Question

In which of the following \(\mathrm{AF}_{n}\) molecules or ions is there more than one \(\mathrm{F}-\mathrm{A}-\mathrm{F}\) bond angle: \(\mathrm{SiF}_{4}, \mathrm{PF}_{5}, \mathrm{SF}_{4}, \mathrm{AsF}_{3}\) ?

Short answer

In the given molecules or ions SiF₄, PF₅, SF₄, and AsF₃, SiF₄, PF₅, and SF₄ have more than one F-A-F bond angle due to their respective molecular geometries: tetrahedral (SiF₄), trigonal bipyramidal (PF₅), and seesaw (SF₄).

Step-by-step solution

Draw Lewis Structures

First, draw the Lewis structure for each of the given molecules or ions: SiF₄, PF₅, SF₄, and AsF₃. To draw the Lewis structure, first, we count the total number of valence electrons in each molecule/ion, then we arrange these valence electrons in such a way that the central atom shares electrons with each surrounding atom to complete their octets and fulfill the octet rule.

Determine Molecular Geometry

Now that the Lewis structures are done, we can determine the molecular geometry of these molecules by using the Valence Shell Electron Pair Repulsion (VSEPR) theory. Based on the number of electron domains (regions of electron density), we can deduce the molecular geometry for each molecule/ion from the AXE notation (A is the central atom and X is the number of atoms bonded to it, while E is the number of lone pairs on the central atom). - For SiF₄, the AXE notation is AX₄. The molecular geometry is tetrahedral. - For PF₅, the AXE notation is AX₅. The molecular geometry is trigonal bipyramidal. - For SF₄, the AXE notation is AX₄E. The molecular geometry is seesaw. - For AsF₃, the AXE notation is AX₃. The molecular geometry is trigonal planar.

Identify Molecules with More Than One F-A-F Bond Angle

Now that we have the molecular geometries, we can identify the molecules with more than one F-A-F bond angle. - SiF₄ (tetrahedral) has 6 F-Si-F bond angles. - PF₅ (trigonal bipyramidal) has 10 F-P-F bond angles. - SF₄ (seesaw) has 6 F-S-F bond angles. - AsF₃ (trigonal planar) has 3 F-As-F bond angles. From this information, we find that SiF₄, PF₅, and SF₄ have more than one F-A-F bond angle.

Key concepts

Understanding Lewis Structures

Lewis structures provide a visual representation of the bonding between atoms within a molecule as well as any non-bonding electron pairs. Drawing Lewis structures helps us determine the arrangement of atoms and the distribution of electrons around them, which is fundamental to predicting the molecule's geometry and reactivity.

To correctly draw a Lewis structure, we must first count the total number of valence electrons available. Each atom contributes its valence electrons to the group, and molecules strive to follow the octet rule, having eight electrons in their valence shell to achieve stability, except for hydrogen which fills its shell with two electrons. Single bonds are represented with a single line connecting two atoms, while lone pairs (pairs of electrons not involved in bonding) are represented as pairs of dots around the respective atoms.

When drawing Lewis structures, pay attention to the electronegativity of the atoms involved. Generally, the least electronegative atom (excluding hydrogen) is placed in the center, serving as the central atom with surrounding atoms bonded to it. Also, distribute the electrons to satisfy the octet rule for each atom as closely as possible. In some cases, resonance structures may occur when more than one valid Lewis structure can be drawn for a molecule.

Determining Molecular Geometry with VSEPR Theory

Molecular geometry is greatly influenced by the distribution of electron pairs around the central atom, as described by the Valence Shell Electron Pair Repulsion (VSEPR) theory. This theory posits that electron pairs repel each other and, as a result, they try to stay as far apart as possible, which then determines the molecule's shape.

The shape of a molecule is deduced from the number of bonding and non-bonding electron pairs (lone pairs) around the central atom, often represented using the AXE notation. The letter 'A' represents the central atom, while 'X' indicates the number of atoms bonded to 'A', and 'E' represents the number of lone pairs on 'A'.

For example, a molecule with an AX₄E notation indicates four bonding pairs and one lone pair around the central atom, which would result in a seesaw-shaped geometry. VSEPR theory helps us to rationalize the number of bond angles and the overall three-dimensional arrangement of atoms in the molecule.

The Significance of F-A-F Bond Angles

Understanding F-A-F bond angles in molecules helps us predict the spatial distribution of the atoms and chemical properties such as reactivity and polarity. The F-A-F bond angle is influenced by the overall molecular shape, which in turn depends on the number of electron domains around the central atom 'A' and the presence of any lone pairs.

In molecules with a symmetrical shape, such as tetrahedral SiF₄, all F-Si-F bond angles are identical. However, in molecules with a less symmetrical shape, such as the seesaw-shaped SF₄, there are variations in bond angles due to the presence of lone pairs, which occupy more space and push the other atoms closer together, resulting in different F-A-F angles.

The presence of multiple F-A-F bond angles in a molecule such as PF₅, which has a trigonal bipyramidal geometry, showcases the complexity and versatility of molecular structure. This complexity is vital to understand as it affects the physical and chemical properties of molecules, including their reactivity, phase of matter, and how they interact with light or other molecules.