Problem 62 - General Chemistry: Principles and Modern Applications

Question

Predict the geometric shapes of (a) \(\mathrm{CO} ;\) (b) \(\mathrm{SiCl}_{4}\); (c) \(\mathrm{PH}_{3} ;\) (d) \(\mathrm{ICl}_{3} ;\) (e) \(\mathrm{SbCl}_{5} ;\) (f) \(\mathrm{SO}_{2} ;\) (g) \(\mathrm{AlF}_{6}^{3-}\).

Step-by-Step Solution

Answer

The shapes of the molecules are: (a) CO, linear; (b) SiCl4, tetrahedral; (c) PH3, trigonal pyramidal; (d) ICl3, T-shaped; (e) SbCl5, trigonal bipyramidal; (f) SO2, bent or V-shaped; (g) AlF6^3-, octahedral.

Step 1: Determine the Central Atom

The first step is to identify the central atom in each molecule. The central atom is generally the one that is linked to all other atoms in the molecule. In our case, for (a) CO, the central atom is C; (b) SiCl4, the central atom is Si; (c) PH3, the central atom is P; (d) ICl3, the central atom is I; (e) SbCl5, the central atom is Sb; (f) SO2, the central atom is S; (g) AlF6^3-, the central atom is Al.

Step 2: Count the Number of Electron Groups Around Central Atom

Count the number of bonding groups (single, double, or triple bonds) and non-bonding groups (lone pairs of electrons) around the central atom. For: (a) CO, 3 groups (two bonding, one non-bonding); (b) SiCl4, 4 groups (all bonding); (c) PH3, 4 groups (3 bonding, 1 non-bonding); (d) ICl3, 5 groups (3 bonding, 2 non-bonding); (e) SbCl5, 5 groups (all bonding); (f) SO2, 3 groups (two bonding, one non-bonding); (g) AlF6^3-, 6 groups (all bonding).

Step 3: Determine the Molecular Geometry

Based on these number of groups and the VSEPR theory, the shapes are: (a) CO, linear; (b) SiCl4, tetrahedral; (c) PH3, trigonal pyramidal; (d) ICl3, T-shaped; (e) SbCl5, trigonal bipyramidal; (f) SO2, bent or V-shaped; (g) AlF6^3-, octahedral.

Key Concepts

Molecular Geometry

Molecular geometry refers to the three-dimensional arrangement of atoms within a molecule. This arrangement determines the overall shape of the molecule and plays a crucial role in its reactivity and properties. According to VSEPR (Valence Shell Electron Pair Repulsion) theory, the geometry of a molecule depends on the number and arrangement of electron groups around the central atom. These electron groups strive to position themselves as far apart as possible to minimize repulsion.

For example,

• In a molecule like \({\mathrm{CO}}\), with a central carbon atom and two electron groups, the molecular geometry is linear.
• This contrasts with a molecule like \({\mathrm{SiCl_{4}}}\), which has four bonding groups and a tetrahedral shape, due to the four groups arranging themselves at maximum distances from each other.

Understanding molecular geometry helps predict how molecules interact with one another and participate in chemical reactions.

Bonding Groups

Bonding groups are critical in understanding molecular geometry as they represent the connections that form between atoms, whether through single, double, or triple bonds. Each bond, regardless of its type, is considered one bonding group within the framework of VSEPR theory.

For instance,

• In \({\mathrm{PH}_{3}}\), there are three bonding groups corresponding to the three hydrogen atoms bonded to phosphorus.
• Similarly, \({\mathrm{SbCl}_{5}}\) has five bonding groups, each chlorine atom individually bonded to antimony.

Evaluating these bonding groups helps in predicting the molecular shape, as they dictate how electrons and thus the atoms associated with these electrons position themselves in space.

Central Atom Identification

Identifying the central atom in a molecule is the first and perhaps most straightforward step in applying VSEPR theory. The central atom is typically the least electronegative and often bears the most capacity to form bonds compared to the other atoms in the molecule. This atom anchors the various bonding and non-bonding groups, determining the molecule's overall geometry.

Let's take

• \({\mathrm{CO}}\): the central atom is carbon, as it's positioned between oxygen and bonds directly with it.
• In \({\mathrm{SiCl_{4}}}\), silicon serves as the central atom because it integrates into four bonds with chlorine atoms.

Recognizing the central atom is essential for understanding and calculating the number of electron groups, and thus, the molecular structure.

Electron Groups

Electron groups include all areas surrounding a central atom where electrons are expected to be found. They consist of both bonding groups (bonds) and lone pairs (non-bonding groups). VSEPR theory uses these electron groups to predict molecular geometry.

Consider these molecules:

• For \({\mathrm{SO}_{2}}\), there are three electron groups: two associated with bonding to oxygen atoms and one lone pair on sulfur, resulting in a bent molecular shape.
• Likewise, in \({\mathrm{AlF}_{6}^{3-}}\), there are six electron groups, all bonding, leading to an octahedral shape.

Evaluating electron groups helps predict molecular geometry by showing how atoms and electrons distribute around the central atom. This knowledge is indispensable for predicting the shapes of even complex molecules.