Optical Activity

so far we learned about chirality that...

A chiral molecule exists in either of two stereoisomeric forms called enantiomers, which are related as object and nonsuperimposable mirror image. Most chiral organic molecules contain stereocenters, although chiral structures that lack such centers do exist. A molecule that contains a plane of symmetry is achiral.

Optical activity is the ability of a chiral substance to rotate the plane of plane-polarized light and is measured using an instrument called a polarimeter.

The light used to measure optical activity has two properties: it consists of a single wavelength and it is plane-polarized. The wavelength used most often is 589 nm (called the D line ), which corresponds to the yellow light produced by a sodium lamp.
when a plane-polarized light, is passed through a sample of one of the enantiomers, the plane of polarization of the incoming light is rotated in one direction (either clockwise or counterclockwise). When the same experiment is repeated with the other enantiomer, the plane of the polarized light is rotated by exactly the same amount but in the opposite direction.

An enantiomer that rotates the plane of light in a clockwise sense as the viewer faces the light source is dextrorotatory (dexter, Latin, right), and the compound is (arbitrarily) referred to as the (+) enantiomer. Consequently, the other enantiomer, which will effect counterclockwise rotation, is levorotatory (laevus, Latin, left) and called the (-) enantiomer.

 Figure : Measuring the optical rotation with a polarimeter.

A substance that does not rotate the plane of polarized light is said to be optically inactive. All achiral substances are optically inactive.

When light travels through a molecule, the electrons around the nuclei and in the various bonds interact with the electric field of the light beam. If a beam of plane-polarized light is passed through a chiral substance, the electric field interacts differently with, say, the “left” and “right” halves of the molecule. This interaction results in a rotation of the plane of polarization, called optical rotation; the sample giving rise to it is referred to as optically active.

The angle of rotation of the plane of polarization is measured by aligning another polarizer — called the analyzer — so as to maximize the transmittance of the light beam to the eye of the observer. The measured rotation (in degrees) is the observed optical rotation, [alpha], of the sample. Its value depends on the concentration and structure of the optically active molecule, the length of the sample cell, the wavelength of the light, the solvent, and the temperature.
To avoid ambiguities, chemists have agreed on a standard value of the specific rotation, [alpha], for each compound. This quantity is defined as;

To be optically active, the sample must contain a chiral substance and one enantiomer must be present in excess of the other.
Mixtures containing equal quantities of enantiomers are called racemic mixtures.
Racemic mixtures are optically inactive. Conversely, when one enantiomer is present in excess, a net rotation of the plane of polarization is observed. At the limit, where all the molecules are of the same handedness, we say the substance is optically pure. Optical purity, or percent enantiomeric excess, is defined as:

Optical purity = percent enantiomeric excess 
                       = Percent of major enantiomer  - Percent of minor enantiomer.

Thus, a material that is 50% optically pure contains 75% of one enantiomer and 25% of the other.

Enantiomer excess (ee) = % of major enantiomer - % of minor enantiomer

Since a racemate constitutes a 1:1 mixture of the two (ee = 0), the ee is a measure of how much one enantiomer is present in excess of racemate. The ee can be obtained from the % optical rotation of such a mixture relative to that of the pure enantiomer, also called
optical purity:

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