Question

Determine the number of symmetry elements for the following molecules: (a) \(\mathrm{SO}_{2}\) (b) \(\mathrm{CCl}_{4}\) (c) \(\mathrm{Fe}(\mathrm{CN})_{6}^{3-}\) (d) \(\mathrm{H}_{2} \mathrm{O}_{2}\)

Short answer

The number of symmetry elements for the molecules are: (a) SO2 has 1, (b) CCl4 has 16, (c) Fe(CN)6 3- has 18, (d) H2O2 has 3.

Step-by-step solution

Identify symmetry elements in SO2

SO2 is a linear molecule with Sulfur in the middle, two oxygen atoms at each end. It has a reflection plane, which is the plane that bisects the molecule into two equal halves. Such a plane is also known as the plane of symmetry or mirror plane. Thus, SO2 has 1 symmetry element.

Identify symmetry elements in CCl4

CCl4 is a tetrahedrally structured molecule with Carbon at the center and four Chlorine atoms on the corners of the tetrahedron. With the Carbon atom at the center, there are 3C2 (perpendicular to C-Cl bonds), 4C3 (passing through C atom and bisecting opposite C-Cl bonds) and 3S4 (passing through C atom and bisecting opposite C-Cl bonds). It also has 6σd (bisecting the angle between adjacent C-Cl bonds). Thus, CCl4 has in total 16 symmetry elements.

Identify symmetry elements in Fe(CN)6 3-

Fe(CN)6 3- is an example of an octahedral complex. Similar to CCl4, it also has 3C2 axes, 4C3 axes and 3S4 axes. But it has more σd (8). Thus, Fe(CN)6 3- has in total 18 symmetry elements.

Identify symmetry elements in H2O2

The molecule H2O2 has a C2 rotation axis and two σv planes through O-O bond. Thus, H2O2 has 3 symmetry elements.

Key concepts

Molecular Symmetry

Molecular symmetry is a fascinating concept that dives into how molecules can be divided or arranged based on their geometric shapes. Essentially, it refers to the symmetry present in the spatial arrangement of atoms within a molecule. This symmetry can make a molecule unique in terms of its physical and chemical properties.

Let's take the molecule \(\mathrm{SO}_{2}\), for example. This molecule is linear with sulfur (S) at its center flanked by oxygen (O) atoms. The symmetry here is captured in the plane that evenly divides the molecule into two equivalent halves, known as the mirror plane or plane of symmetry.

• A molecule like \(\mathrm{CCl}_{4}\) has much more extensive symmetrical features, due to its tetrahedral structure. It includes several types of axes (denoted as C2, C3) and perpendicular reflection planes (\(\sigma_d\)).
• Even the complex \(\mathrm{Fe}(\mathrm{CN})_{6}^{3-}\), with its octahedral configuration, exhibits myriad symmetry elements similar to those found in \(\mathrm{CCl}_{4}\), but with slight differences in the number of planes it possesses.

Understanding symmetry can tell us much about how molecules interact, how they absorb light, and even predict their chemical reactivity.

Inorganic Chemistry

Inorganic chemistry primarily involves the study of inorganic compounds, which often comprise metals and non-metals. Within this field, the study of symmetry is crucial because it helps in understanding the spatial arrangement of atoms in a compound.

Symmetry plays a dominant role in interpreting the structure and behavior of compounds like \(\mathrm{CCl}_{4}\) and \(\mathrm{Fe}(\mathrm{CN})_{6}^{3-}\). Inorganic compounds can form a variety of geometrical shapes, ranging from simple linear structures to complex three-dimensional forms.

• By examining the symmetry elements within a molecule, chemists can predict bonding patterns and reactivity. For instance, octahedral complexes such as \(\mathrm{Fe}(\mathrm{CN})_{6}^{3-}\) show high symmetry, making them stable and predictable in reactions.
• In \(\mathrm{CCl}_{4}\), the tetrahedral symmetric nature allows for a uniform distribution of charge, making it relatively nonpolar.

Inorganic chemistry intertwines heavily with symmetry, making it essential for students to appreciate how spatial arrangement affects compounds' inherent properties.

Symmetry in Molecules

Symmetry in molecules refers to the balanced arrangement of atoms that obey certain rules of symmetry and geometry. It is not merely about aesthetic balance but affects how molecules behave chemically and physically. Determining the symmetry elements in a molecule involves identifying specific types of symmetry operations, such as rotations, reflections, and inversions.

For instance, in \(\mathrm{H_{2}O_{2}}\), a common substance, there's a presence of a C2 axis—meaning it can be rotated by 180 degrees to appear unchanged. It also possesses vertical reflection planes, demonstrating two \(\sigma_v\) planes that align along the molecule’s O-O bond line.

• In molecules like \(\mathrm{CCl}_{4}\), symmetry includes axes like C2, C3, and reflective planes, contributing to a total of 16 symmetry operations.
• Molecules with a high degree of symmetry, such as \(\mathrm{Fe}(\mathrm{CN})_{6}^{3-}\), have numerous symmetry elements, rendering them unique for octahedral complexes, leading to 18 distinct operations.

Understanding these symmetry elements leads to better insights into how molecules interact, form, and break bonds, which is pivotal for predicting the diverse outcomes in chemical reactions.