If linearly-polarized light passes a cuvette with a chiral molecule in solution, the plane of the linearly-polarized light can rotate. Direction and value of the rotation depend on the chiral molecule itself, its configuration, and parameters like wavelength (X), concentration (c), path length (d), solvent, and temperature (T). Racemic mixtures let the light pass unrotated, since each enantiomer compensates the optical activity of the other.
The study of the rotation of linearly-polarized light caused by chiral molecules is called polarimetry. Polarimeters are composed of a monochromatic light source, a linear-polarizing filter that converts unpolarized light into linearly-polarized light, a cuvette including the chiral analyte under examination, and a detector indicating value and direction of the rotated light. By convention, rotation of the plane of linearly-polarized light to the left (counterclockwise) as viewed towards the light source gives a negative value for the rotation angle a and the medium is said to be laevo rotatory. Rotation to the right (clockwise) corresponds to a positive value for a and the medium is said to be dextro rotatory (Barron 2004).
The Biot-Savard law, given in Eq. 2.2, calculates the specific rotation [a], also called the specific optical rotatory power, of a chiral compound from the observed rotation angle a (in degrees), concentration c (in g per 100 cm3), and path length d (in dm). Unfortunately, CGS units instead of SI units are still in use, here. The specific rotation [a] is usually quoted without units.
For data comparison, the specific rotation [a] of a chiral analyte is usually measured at T = 20°C with light emitted from a sodium lamp at 589.3 nm, called the sodium D-line. Under such conditions, values for specific rotations are commonly quoted as [a]D°.
The Biot-Savard law (Eq. 2.2) corresponds to the generally known Beer-Lambert law describing the absorption of light passing a liquid solution in the form of e = Ac-1d-1 with e molar extinction coefficient and A absorption. The absorption can also be expressed as A = log10(/o//) with I0 the intensity of the incident and I the intensity of the transmitted light.
Is there any application-oriented interest to determine the specific rotation of a chiral compound? Yes, indeed, its determination is often applied to investigate the enantiomeric purity of an optically active product. The knowledge of the specific rotation is, however, not necessarily sufficient to determine the absolute configuration of a chiral molecule. To present an industrial-scale example, sugar beets, delivered by the farmer to sugar factories at the end of a year, are immediately extracted and subjected to polarimetric measurement in order to determine the optical activity indicating the sugar yield. The higher the optical activity, the higher the amount of sugar and the more the farmer will be recompensed.
The specific rotation [a] is proportional to the specific molar rotation [M] designating the optical rotation as function of the molecular weight (MW) as given in Eq. 2.3.
In Chap. 9 we will discuss how polarimetric measurements of the optical activity are used to study the origin of life's molecular asymmetry by determining minute amounts of chiral organic molecules in extraterrestrial objects such as Mars and cometary matter. Before that, we will have to find a consensus of how to classify and to name chiral molecules systematically.
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