SYMMETRY, 2, 3 AND 6 FOLD AXIS IN BENZENE

Last Update 14/ 05/ 2000

in English/ in Esperanto/ in French/ in Portuguese

The benzene molecule is initially presented with activated button A=B=C=D=E=F showing the six carbon atoms in black balls and the six hydrogen atoms in blue. Clicking on button A=X one hydrogen will be substituted by another atom or group of atoms (in green), for example chlorobenzene. The three next buttons A=X, BOX through A=X, D=X show ortho-, meta- and para-  twice substituted benzene. The last three buttons on the same column show three substituted atoms in different positions. The green ball can represent atoms as bromine, iodine, and groups as methyl, hydroxyl and so on. Turning the molecule around the axis passing through the centre of the molecule and perpendicular to its plane it is possible to recognize if some particular symmetry axis is acting. If the same image is observed at every 60 o or 2p/6 radians of rotation the rotation axis is a six fold axis, it has a symbol 6 using Herman Margin international notation or C6 using Schoenflies notation. If the same image is repeated at rotation angles of 120 o or 2p/3 radians the axis is named three fold axis, with symbol 3 or C3 and if the repetition of the same image is at every 180o or p radians it is a two fold rotation axis with symbol 2 or C2.When the image is repeated only after a complete turn of 360o or 2p radians the symmetry axis is the trivial identity symmetry element, present in any object or molecule. The figure can be turned sequentially by a push and drag mouse action on the yellow square. Exact angles can be selected clicking on the buttons in the horizontal line.

The interested person is invited to discover the presence or absence of any symmetry axis on each of the eight kinds of molecules available in this figure.

Other symmetry axis or symmetry elements in different orientations are not studied in this page.

Symmetry operations are used in crystallography.

Bibliography

[1] Experiments in Physical Chemistry, D.P. Shoemaker, C.W. Garland and J.W. Nibler, McGraw-Hill, Inc, (1989).

[2] Inorganic Chemistry, J.E. Huheey, E.A. Keiter and R.L. Keiter, Harper Collins College Pub. (1993).

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Table of subjects.
Presentation
Chemistry Analytical Chromatography
Elemental organic analysis
Volumetric analysis, simulation
Crystallography 3 fold screw axis
4 fold inversion axis on tetrahedron
5 fold rotation axis absent in crystallography
Binary axis and reflection plane in stereographic projection
Bravais lattices
Conic sections under symmetry operators
Converting from spherical coordinates to stereographic projection
Crystal lattice and unit cell
Determination of unit cell
Elements of symmetry in action - animation
Elements of symmetry in action - cube game
Elements of symmetry in action - dodecahedron game
Elements of symmetry in action - icosahedron game
Elements of symmetry in action - octahedron game
Elements of symmetry in action - tetrahedron game
Ewald sphere and crystal measurements
Extinctions
Five classes in the cubic system
Five classes in the rhombohedral system
From tetrahedron to prism
Gnomonic projection
Improper symmetry axis
Miller indices
Miller indices - animation
Miller indices - cube game
Miller indices - octahedron game
Miller indices - rhombic dodecahedron game
Miller indices - tetrahedron game
Mirror plane
Mirror planes and Miller indices game - tetrahedron
Orientations of the cube
p2mm
Plane symmetry groups
Question on point group
Rotation axis in octahedron and Werner compounds
Rotation axis on tetrahedron and organic molecules
Rotation of objects about an arbitrary axis
Rotation of the parallel and stereographic projections of the cube
Rotation of the stereographic and parallel projection of the cube III
Seven faces in stereographic projection
Seven classes in the hexagonal system
Seven classes in the tetragonal system
Six elements of symmetry in seven orientations
Spherical projection of the octahedron
Stereographic projection
Stereographic projection of six polyhedra in different orientations
Straight line equations and symmetry elements
Symmetry, 2 fold axis
Symmetry, 2, 3 and 6 fold axis in benzene
Symmetry, 3 fold axis in the cube
Symmetry, 4 fold axis in the cube
Symmetry, 4 fold axis in the unit cell of gold
Symmetry elements and Miller indices game
Symmetry elements and Miller indices game - octahedron
Symmetry in art and in crystallography
Three classes in the monoclinic system
Three classes in the orthorhombic system
Twin crystals
Two classes in the triclinic system
Unit cell in hexagonal net
General Butane conformations
Density
Electrochemical cell
Ethane conformations
Oxidation and reduction
Resources of chemical-ICT: water, health and symmetry
Solid and liquid gold