of \(\mathrm{XeF}_{4}\) is square planar with bond angles of 90°. It has a total of 6 electron pairs (4 bonding pairs and 2 lone pairs) around xenon.

- Molecular Geometry of \(\mathrm{XeF}_{5}^{-}\)

The molecular geometry of \(\mathrm{XeF}_{5}^{-}\) is square pyramidal with bond angles (less than 90°) smaller compared to \(\mathrm{XeF}_{4}\), slightly distorted due to the lone pair.

- Comparing Bond Angles

Compare the bond angles to determine the increasing order: \(\mathrm{XeF}_{2} (\text{180°}) < \mathrm{XeF}_{5}^{-} (\text{< 90°}) < \mathrm{XeF}_{4} (\text{90°})\).

Key concepts

Molecular Geometry

Understanding the molecular geometry of a molecule helps in predicting its shape and bond angles. Molecular geometry refers to the three-dimensional arrangement of atoms in a molecule. This geometry is influenced by the number of bonding pairs and lone pairs of electrons around the central atom.

For example, in \(\text{XeF}_{2}\), the molecular geometry is linear. This means that the two fluorine atoms are positioned on opposite sides of the central xenon atom, creating a straight line. This linear shape is due to the presence of three lone pairs and two bonding pairs of electrons, giving it a bond angle of 180°. Here, the three lone pairs position themselves far apart to minimize repulsion.

In \(\text{XeF}_{4}\), the molecular geometry is square planar. The four fluorine atoms form a square around the central xenon atom, with two lone pairs placed above and below the plane. This arrangement aims to reduce electron pair repulsion and results in bond angles of 90°.

Lastly, \(\text{XeF}_{5}^{-}\) has a molecular geometry that is square pyramidal. This shape is characterized by one apex fluorine atom above the square plane formed by the other four fluorine atoms, where the lone pair is slightly distorting the angles. Thus, the bond angles are slightly less than 90°. Such distortions happen due to the lone pair taking up more space.

Electron Pairs

Electron pairs come in two types: bonding pairs and lone pairs. Bonding pairs are shared between atoms and form the bonds, while lone pairs are the electrons that are not shared and remain on the central atom.

In \(\text{XeF}_{2}\), the central xenon atom has three lone pairs and two bonding pairs. These lone pairs repel the bonding pairs, forcing the molecule into a linear shape.

For \(\text{XeF}_{4}\), the xenon atom has two lone pairs and four bonding pairs. The lone pairs try to get as far away from each other as possible, leading to a square planar arrangement.

In \(\text{XeF}_{5}^{-}\), there is one lone pair and five bonding pairs. The lone pair again distorts the molecule, resulting in a square pyramidal shape. This distortion slightly reduces the bond angles.

Bond Angles

Bond angles are the angles between adjacent bonds of a molecule and can be predicted based on its molecular geometry and electron pair repulsion.

For instance, \(\text{XeF}_{2}\) has a bond angle of 180° due to its linear geometry. The repulsion caused by the lone pairs forces the fluorine atoms to be as far apart as possible.

The bond angles in \(\text{XeF}_{4}\) are 90°. This is typical for a square planar shape where each bond angles are right angles due to the symmetrical arrangement of the bonding pairs and the lone pairs above and below the plane.

In \(\text{XeF}_{5}^{-}\), the bond angles are slightly less than 90°. The lone pair in this molecule creates a small distortion, decreasing the ideal square pyramidal bond angles slightly.

To summarize, comparing these three xenon fluorides, the bond angles increase in the order: \(\text{XeF}_{5}^{-}\) (less than 90°), \(\text{XeF}_{4}\) (90°), and \(\text{XeF}_{2}\) (180°).