Problem 118 - General Chemistry: Principles and Modern Applications

Question

One possibility for the electron-group geometry for seven electron groups is pentagonal-bipyramidal, as found in the IF \(_{7}\) molecule. Write the VSEPR notation for this molecule. Sketch the structure of the molecule, labeling all the bond angles.

Step-by-Step Solution

Answer

The VSEPR notation for the IF\(_7\) molecule is AX7. The molecule has a pentagonal-bipyramidal shape. Bond angles are \(90°\) from the equatorial to axial plane, \(72°\) in the equatorial plane, and \(180°\) in the axial plane.

Step 1: Identifying the Central Atom

In the IF\(_7\) molecule, iodine (I) is the central atom. Iodine has seven valence electrons. Each of the seven fluoride (F) atoms will share one electron with iodine to form a single bond.

Step 2: Writing the VSEPR Notation

The VSEPR notation for this molecule is AX7 where A represents the central atom (iodine), X represents the surrounding atoms (fluoride), and the number (7) refers to the number of surrounding atoms.

Step 3: Sketching the Structure

The molecular geometry of IF7 according to the VSEPR is a pentagonal bipyramid. The central iodine atom is surrounded by five fluorine atoms forming the base of the pentagonal pyramid. Two fluorine atoms are located above and below the iodine atom along the perpendicular axis forming the 'bi-pyramid'.

Step 4: Labeling the Bond Angles

In a pentagonal-bipyramidal arrangement, the bond angle from the equatorial plane (formed by the five fluorine atoms in the pentagon) to the axial plane (formed by the central iodine atom and the two other fluorine atoms) is \(90°\). The bond angle in the pentagon (equatorial plane) is \(72°\) and the bond angle between the two fluorine atoms in the axial plane is \(180°\).

Key Concepts

Molecular Geometry

In the realm of chemistry, understanding molecular geometry is crucial for predicting the structure and behavior of molecules. Molecular geometry refers to the three-dimensional arrangement of atoms around a central atom, which determines the shape of the molecule.
For instance, in VSEPR (Valence Shell Electron Pair Repulsion) theory, the fundamental idea is that electron pairs around a central atom will arrange themselves to minimize repulsion, resulting in specific molecular shapes.
The shape is governed by the number of bonded atoms and lone pairs of electrons. By knowing the structure, chemists can predict molecular properties like polarity and reactivity.

• VSEPR Notation: It's a formula that encapsulates the number of bonded atoms (X) and lone pairs (E) on a central atom (A), usually in the form AX extsubscript{n}E extsubscript{m}.
• Example: For IF extsubscript{7}, the VSEPR notation is AX extsubscript{7}, reflecting seven atoms bonded to iodine without any lone pairs.

By visualizing these arrangements through models and illustrations, one gains a better understanding of complex molecular geometries.

Pentagonal Bipyramidal

The term 'pentagonal bipyramidal' describes a specific molecular shape in which there are seven electron groups around a central atom. In this arrangement, particularly in the IF extsubscript{7} molecule, five atoms form the base pentagon at the equator of the structure.
Two additional atoms are positioned above and below the central atom, forming the axial positions, hence the term 'bipyramidal.'
This arrangement is seen as a characteristic geometry for molecules with seven bonding pairs and is quite rare in comparison to simpler geometries.

• The central atom, such as iodine in IF extsubscript{7}, is at the center of the pentagon.
• The equatorial atoms contribute to the pentagon's base, making the plane horizontal and stable.
• The axial atoms are perfectly perpendicular to the equatorial plane, achieving optimal repulsion reduction.

This geometry balances the repulsions among seven fluorine atoms, providing a fascinating example of VSEPR theory at work.

Bond Angles

Bond angles are vital for understanding the spatial arrangement of atoms in a molecule. They are the angles between adjacent bonds and can influence a molecule's shape and functions greatly. In the context of the VSEPR theory, bond angles arise due to electron pair repulsions.
For a pentagonal bipyramidal structure like IF extsubscript{7}, analyzing bond angles helps explain the molecule's geometry.
The geometry includes:

• Axial to equatorial angles: These bond angles are typically at 90°, representing the connection from the base pentagon up to the axial atoms.
• Equatorial angles: The angles within the pentagon (equatorial plane) are 72°, because the 360° circle of the pentagon is divided amongst the five bonds.
• Axial to axial angles: At 180°, these measure the complete angle across the central iodine atom.

By identifying these angles, one can appreciate the tidy and efficient nature of molecular geometries according to VSEPR theory. Understanding these angles helps in predicting molecular behavior, such as reaction pathways or interaction with other molecules.