Chapter 13: Problem 28
Determine the point groups of the following molecules. (a) Hydrogen selenide, \(\mathrm{H}_{2} \mathrm{Se}\) (b) Partially deuterated hydrogen sulfide, or HDS (c) The chair conformer of cyclohexane, \(\mathrm{C}_{6} \mathrm{H}_{12}\) (d) The boat conformer of cyclohexane, \(\mathrm{C}_{6} \mathrm{H}_{12}\)
Short Answer
Step by step solution
Identify Molecular Shape and Symmetry for H2Se
Analyze Symmetry Elements for HDS
Determine Symmetry for Chair Cyclohexane
Examine Symmetry for Boat Cyclohexane
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Point Group Determination
When identifying the point group of a molecule, you start by analyzing its shape and the presence of certain symmetry elements, such as axes of rotation or mirror planes. Take hydrogen selenide, \(\mathrm{H}_{2}\mathrm{Se}\), for example. By observing its bent molecular shape, we can ascertain that it has a mirror plane but no inversion center or higher-order rotation axes. Consequently, it fits into the \(C_{2v}\) point group. Accurate point group determination requires careful examination of all symmetry features of the molecule.
Symmetry Elements
1. **Planes of Symmetry (\(\sigma\))**: These are imaginary planes that divide a molecule into two mirror-image halves. For instance, in the chair conformer of cyclohexane, several of these planes can be identified.2. **Axes of Rotation (\(C_n\))**: These are lines about which a molecule can be rotated by \(360/n\) degrees to yield an equivalent structure. Hydrogen selenide lacks any such axes except maybe a simple \(C_2\), justifying its \(C_{2v}\) designation.3. **Center of Inversion (\(i\))**: If every part of a molecule predates to its equivalent on the opposite side through a center point, then it has a center of inversion. HDS does not possess such a feature.Recognizing these symmetry elements is crucial for defining the correct point group and understanding the physical and chemical behavior of molecules.
Molecular Conformers
The chair and boat conformers of cyclohexane offer excellent examples. The chair conformer is highly symmetrical, with \(D_{3d}\) symmetry due to its multitude of rotation axes and mirror planes, making it the more stable and prevalent structure. Meanwhile, the boat conformer, while still cyclic, bears less symmetry (\(C_{2v}\)), leading to different characteristics and reactivity.
Chemical Bonding Angles
In structures like hydrogen selenide or partially deuterated hydrogen sulfide, the angles between bonds have pronounced effects on symmetry. For instance, in the bent shape of \(\mathrm{H}_{2}\mathrm{Se}\), the bond angles fall between \(90\) and \(105\) degrees. This geometrical tension results in reduced symmetry compared to other symmetrical molecules like \(\mathrm{CO}_2\), which exhibits linear geometry. These angles not only reveal symmetry but also predict the resulting molecular interactions, stability, and reactive sites during chemical reactions.