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Unformatted text preview: y using the polarimeter, they
should have equal values with opposite signs. If an equal mixture of the two enantiomers is
prepared and measured, the observed rotation will be zero. In this mixture, called a racemic
mixture, the rotation imparted by a molecule of one enantiomer is countered in an equal, but
opposite, rotation by a molecule of the other enantiomer. If the mixture is not equal, i.e., if there
is more of one enantiomer than of the other, the rotation will change, but not be zero. The value
of the rotation can be used to calculate the amount of each enantiomer in the mixture. This is
done by first calculating the optical purity or enantiomeric excess of the enantiomer in greatest
amount by the following formula.
Enantiomeric Excess = (observed specific rotation / specific rotation of pure enantiomer) x 100
(Optical Purity) The mixture then contains the EE% of one enantiomer and 100 - EE% of a racemic mixture, so
the amount of the enantiomer in excess is equal to the sum of the EE% and 1/2 (100 - EE%). The
amount of the lesser enantiomer is 1/2 (100 - EE%). Example: A mixture of the two enantiomers of 2-butanol gives a specific rotation
of -4.2°. What percent of each enantiomer is present in the mixture?
Enantiomeric excess = (observed [α] / [α] of pure enantiomer) x 100
= (-4.2° / -13°) x 100 = 32.3%
% (-)-enantiomer = 32.3 + 1/2(100 - 32.3) = 32.3 + 33.85 = 66.15%
% (+)-enantiomer = 1/2(100 - 32.3) = 33.85% Note that the specific rotation of an optically active compound is a measured physical property.
It does not have any correlation to the nomenclature conventions used to identify individual
enantiomers. A compound designated by the Cahn-Ingold-Prelog convention as R does not
necessarily rotate the plane of polarized light in a clockwise or + direction. Similarly, a
compound designated S does not necessarily rotate the plane of polarized light in a
counterclockwise or - direction. In fact, the (+)-enantiomer of 2-butanol is the S-enantiomer and
the (-)-enantiomer is the R-enantiomer....
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- Spring '07