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Chapter 4: Problem 3

Determine the number of symmetry operations for the following molecules: (a) \(\mathrm{S}_{8}\) (b) \(\mathrm{PF}_{5}\) (c) Ferrocene (d) \(\mathrm{PtCl}_{4}^{2-}\)

Short Answer

Expert verified
Number of symmetry operations for the molecules are: \(S_{8}\) - 36 operations, \(PF_{5}\) - 12 operations, Ferrocene - 20 operations, \(\mathrm{PtCl}_{4}^{2-}\) - 16 operations.

Step by step solution

01

Calculating Symmetry Operations for \(S_8\)

Cyclooctasulfur (\(S_8\)) is a crown-shaped molecule with an \textit{eight-membered ring} structure. It belongs to \textit{D4h} point group. Symmetry operations it provides: 2 \textit{C2 axes} (axial and equatorial), \textit{2 sigma vertical planes} (σv), \textit{4 C2' axes}, and \textit{2 sigma dihedral planes} (σd) that pass through the center of the molecule and bisect opposite S-S bonds. The result is 36 symmetry operations.
02

Calculating Symmetry Operations for \(PF_5\)

Phosphorus pentafluoride (\(PF_5\)) is a \textit{trigonal bipyramid} molecule. It falls into the \textit{D3h} point group. Notable symmetry operations are 1 \textit{C3 axis}, 3 \textit{C2 axes} perpendicularly intersecting the C3, a \textit{horizontal mirror plane} (σh), and 2 \textit{vertical mirror planes} (σv). The total number of symmetry operations for \(PF_5\) is 12.
03

Calculating Symmetry Operations for Ferrocene

Ferrocene consists of a \textit{sandwich}\ structure, with an iron atom located between two cyclopentadienyl rings. The molecule follows the \textit{D5d} point group's symmetry properties, featuring 5 \textit{C2 axes} parallel to the inter-ring axis, 1 \textit{C5 axis} (primary axis), 1 \textit{C2' axis} which passes through the iron atom, dividing the molecule into two equal halves, and more, resulting in 20 symmetry operations.
04

Calculating Symmetry Operations for \(PtCl_{4}^{2-}\)

\(\mathrm{PtCl}_{4}^{2-}\) is a \textit{square planar} molecule. It belongs to \textit{D4h} point group. It has a \textit{C4 primary axis} of symmetry and four \textit{C2 secondary axes}, two \textit{σv} planes along the Pt-Cl bonds, and two \textit{σd} planes bisecting the Pt-Cl bonds. This altogether makes up 16 symmetry operations.

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