The chairman of the chemistry department at a pretentious local university hires
ID: 894242 • Letter: T
Question
The chairman of the chemistry department at a pretentious local university hires you to design an air freshener to mask the foul smell of the lecture hall bathrooms immediately prior to their general chemistry exams. You decide that a mixture of (R)-carvone (which smells like spearmint) and (S)-carvone (which smells like caraway) would make an excellent fragrance, and you form a solution of these compounds that meets your olfactory satisfaction. After evaporating the solvent to leave just the solid, you find that a 1.0 g sample in 0.010 L of ethanol has an observed counterclockwise rotation of 4.2 degrees through a 10 cm polarimetry cell. What is the ratio of RS enantiomers present in your solid sample? Express your answer with the lesser enantiomer having a value of 1 (e.g., 1:2.25 instead of 4:9).Explanation / Answer
Answer – We are given, mass = 1.00 g , volume = 0.010 L = 10 mL
= 4.2o, l = 10 cm = 1.0 dm
C = 1.00 g/10 mL = 0.10 g/mL
Specific rotation of the pure R-enantiomer = + 62.7o (g/mL)-1.dm-1
We know the formula for calculating the specific rotation –
[]lT = a /l*C
= 4.2o / 1.0 dm*0.1 g.mL-1
= 42o (g/mL)-1.dm-1
This is the specific rotation of mixture
Now we know enantiomeric excess (ee) formula
ee = specific rotation of mixture / Specific rotation of the pure enantiomer *100
= 42o (g/mL)-1.dm-1 / + 62.7o (g/mL)-1.dm-1 *100
= 66.98
From the enantiomeric excess (ee) another expression
ee = (%more abundance enantiomers -50)*100 / 50
66.98 = (x -50)100 /50
(x-50)100 = 50*66.98
= 3349.28
100x -5000 =3349.28
100x = 3349.28+5000
= 8349.28
x = 8349.28 /100
= 83.49 %
So there enantiomer is = 100 -83.49
= 16.51 %
So ratio of R-S enantiomer = 83.49/16.51 =5.05
So ratio is 1:5.05
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