# Specific angle of rotation

 Specific angle of rotation ${\ displaystyle \ left [\ alpha \ right] _ {\ text {D}} ^ {25} = + 28 \ mathrm {\ (\ rho = 2; \ H_ {2} O)}}$ ${\ displaystyle \ left [\ alpha \ right] _ {589} ^ {20} = - 147 \ mathrm {\ (\ rho = 4; \ CHCl_ {3})}}$ Examples for specifying the specific angle of rotation [α] of a chiral substance including the measurement conditions. Above: positive sign, 25 ° C measurement temperature, yellow sodium light ( sodium D line ), concentration 2 g of substance dissolved in 100 ml in water. Bottom: negative sign, 20 ° C measuring temperature, 589 nm wavelength , concentration 4 g substance dissolved in 100 ml in chloroform .

The specific rotation angle , often also called specific rotation , is a physical quantity in polarimetry that indicates the optical activity of a chemical substance or its solution . The angle of rotation, also called rotation or rotation value , is a measured variable . It is determined with the help of a polarimeter and indicates the rotation of the plane of linearly polarized light when it passes through an optically active substance. ${\ displaystyle [\ alpha]}$ ${\ displaystyle \ alpha}$

## Rotation angle

The angle of rotation usually has the unit degree and a sign . If the plane of light is rotated clockwise when looking in the direction of the light source, the sign is positive (+) and one speaks of a clockwise rotation. In the opposite case, the sign is negative (-), one speaks of a left turn. Pure substances , the molecules of which have a rotating mirror axis - and only this - have an angle of rotation of 0 ° and are therefore optically inactive. Racemates (1: 1 mixtures of enantiomers ) also have a rotation value of 0 °, since the angles of rotation of the enantiomers cancel each other out. In contrast, many natural substances ( alkaloids , amino acids , terpenes , sugars etc.) are chiral and almost always occur in nature as enantiomerically pure substances that have a rotational value . ${\ displaystyle \ alpha}$${\ displaystyle \ alpha \ neq 0}$

## Specific angle of rotation

The measured angle of rotation depends on the sample used and the measurement conditions used in the polarimeter . In addition to the concentration of the chemical substance and the irradiated sample thickness, the value depends on the solvent used (if used), the temperature and the wavelength of the light source used. In order to still be able to compare substances with one another, the specific angle of rotation was introduced, which can be determined by the Biot law (according to Jean-Baptiste Biot ) as follows: ${\ displaystyle \ alpha}$${\ displaystyle [\ alpha]}$

Pure liquids:

${\ displaystyle \ left [\ alpha \ right] = {\ frac {\ alpha} {\ rho \ cdot d}}}$

Similarly for solutions:

${\ displaystyle \ left [\ alpha \ right] = {\ frac {\ alpha} {\ beta \ cdot d}}}$

With

• the measured angle of rotation ; usually in degrees${\ displaystyle \ alpha}$
• the penetrated thickness ; usually in decimeters (dm)${\ displaystyle d}$
• the density of a pure liquid; usually in grams (g) per milliliter (ml)${\ displaystyle \ rho}$
• the mass concentration of the solution; usually in grams (g) of substance per milliliter (ml) of solution${\ displaystyle \ beta}$

Like the (absolute) angle of rotation, the specific angle of rotation is also given with a positive sign (+) if the connection is clockwise, i.e. This means that the rotation is clockwise, looking against the direction of the beam. On the other hand, counterclockwise connections are given a negative sign. Mirror image isomers ( enantiomers ) therefore have the same amount but different signs.

From the unit account the above equation and the units of measurement parameters are used is for the specific rotation angle is given in degrees times milliliters per decimeter and grams (° · ml · dm -1 · g -1 ). By shortening it, you get ° cm 2 10 g −1 or rad m 2 kg −1 in SI units . It should be noted here that information in degrees or without dimensions can often be found in the specialist literature, which does not reflect the correct dimension of the specific angle of rotation. It is rather to the usual measurement conditions (° · ml · dm -1 · g -1 for pure liquids or solutions or ° · ml · g -1 · mm -1 for solids) normalized values, the citation merely under their can be correctly assigned. Even if this form of information is more convenient and widespread, it is advisable not to use it at this point because of the increased risk of incorrect assignment. ${\ displaystyle [\ alpha]}$

The wavelength of the light used and the measuring temperature are not included in the calculation of the specific angle of rotation - such a model for all substances and concentrations does not yet exist and would be very complex. The measurement conditions are instead added the specific rotation as an index or as a high number: . The indication of the temperature measurement is usually carried out in degrees Celsius (° C), therefore the value of the temperature is often provided, for example 20 to 20 ° C . Similarly, also eliminates at the wavelength of the light usually in nanometers (nm), the unit indication,: . Furthermore, the abbreviation is often used instead of the wavelength 589 nm for measurements with yellow light of the Na-D line (589.3 nm) . ${\ displaystyle \ lambda}$${\ displaystyle t}$${\ displaystyle \ left [\ alpha \ right] _ {\ lambda} ^ {t}}$${\ displaystyle t}$${\ displaystyle \ left [\ alpha \ right] _ {\ lambda} ^ {20}}$${\ displaystyle \ lambda}$${\ displaystyle \ left [\ alpha \ right] _ {589} ^ {t}}$${\ displaystyle \ left [\ alpha \ right] _ {\ text {D}} ^ {t}}$

Since the solvent used can also have a major influence on the specific rotation value (see table), this must also be specified. Because for a substance X is actually an intense quantity , but in some circumstances it depends on the concentration; therefore the concentration should be given when measuring. A solvent can also trigger chemical reactions, see mutarotation . In the single-line specification, the solvent used and the mass concentration are stated in brackets afterwards, for example for 10.3 g of L -alanine dissolved in 100 ml of water measured at 25 ° C with the light of the Na-D line: ${\ displaystyle [\ alpha]}$${\ displaystyle [\ alpha]}$${\ displaystyle \ beta}$

${\ displaystyle \ left [\ alpha \ right] _ {\ text {D}} ^ {25} = + 2 {,} 7 ^ {\ circ} \ cdot \ mathrm {\ frac {ml} {dm \ cdot g }} \ \ left (\ mathrm {H_ {2} O}, \ beta = 103 \ \ mathrm {\ frac {mg} {ml}} \ right)}$

It should also be pointed out here that the unit of concentration used is often omitted or mentioned separately.

Examples
substance concentration solvent ${\ displaystyle \ left [\ alpha \ right] _ {\ text {D}} ^ {20}}$in ° ml dm −1 g −1 source
α- D -glucose n / A water +112.2
β- D -glucose n / A water +17.5
D -glucose
in solution equilibrium
(mutarotation)
n / A water +52.5
Sucrose n / A water +66.4
Vitamin D n / A Ethanol +102.5
n / A acetone +82.6
n / A chloroform +52.0

## Molar specific rotation angle

Molar specific angles of rotation are occasionally given, as they allow a better comparison of different optically active compounds.

${\ displaystyle \ left [\ alpha \ right] _ {\ text {mol}} = {\ frac {M [\ alpha]} {100}}}$

This rotation angle is also molar rotation or Molrotation mentioned. Also , and according to IUPAC are used as symbols . ${\ displaystyle [M]}$${\ displaystyle [\ Phi]}$${\ displaystyle \ alpha _ {\ text {m}}}$

## Application in pharmacy and chemistry

With the help of the specific angle of rotation, chiral drugs can be identified and their purity controlled.

In enantioselective syntheses was formerly using the rotation angle of the optical purity  op ( English optical purity determined) of the substance produced: when the measured optical rotation at known substances - z. B. Natural materials - was identical to the highest literature rotation, the optical purity was classified as 100%. Today such analytical investigations are mostly carried out chromatographically ( thin layer chromatography according to the principle of chiral ligand exchange chromatography, gas chromatography , high pressure liquid chromatography ) using a chiral stationary phase .

In food chemistry , polarimetry is used to determine the concentration of sugar solutions ( saccharimetry ).

## literature

• H.-D. Belitz, Werner Grosch, Peter Schieberle: Food Chemistry . Springer Science & Business Media, 2009, ISBN 978-3-540-69933-0 , p. 258 ( limited preview in Google Book search - further sample values).

## Individual evidence

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2. Entry on angle of optical rotation . In: IUPAC Compendium of Chemical Terminology (the “Gold Book”) . doi : 10.1351 / goldbook.A00348 Version: 2.3.1.
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