Specific rotation observed

One of the terms for describing enantiomer composition is optical purity. It refers to the ratio of observed specific rotation to the maximum or absolute specific rotation of a pure enantiomer sample. For any compound for which the optical rotation of its pure enantiomer is known, the ee value may be determined directly from the observed optical rotation. 

For a nonracemic mixture of enantiomers prepared by resolution or asymmetric synthesis, the composition of the mixture was given earlier as percent optical purity (equation 1), an operational term, which is determined by dividing the observed specific rotation (Mobs) of a particular sample of enantiomer with that of the pure enantiomer ( max), both of which were measured under identical conditions. Since at the present, the amount of enantiomers in a mixture is often measured by nonpolarimetric methods, use of the term percent optical purity is obsolete, and in general has been replaced by the term percent enantiomeric excess (ee) (equation 2) introduced in 197163, usually equal to the percent optical purity, [/ ] and [5] representing the relative amounts of the respective enantiomers in the sample. 

Similarly, establishment of a furanoid ring in a compound of undetermined structure was applied by Green and Pacsu82 to ethyl 1-thio-a-D-glucofuranoside the observed specific rotation of this compound in aqueous... 

For a medium with a standard concentration of identical noninteracting chiral molecules, the molecular OR parameter [i can be directly converted to the observed specific rotation via... 

For example, the observed specific rotation of the racemic mixture is -(-8.52 degrees of rotation. The specific rotation of the pure S-enantiomer is —15.00 degrees of rotation. Since the pure S-enantiomer has —15.00° and the specific rotation of mixture is -(-8.52°,... 

Enantiomeric excess or % ee (or % optical purity) = [observed specific rotation] divided by [specific rotation of pure enantiomer] X 100. Note that there are examples where the linear relationship between enantiomeric excess and optical rotation fails. A percent enantiomeric excess (% ee) of less than 100% indicates that the compound is contaminated with the other enantiomer. The ratio of enantiomers in a sample of known (measured) optical purity may be calculated as follows fraction of the major isomer = [(% ee) + 0.5 (100 - % ee)]. Thus,... 

Optical purity (op, % op) The ratio of the observed specific rotation of a substance to the maximum possible rotation of the substance, expressed as a percent ... 

Whether a particular sample consists of a single enantiomer or a mixture of enantiomers can be determined by its observed specific rotation. For example, an enantiomerically pure sample—meaning only one enantiomer is present—of (5)-(+)-2-bromobutane will have an observed specific rotation of -1-23.1° because the specific rotation of (6)-(-l-)-... 

For example, if a sample of 2-bromobutane has an observed specific rotation of +9.2°, its optical purity is 0.40. In other words, it is 40% optically pure—40% of the mixture consists of an excess of a single enantiomer. 

Because the observed specific rotation is positive, we know that the solution contains excess (5)-(+)-2-bromobutane. The enantiomeric excess (ee) tells us how much excess (5)-(+)-2-bromobutane is in the mixture. As long as the compound is chemically pure, enantiomeric excess and optical purity will be the same. 

Mandelic acid has a specific rotation of +158°. What would be the observed specific rotation of each of the following mixtures ... 

McCasland, G. E. Proskow, S. /. Am. Chem. Soc. 1955,77,4688 1956,78,5646. It is interesting to note that 22 was reported to be "optically inactive within experimental error." The observed specific rotation of 22 was found to be [ajj + 0.012° (water, c 5,1 0.5) when prepared from one precursor and [a]o -0.027° when prepared from the enantiomeric precursor. The small optical achvities apparently resulted from trace impurities in the final products. 

Optical purity (Section 5.9B) A percentage calculated for a mixture of enantiomers by dividing the observed specific rotation for... 

Quantitative Distribution of Adducts as a Function of Dienophile Stereochemistry. For accurate quantitation of the isomer distribution in the products of cycloaddition to each of the dienophiles 5—8, the entire mixtures of the four stereoisomeric products in each instance were first subjected to sequential Q-deacetylation and periodate oxidation to afford a mixture of two aldehydo esters 29 and 30, which upon reduction with LiAlH afforded trans-2-norbornene-5,6-dimethanol as an unequal mixture of the two enantiomers (only the 5S,6g enantiomer is shown). NMR analysis of the mixture of 29 and 30 showed distinctive resonances for the CH3O and CHO groups in exo and endo orientations, permitting accurate determination of the endo/exo ratio of the products in the mixture. The observed specific rotation of the diol, in comparison with that (+23 ) determined for the enantiomerically pure 5S,6S diol 26 (and its enantiomer), provided a quantitative measure of the si.re diastereofacial selectivity. 

The instructor may ask you to combine your remaining resolved naproxen with other students for determining the rotation of your (S)-naproxen by polarimetry. If so, your instructor will supply instructions. (S)-Naproxen has an observed specific rotation of +66°. The solvent, chloroform, will be used as the solvent, unless you are told otherwise. Calculate the % optical purity (% enantiomeric excess) for your sample and compare the results with the chiral HPLC results. Remember that the sample may only contain about 82% of the (S) enantiomers (Technique 23, Section 23.5) so you will not obtain a value of +66° from the polarimeter. 

Often, it is difficult to apply the previous equation because you do not know the exact amount of each enantiomer present in a mixture. It is far easier to calculate the optical purity (ee) by using the observed specific rotation of the mixture and dividing it by the specific rotation of the pure enantiomer. Values for the pure enantiomers can sometimes be found in literature sources. 

The specific rotation of optically pure adrenaline in water (at 25°C) is —53. A chemist devised a synthetic route to prepare optically pure adrenaline, but it was suspected that the product was contaminated with a small amount of the undesirable enantiomer. The observed specific rotation was found to be —45°. Calculate the % ee of the product. 

Optical purity (Section 5.9B) A percentage calculated for a mixture of enantiomers by dividing the observed specific rotation for the mixture by the specific rotation of the pnre enantiomer and multiplying by 100. The optical purity equals the enantiomeric purity or enantiomeric excess. 

For example, if a sample of (5)-(-l-)-2-bromobutane is enantiomerically pure (meaning only one enantiomer is present), it will have an observed specific rotation of -1-23.1 because its specific rotation is -1-23.1. If, however, the sample of 2-bromobutane is a racemic mixture, it will have an observed specific rotation of 0. If the observed specific rotation is positive but less than -1-23.1, we will know that the sample is a mixture of enantiomers and that the mixture contains more of the S enantiomer than the R enantiomer, because the S enantiomer is dextrorotatory. 

Solution One mmol (10 mL X 0.10 M) of the R enantiomer is mixed with 3 mmol (30 mL X 0.10 M) of the S enantiomer 1 mmol of the R enantiomer plus 1 mmol of the S enantioma- will form 2 mmol of a racemic mixture, so there will be 2 mmol of S enantiomer left over. Because 2 out of 4 mmol is excess S enantiomer, the solution has a 50% enantiomeric excess. Knowing the enantiomeric excess and the observed specific rotation allows us to calculate the specific rotation. 

Calculate the equilibrium ratio of a- and j8-glucopyranose (which has been given in the text) from the specific rotations of the pure anoints and the observed specific rotation at mutarotational equilibrium. 

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