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Solutions to Problems 99 50. (a) Ring carbons 1, 2, and 5 are stereocenters. (b) Having three stereocenters, menthol can possess up to 2³ = 8 stereoisomers. The menthol structure does not have the characteristics that might lead to achiral meso stereoisomers, so there will be eight stereoisomers in all. (c) The eight stereoisomers are shown below, in their four pairs of enantiomers, with all stereocenters labeled. R R S R S S R R R S OH OH OH OH (1R, 2R, 5R) (1S, 2S, 5S) (1S, 2R, 5R) (1R, 2S, 5S) Enantiomers Enantiomers R S R R S R S S R R S OH OH OH OH (1R, 2S, 5R) (1S, 2R, 5S) (1R, 2R, 5S) (1S, 2S, 5R) Enantiomers Enantiomers 51. (a)-(c) See solution to Problem 50, above. (d) Only menthol possesses a chair conformation in which all three substituents are equatorial. It will be the most stable isomer. Neomenthol's two alkyl groups, like those in menthol, are trans and in a 1,4 relationship in the ring. Neomenthol therefore has a conformation in which both alkyl groups are equatorial and only the relatively "small" hydroxy group is axial. Isomenthol, on the other hand, possesses cis alkyl groups, one of which therefore must be axial in any chair conformation. So the stability order is menthol > neomenthol > isomenthol 52. The problem asks for you to solve the equation below for the proportions of menthol and neomenthol: -33° = (-51°)(mole fraction menthol) + (+21°)(mole fraction neomenthol) That's one equation and two unknowns. However, if we take the information in the problem to mean that menthol and neomenthol together make up virtually 100% of Mentha oil, then their mole fractions will add up to approximately 1: mole fraction menthol + mole fraction neomenthol = Now we have two equations to use to solve for two unknowns. Using the general symbol X for mole frac- tion, substitute = 1 - so as to get -33° = + (+21°)(1 Solve to get = 75% and therefore = 25%.