Problem 81 - General Chemistry: Principles and Modern Applications

Question

Predict the shapes of the following molecules, and then predict which would have resultant dipolemoments: (a) \(\mathrm{SO}_{2} ;\) (b) \(\mathrm{NH}_{3} ;\) (c) \(\mathrm{H}_{2} \mathrm{S} ;\) (d) \(\mathrm{C}_{2} \mathrm{H}_{4} ;\) (e) \(\mathrm{SF}_{6}\); (f) \(\mathrm{CH}_{2} \mathrm{Cl}_{2}\).

Step-by-Step Solution

Answer

\( \mathrm{SO}_{2} \), \( \mathrm{NH}_{3} \), \( \mathrm{H}_{2} \mathrm{S} \) and \( \mathrm{CH}_{2} \mathrm{Cl}_{2} \) have a net dipole moment. \( \mathrm{C}_{2} \mathrm{H}_{4} \) and \( \mathrm{SF}_{6} \) do not have a dipole moment.

Step 1: Identify the Molecular Shapes

Based on the VSEPR theory, the shapes of molecules can be predicted. For \( \mathrm{SO}_{2} \), there are 2 bond pairs and 1 lone pair around the central atom, so its shape is bent or V-shaped. For \( \mathrm{NH}_{3} \), there are 3 bond pairs and 1 lone pair around the central atom, giving it a trigonal pyramidal shape. \( \mathrm{H}_{2} \mathrm{S} \) has 2 bond pairs and 2 lone pairs around the central atom, also providing a bent or V-shaped form. \( \mathrm{C}_{2} \mathrm{H}_{4} \) is a planar molecule since both carbon atoms are sp2 hybridized, forming a trigonal planar geometry. For \( \mathrm{SF}_{6} \), there are 6 bond pairs around the central atom, giving an octahedral shape. Lastly, \( \mathrm{CH}_{2} \mathrm{Cl}_{2} \) has a tetrahedral shape since there are 4 bond pairs around the central carbon atom.

Step 2: Predict the Dipole Moment

A molecule will have a net dipole moment if its structure is unsymmetrical, which creates an imbalance of electron charge. Hence, \( \mathrm{SO}_{2} \), \( \mathrm{NH}_{3} \) and \( \mathrm{H}_{2} \mathrm{S} \) being V-shaped and trigonal pyramidal, will have a net dipole moment. \( \mathrm{C}_{2} \mathrm{H}_{4} \), being a symmetrical planar molecule, will not have a dipole moment. \( \mathrm{SF}_{6} \), being a symmetrical octahedral molecule, will not have a dipole moment. \( \mathrm{CH}_{2} \mathrm{Cl}_{2} \), although is a tetrahedral, it will have a net dipole moment due to the different atoms (H and Cl) connected to the central atom leading to a difference in electronegativities.

Key Concepts

VSEPR Theory

The Valence Shell Electron Pair Repulsion (VSEPR) theory is a model used to predict the shape of individual molecules. It is based on the premise that electron pairs around a central atom will arrange themselves as far apart as possible to minimize the repulsive forces between them.
This model is incredibly useful because the shape of a molecule significantly affects its chemical properties and reactivity. For VSEPR, we consider both bonding pairs (shared between atoms) and lone pairs (non-shared) of electrons around the central atom.

• Bent or V-shaped geometry occurs when there are two bonding pairs and one or more lone pairs, like in \((\mathrm{SO}_{2})\).
• Trigonal pyramidal shapes, found in molecules like \((\mathrm{NH}_{3})\), arise from three bonding pairs and one lone pair.
• When molecules have a planar shape, like \((\mathrm{C}_{2}\mathrm{H}_{4})\), the atoms are organized such that their electron pairs are in the same plane, often as a result of \(sp^2\) hybridization.
• Octahedral shapes, such as in \((\mathrm{SF}_{6})\), occur with six bonding pairs symmetrically arranged around the central atom.

Understanding VSEPR theory helps in predicting molecular geometry, which is crucial for understanding molecular interactions and properties.

Dipole Moment

Dipole moment is a measure of the separation of positive and negative charges in a molecule. It arises from differences in electronegativity between atoms that create polar bonds within a molecule.
The presence and magnitude of a dipole moment can greatly affect a molecule's behavior and interactions, such as solubility and boiling point. Notably, a molecule will only have a net dipole moment if it is asymmetrical.

• In a bent or V-shaped molecule like \((\mathrm{SO}_{2})\), the asymmetry leads to a net dipole moment despite symmetrical polar bonds.
• \(\mathrm{NH}_{3},\) with its trigonal pyramidal shape and non-symmetrical distribution of polar bonds, exhibits a dipole moment as well.
• \(\mathrm{CH}_{2}\mathrm{Cl}_{2}\) has a dipole moment because its tetrahedral shape is asymmetrical due to the differences in electronegativity between hydrogen and chlorine atoms.
• For symmetric molecules, such as \(\mathrm{C}_{2}\mathrm{H}_{4}\) and \(\mathrm{SF}_{6},\) there is no dipole moment as the polarities cancel each other out.

The concept of dipole moment plays a vital role in understanding molecular interactions in solution and in the prediction of molecule behavior under external electric fields.

Molecular Geometry

Molecular Geometry refers to the three-dimensional arrangement of atoms in a molecule. It is a key factor that determines many physical and chemical properties of a substance.
Each geometry type gives unique characteristics to the molecule in terms of spatial configuration. VSEPR theory helps predict these geometries by considering electron pairs around a central atom.

• For example, \(\mathrm{SO}_{2}\) has a bent or V-shaped geometry due to the influence of lone pairs on the central sulfur atom.
• In \(\mathrm{NH}_{3},\) the trigonal pyramidal geometry is influenced by a lone pair on the nitrogen atom, deviating the hydrogen bonds from a perfect tetrahedral layout.
• \(\mathrm{C}_{2}\mathrm{H}_{4}\) is planar due to \(sp^2\) hybridization in carbon atoms, leading to a single plane arrangement of atoms.
• \(\mathrm{SF}_{6},\) on the other hand, exhibits an octahedral geometry with no lone pairs, giving it a highly symmetrical spatial configuration.

Correctly understanding molecular geometry helps to predict molecular reactivity, polarity, phase of matter, color, magnetism, biological activity, and chemical properties.