Question

The anion \(I_{4}^{2-}\) is linear, and the anion \(I_{5}^{-}\) is V-shaped, with a \(95^{\circ}\) angle between the two arms of the V. For the central atoms in these ions, propose hybridization schemes that are consistent with these observations.

Short answer

The hybridization of iodine in the \(I_{4}^{2-}\) anion is sp3d, and in the \(I_{5}^{-}\) anion is sp3d2.

Step-by-step solution

Analysis of \(I_{4}^{2-}\) Anion

In the \(I_{4}^{2-}\) anion, the central iodine atom is bonded to two other iodine atoms and also has three lone pairs. The geometry is linear, meaning all atoms and lone pairs are in one line.

Determine Hybridization of \(I_{4}^{2-}\)

The number of electron pairs around the central atom is the sum of bonded atoms and lone pairs, which is 2 (bonds) + 3 (lone pairs) = 5. According to the hybridization theory, this corresponds to sp3d hybridization.

Analysis of \(I_{5}^{-}\) Anion

In the \(I_{5}^{-}\) anion, the central iodine atom is bonded to five other iodine atoms and has no lone pairs. The molecule is V-shaped with a \(95^{\circ}\) angle between the two arms of the V.

Determine Hybridization of \(I_{5}^{-}\)

The number of electron pairs around the central atom is 5, all of which are bonding pairs. This corresponds to sp3d2 hybridization.

Key concepts

Hybridization

Hybridization is a key concept in understanding the shape and geometry of molecules. It refers to the mixing of atomic orbitals to form new hybrid orbitals suitable for the pairing of electrons during bond formation. This process allows atoms to form stable chemical bonds in various geometries.

The type of hybridization depends on the number of electron domains, which are defined as regions of electron density around the central atom. These include both bonding pairs (shared between atoms) and lone pairs (non-bonded pairs). For example, if there are five electron domains around the central atom, the hybridization is sp3d. Here, one s orbital, three p orbitals, and one d orbital mix together.

• sp hybridization involves mixing one s and one p orbital, leading to a linear shape.
• sp2 hybridization includes one s and two p orbitals, often resulting in trigonal planar shapes.
• sp3 hybridization involves mixing one s and three p orbitals, commonly leading to a tetrahedral shape.
• sp3d and sp3d2 hybridizations involve mixing additional d orbitals, which allow for more complex shapes such as trigonal bipyramidal and octahedral structures.

Linear Geometry

Linear geometry arises in molecular shapes where all atoms and lone pairs align in a straight line. This is typically seen in molecules where the central atom has a total of two bonded electron pairs resulting in no angle or a 180-degree angle between the bonds. Such a setup minimizes repulsion between electron pairs, making the molecule more stable.

For the anion \(I_{4}^{2-}\), the central iodine atom uses an sp3d hybridization scheme. Although this hybridization suggests a trigonal bipyramidal shape, the presence of lone pairs in equatorial positions forces the bonded atoms to be positioned linearly, resulting in a linear geometry. Here, the three lone pairs occupy the most space-efficient positions in the trigonal bipyramidal arrangement to minimize repulsion, leaving the bonded pairs in a line.

• Straight-line electron pairs reduce repulsion.
• An example is carbon dioxide \(CO_{2}\), where the central carbon forms two double bonds in opposite directions.
• Being linear, these structures often have similar properties like nonpolarity and are common in diatomic molecules.

V-Shaped Molecular Structure

The V-shaped molecular structure, also known as bent or angular structure, is characterized by a central atom bonded to two others with a non-180-degree angle, creating a V or bent shape. This form arises from specific hybridization scenarios in certain molecules.

In the case of the \(I_{5}^{-}\) anion, the central iodine atom is involved in sp3d2 hybridization. While this hybridization suggests an octahedral geometry, the molecular shape becomes V-shaped due to the presence of lone pairs or bending in bonding pairs, which naturally form angles less than 180 degrees. Here, the angle formed is approximately 95 degrees.

• The V-shape is a result of lone pair-bond pair repulsion.
• Water \(H_{2}O\) is a classic example of a V-shaped molecule, where the bond angle is about 104.5 degrees.
• This structure leads to polar molecules with distinctive properties due to the uneven distribution of charge.