CHAPTER SEVEN Stereochemistry pposite directions. A solution containing equal quantities of enantiomers therefore exhibits rotation because all the tiny increments of clockwise produced by molecules of one"handedness"are canceled by an equal number of increments of anticlockwise rotation produced by molecules of the opposite handedness 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 Optical purity percent enantiomeric excess Thus, a material that is 50%o optically pure contains 75%o of one enantiomer and 25%o of Rotation of the plane of polarized light in the clockwise sense is taken as positive (+) and rotation in the anticlockwise sense is taken as a negative(-)rotation. The clas ical terms for positive and negative rotations are dextrorotatory and levorotatory, from the Latin prefixes dextro-("to the right")and levo-(to the left), respectively. At one time, the symbols d and l were used to distinguish between enantiomeric forms of a sub- stance. Thus the dextrorotatory enantiomer of 2-butanol was called d-2-butanol, and the levorotatory form 1-2-butanol; a racemic mixture of the two was referred to as dl-2- butanol. Current custom favors using algebraic signs instead, as in(+)-2-butanol, (-)-2-butanol, and(+)-2-butanol, respectively The observed rotation a of an optically pure substance depends on how many mol- ecules the light beam encounters. A filled polarimeter tube twice the length of another produces twice the observed rotation, as does a solution twice as concentrated. To account for the effects of path length and concentration, chemists have defined the term specific rotation, given the symbol [a]. Specific rotation is calculated from the observed rotation according to the expression ams per milliliter of so la lution instead of grams per where c is the concentration of the sample in grams per 100 mL of solution, and l is the length of the polarimeter tube in decimeters. (One decimeter is 10 cm Specific rotation is a physical property of a substance, just as melting point, boil ing point, density, and solubility are. For example, the lactic acid obtained from milk is exclusively a single enantiomer. We cite its specific rotation in the form [a]=+3.8% The temperature in degrees Celsius and the wavelength of light at which the measure ment was made are indicated as superscripts and subscripts, respectively PRoBLEM 7. 4 Cholesterol, when isolated from natural sources, is obtained as a single enantiomer. The observed rotation a of a 0.3-g sample of cholesterol in 15 L of chloroform solution contained in a 10-cm polarimeter tube is -0.78. Cal culate the specific rotation of cholesterol PROBLEM 7. 5 A sample of synthetic cholesterol was prepared consisting entirely of the enantiomer of natural cholesterol. a mixture of natural and synthetic cho- lesterol has a specific rotation [a] of -13. What fraction of the mixture is nat- ural cholesterol? Back Forward Main MenuToc Study Guide ToC Student o MHHE Websiteopposite directions. A solution containing equal quantities of enantiomers therefore exhibits no net rotation because all the tiny increments of clockwise rotation produced by molecules of one “handedness” are canceled by an equal number of increments of anticlockwise rotation produced by molecules of the opposite handedness. 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 one enantiomer percent of other enantiomer Thus, a material that is 50% optically pure contains 75% of one enantiomer and 25% of the other. Rotation of the plane of polarized light in the clockwise sense is taken as positive (), and rotation in the anticlockwise sense is taken as a negative () rotation. The clas￾sical terms for positive and negative rotations are dextrorotatory and levorotatory, from the Latin prefixes dextro- (“to the right”) and levo- (“to the left”), respectively. At one time, the symbols d and l were used to distinguish between enantiomeric forms of a sub￾stance. Thus the dextrorotatory enantiomer of 2-butanol was called d-2-butanol, and the levorotatory form l-2-butanol; a racemic mixture of the two was referred to as dl-2- butanol. Current custom favors using algebraic signs instead, as in ()-2-butanol, ()-2-butanol, and ()-2-butanol, respectively. The observed rotation of an optically pure substance depends on how many mol￾ecules the light beam encounters. A filled polarimeter tube twice the length of another produces twice the observed rotation, as does a solution twice as concentrated. To account for the effects of path length and concentration, chemists have defined the term specific rotation, given the symbol []. Specific rotation is calculated from the observed rotation according to the expression [] where c is the concentration of the sample in grams per 100 mL of solution, and l is the length of the polarimeter tube in decimeters. (One decimeter is 10 cm.) Specific rotation is a physical property of a substance, just as melting point, boil￾ing point, density, and solubility are. For example, the lactic acid obtained from milk is exclusively a single enantiomer. We cite its specific rotation in the form [] D 25 3.8°. The temperature in degrees Celsius and the wavelength of light at which the measure￾ment was made are indicated as superscripts and subscripts, respectively. PROBLEM 7.4 Cholesterol, when isolated from natural sources, is obtained as a single enantiomer. The observed rotation of a 0.3-g sample of cholesterol in 15 mL of chloroform solution contained in a 10-cm polarimeter tube is 0.78°. Cal￾culate the specific rotation of cholesterol. PROBLEM 7.5 A sample of synthetic cholesterol was prepared consisting entirely of the enantiomer of natural cholesterol. A mixture of natural and synthetic cho￾lesterol has a specific rotation [] D 20 of 13°. What fraction of the mixture is nat￾ural cholesterol? 100 cl 266 CHAPTER SEVEN Stereochemistry If concentration is expressed as grams per milliliter of so￾lution instead of grams per 100 mL, an equivalent ex￾pression is []  cl Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website