STEREOCHEMISTRY 157 7.3 (b) There are two planes of symmetry in(2)-1, 2-dichloroethene, of which one is the plane of the molecule and the second bisects the carbon-carbon bond. There is no center of symmetry. The nolecule is achiral Planes of symmetry (c) There is a plane of symmetry in cis-1, 2-dichlorocyclopropane that bisects the C-1-C-2 bond and passes through C-3. The molecule is achiral Plane of symmetry (d) trans-1, 2-Dichlorocyclopropane has neither a plane of symmetry nor a center of symmetry. Its two mirror images cannot be superposed on each other. The molecule is chiral CI are nonsuperposable 7.4 The equation relating specific rotation [a]to observed rotation a is 100a The concentration c is expressed in grams per 100 mL and the length l of the polarimeter tube in decimeters. Since the problem specifies the concentration as 0.3 g/15 mL and the path length as 10 cm, the specific rotation [a] is 100(-0.78°) 100(0.3g/15mL10cm/10cm/dm 7.5 From the previous problem, the specific rotation of natural cholesterol is [a]=-390. The mixture of natural(-)-cholesterol and synthetic (+)-cholesterol specified in this problem has a specifi rotation[aof-13° Optical purity =%( 33.3%=%(-)-cholesterol -[100-%(-)-cholesterol 133.3%=2 %(-)-cholesterol] 66.7%=%(-)-cholesterol The mixture is two thirds natural(-)-cholesterol and one third synthetic(+)-cholesterol Back Forward Main Menu TOC Study Guide Toc Student OLC MHHE Website7.3 (b) There are two planes of symmetry in (Z)-1,2-dichloroethene, of which one is the plane of the molecule and the second bisects the carbon–carbon bond. There is no center of symmetry. The molecule is achiral. (c) There is a plane of symmetry in cis-1,2-dichlorocyclopropane that bisects the C-1@C-2 bond and passes through C-3. The molecule is achiral. (d) trans-1,2-Dichlorocyclopropane has neither a plane of symmetry nor a center of symmetry. Its two mirror images cannot be superposed on each other. The molecule is chiral. 7.4 The equation relating specific rotation [] to observed rotation is [] The concentration c is expressed in grams per 100 mL and the length l of the polarimeter tube in decimeters. Since the problem specifies the concentration as 0.3 g/15 mL and the path length as 10 cm, the specific rotation [] is: [] 39° 7.5 From the previous problem, the specific rotation of natural cholesterol is [] 39°. The mixture of natural ()-cholesterol and synthetic ()-cholesterol specified in this problem has a specific rotation [] of 13°. Optical purity %()-cholesterol % ()-cholesterol 33.3% %()-cholesterol [100 % ()-cholesterol] 133.3% 2 [% ()-cholesterol] 66.7% % ()-cholesterol The mixture is two thirds natural ()-cholesterol and one third synthetic ()-cholesterol.  100(0.78°) 100(0.3 g15 mL)(10 cm10 cm/dm) 100  cl Cl H H Cl H Cl and are nonsuperposable mirror images Cl H Cl H Cl H 1 2 3 Plane of symmetry C C Cl Cl H H Planes of symmetry STEREOCHEMISTRY 157 Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website