Optical Activity: Specific vs. Observed Rotation

One of the special features of chiral molecules is that they are able to rotate plane-polarized light. Unfortunately, this means that now professors have an excuse to ask you math problems. Let’s see how this works. 

The Concept of Optical Activity

  • Clockwise rotation = dextrorotary (d) or (+)
  • Counterclockwise rotation = levororatory (l) or (-)

These random names/signs have nothing to do with the chirality of a molecule!

Enantiomeric Excess

Some more facts about optical activity:

  • Specific rotation [α] is the rotation that 100% pure enantiomers produce.
  • Opposite enantiomer = opposite rotation.
  • Racemic: A perfect 1:1 ratio of enantiomers
  • Scalemic: A non-1:1 ratio of enantiomers

Example: Calculate the ee and observed rotation for the following chiral mixture where S-enantiomer has [α] = +20.

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We can also use these equations to calculate specific and observed rotation when other variables are given to us. Just plug the numbers in! Let's try a few. 

Example: When 0.200 g of lactose is dissolved in 10.0 ml of water and placed in a sample cell 10.0 cm in length, the observed rotation is +2°. Calculate the specific rotation of lactose.

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Example: Calculate the observed rotation of a chiral mixture that contains 65% (S)-stereoisomer where the [α] of pure (S)-stereoisomer = -118.

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Example: An optically pure (R)-stereoisomer of a molecule has a specific rotation of – 20°. What specific rotation would be observed for a mixture of the (R) and (S) stereoisomer where there is an enantiomeric excess equal to (S) 60%.

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Solving for Enantiomeric Percentages

Sometimes professors will ask us to solve for exact the percentage of each enantiomer in solution. For that we’ll need some new equations. 

Example: The [α] of pure S-epinephrine is +50°. Calculate the ee of a solution with an observed value of +25°. Calculate percent of each enantiomer. Then sketch the approximate mixture in our sample polarimeter tube.

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Example: The [α] of pure S-epinephrine is +50°. Calculate the ee of a solution with an observed value of -40°. Calculate percent of each enantiomer. Then sketch the approximate mixture in our sample polarimeter tube.

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