Center of Symmetry
A point in space such that if a line is drawn from any part (atom) of the molecule to that point and extended an equal distance beyond it, an analogous part (atom) will be encountered. An example of point of symmetry is 1,3-trans-disubstituted cyclobutane.This symmetry element is sometimes also called "the point of inversion".Molecules which have a center of symmetry are achiral, even though they may have chiral fragments in them.
Example 1 :
Methene : It has no center of Symmetry but has plane of symmetry hence optically inactive.
Example 2 :
Ethene : It has both center of Symmetry but has plane of symmetry hence optically inactive.
Example 3 :
Ethane: It has center of symmetry as well as plane of symmetry hence optically inactive.
Example 4 :
Butadiene : It has center of Symmetry as well as plane of symmetry hence optically inactive.
Example 5 :
Cyclobutadiene : It has center of Symmetry as well as plane of symmetry hence optically inactive.
Example 6 :
Allene : It has no center of Symmetry but has plane of symmetry hence optically inactive.
Example 7 :
trans-Cyclohexane-1,4-diol : It has center of Symmetry as well as plane of symmetry hence optically inactive.
Example 8 :
Cyclohexane-1,4-dione : It has center of Symmetry as well as plane of symmetry hence optically inactive.
Example 9 :
Cubane : It has center of Symmetry as well as plane of symmetry hence optically inactive.
Example 10 :
Lactic acid : It has neither center of symmetry nor plane of symmetry hence optically inactive.