The chairman of the chemistry department at a pretentious local university hires

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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