Optical Activity Enantiomers have virtually identical physical properties. Exactly how do they differ from each other? Solutions of them rotate planepolarized light in opposite directions. They react with enzymes differently (actually, one usually reacts and the other does not). Plane-Polarized Light Light with an E (or H) field that oscillates in a single plane. Figure 5-10. Schematic diagram of a polarizing filter. Polarimeter A solution of a pure enantiomer rotates plane-polarized light. Figure 5-13. Schematic diagram of a polarimeter. Optical Activity-Designation A solution of a pure enantiomer that rotates plane-polarized light to the left (CCW) is designated (-) or l (levorotatory) right (CW) is designated (+) or d (dextrorotatory) These do NOT correlate with (R) and (S)! Specific Rotation The specific rotation [α] of a solution of a pure enantiomer is [α] = α(observed) c l where c is the concentration of enantiomer in g/mL and l is the length of the sample cell in dm. Specific Rotation A solution of 0.5 g of (-)-epinephrine dissolved in 10 mL of dilute HCl was placed in a 20-cm polarimeter tube. Using the sodium D line, the rotation was found to be -5.0° at 25°C. Determine the specific rotation of epinephrine. [α] = α(observed)/(c l) = -5.0°/[(0.5 g/10 mL)(20 cm x 0.1 dm/1 cm) ] = -5.0°/[(0.05 g/mL)(2.0 dm)] = -5.0°/0.10 = -50.° [ ] 25 D 50 . Racemic Mixture A 50/50 mixture of enantiomers. Since solutions of pure enantiomers rotate plane-polarized light in opposite directions, a 50/50 solution will NOT rotate plane-polarized light. The solution is optically inactive. A racemic mixture is also called a racemate a (d,l) pair a (±) pair Other Mixtures of Enantiomers % _ optical _ purity 100 ( observed _ rotation ) ( rotation _ of _ pure _ enantiomer ) % _ enantiomer ic _ excess 100 |d l| |d l| If the mixture contains only the pure enantiomers, these two equations give the same value. If the mixture contains other optically active compounds, op will differ from ee. Enantiomeric Excess (e.e.) Problem 5-12: When optically pure (R)-(-)-2bromobutane is heated with water, 2-butanol is the product. Twice as much (S)-2-butanol forms as (R)-2-butanol. Find the e.e. and the observed rotation of the product. [α]=13.50° for pure (S)-2butanol. Let x = amount of (R) enantiomer formed e.e. = 100 |d-l|/|d+l| = 100 |2x-x|/|2x+x| = 100 (1/3) = 33% Using Optical Purity Since 2-butanol is the only product, e.e. = o.p. Since o.p. = 100 (observed rotation)/(rotation of pure enantiomer) 33 = 100 (observed rotation)/ 13.50° observed rotation = 33(13.50)/100 = +4.5° The predominance of the (S)-(+)-2-butanol causes the specific rotation of the solution to be positive. Specific Rotation of a Mixture Sucrose is a disaccharide of D-glucose and Dfructose. Sucrose has a specific rotation of +66.5°. When sucrose is hydrolyzed by an invertase, a mixture of glucose (C6H12O6, +52.7°) and fructose (C6H12O6, -92.4°) results and the observed rotation of the mixture is (-). Because of this, the mixture is called an invert sugar. Can you calculate the specific rotation of invert sugar? (-39.7º, since glucose and fructose have the same molar mass.) Chirality of Conformationally Mobile Systems A molecule cannot be optically active if its chiral conformations are in equilibrium with their mirror images. Chirality of Conformationally Mobile Systems Such enantiomers are in equilibrium with each other through ring flipping. One enantiomer cannot be separated from the other. Chirality of Conformationally Mobile Systems To determine whether a conformationally mobile molecule can be optically active, consider tis most symmetric conformation. cis-1,2-dibromocyclohexane is achiral…is the trans isomer achiral? Chirality of Conformationally Mobile Systems Chiral or achiral? Optically active or optically inactive? Enantiomers with No Chiral Carbon Atoms Conformers that cannot interconvert (due to steric hindrance) can be enantiomers. Enantiomers with No Chiral Carbon Atoms H2C=C=CH2 is allene. A disubstituted allene can be chiral, because the substituents are in perpendicular planes. Why aren’t all the H’s and Cl’s in the same plane?