Optical Activity
Optical Activity
There are very few differences between enantiomers of chiral compounds. They have the same melting points, the same boiling points, and the same IR spectra. One difference they do have is that they rotate plane-polarized light in different directions. This rotation of plane polarized light is called optical activity. This rotation of plane polarized light is detected in an instrument called a polarimeter.
Plane Polarized Light
Most light you encounter is not polarized. The electromagnetic waves vibrate in all directions. But, if this unpolarized light passes through a polarized filter, the light vibrates in only one direction. This light that vibrates in only one direction is plane-polarized light. Polarizing filters that are aligned in parallel allow light to pass through them. If polarizing filters are aligned perpendicularly, light cannot pass through them. This is useful for us to analyze how the plane-polarized light is rotated.
Polarized lenses aligned parallel and perpendicular to each other
Polarimeter
A polarimeter is an instrument that lets us tell how a chiral sample rotates plane-polarized light. A light source emits unpolarized light. This light passes through a polarizing filter. The plane-polarized light transmits through a sample tube containing the chemical sample. Typically, the chemical sample is an enantiomer or a mixture of enantiomers. The rotated plane-polarized light that transmits through the sample tube is invisible; we cannot see it with our eyes. The way it is analyzed is by using a polarizing filter. This analyzing filter is rotated until a maximum amount of light comes through it. This angle we turn this filter is equal to the angle of the plane-polarized light.
A polarimeter
If an enantiomer in the sample tube rotates the plane-polarized light to the right (clockwise), that enantiomer is called dextrorotatory (Latin: dexter = right). These enantiomers may also be called d or +. If an enantiomer in the sample tube rotates the plane-polarized light to the left (counterclockwise), the enantiomer is called levorotatory (Latin: laevus = left). These enantiomers may also be called l or -.
Why does an enantiomer rotate plane-polarized light?
When plane-polarized light enters an enantiomer, it encounters an unsymmetrical set of atoms with an unsymmetrical amount of electrons around the atoms. This helical electron density that is encountered rotates the electromagnetic wave of the plane-polarized light. The mirror image enantiomer has the exact opposite helical electron density and therefore rotates the plane-polarized light in the opposite direction (with the same amount of rotation). The helical electron density is what determines the rotation of light. This rotation must be determined experimentally. The (R) or (S) designation does not tell us which way the plane-polarized light will rotate. This is because the (R) or (S) designation is an accounting trick. It doesn’t necessarily correspond to electron density. So, don’t assume the optical rotation unless the experiment is done.
Enantiomers rotate plane polarized light in opposite directions
Specific Rotation
How much an enantiomer rotates plane-polarized light can be useful information about a compound. The length of the sample tube affects the amount the light rotates (the longer the tube is, the more it can rotate the light). The concentration of the enantiomer solution in the sample tube also affects the amount the light rotates (the more concentrated it is, the more it will rotate the light). Chemists have devised a standard way to measure this rotation. This standardized rotation is called specific rotation [α]. If the specific rotation is being very carefully measured, the color of light used and the temperature can affect the rotation. For example, you may see the specific rotation for a dextrorotatory enantiomer written as:
The superscript, 25, means the rotation was observed at a temperature of 25°C. The subscript, D, means the D line of a sodium lamp (λ = 589.6 nm) was used. This is a yellow color of light.
The dextrorotatory enantiomer always has a + specific rotation. The levorotatory enantiomer always has a – specific rotation.
Typically, the polarimeter contains a 1-decimeter (10-centimeter) long sample tube. The concentration of the enantiomer in the tube is 1 g/mL.
If these conditions vary, the following equation can be used to correct for it.
[α] = specific rotation (degrees)
α = observed rotation (degrees)
c = concentration (in g/mL)
l = the length of the sample tube in decimeters (1 decimeter = 10 centimeters)
If the dextrorotatory form of an enantiomer has a specific rotation of +15°, the levorotatory form of the mirror image enantiomer has a specific rotation of -15°.
Example:
Question: The specific rotation of (S)-2-butanol is -13.5°. What is the specific rotation of (R)-2-butanol?
Answer: (R)-2-butanol = +13.5°. We would call this (R)-(+)-2-butanol.
10. Without looking it up, would we predict (R)-2-bromobutane to be dextrorotatory or levorotatory?
Racemic mixture
What happens if we have an equal amount of the dextrorotatory and levorotatory enantiomers in the polarimeter’s sample tube? A solution with equal amounts of d and l enantiomers is called a racemic mixture or a racemate. A racemic mixture of 2-butanol could be called (±)-2-butanol or (d,l)-2-butanol. If there is a racemic mixture of 2-butanol, d-2-butanol would rotate the plane-polarized light to the right and l-2-butanol would rotate the plane-polarized light equally to the left. The net effect will be a 0° rotation of the light.
How racemic mixtures bend plane polarized light
Enantiomeric Excess
A racemic mixture of two enantiomers rotates plane polarized light 0°, but what happens if there is not an equal mixture of the two enantiomers? What if there is a more of one enantiomer than the other. In this case, there is an excess of one enantiomer. If there is more of the d-enantiomer, the light will rotate more to the right and will give an overall rotation to the right (+). If there is more of the l-enantiomer, the light will rotate more to the left and will give an overall rotation to the left (-). How much more of one enantiomer there is over the other is called the enantiomeric excess, e.e.
The enantiomeric excess (e.e.) is measured by the following equation:
Example 1
There is 98% of the d-enantiomer and 2% of the l-enantiomer in a mixture. What is the enantiomeric excess of d over l?
Example 2
A mixture contains 7 grams of the l-enantiomer and 3 grams of the d-enantiomer. What is the enantiomeric excess of l over d?
Example 3
A pharmaceutical company developed a new drug that was produced in 98% e.e. The d-enantiomer was produced in excess. This drug mixture contains how much of the d-enantiomer and how much of the l-enantiomer?
Answer: There is 99% of the d-enantiomer and 1% of the l-enantiomer.
Notice, the difference between the two percentages is 98%. The common wrong answer a student might make here is 98% of d and 2% of l. This is NOT the case as this mixture would give 96% e.e, not 98%.
How can we experimentally measure the e.e. of a mixture?
If we know the specific rotation of a compound, we can find the enantiomeric excess using a polarimeter.
For example, (R)-(+)-2-butanol has a specific rotation of +13.5°. If we have a racemic mixture of (±)-2-butanol (equal amounts), the rotation in the polarimeter would be 0°. If we have 100% of (+)-2-butanol, the rotation in the polarimeter would be +13.5°. What if the polarimeter gave a result of +5.4°? We would know that there is a little more of (+)-2-butanol than (-)-2-butanol because the rotation is positive. We can tell that the polarimeter only rotated 40% of the way to +13.5° (+5.4/+13.5 X 100% = 40%). The e.e. is therefore 40%. So, the excess of (+) over (-) is 40%. We could quickly determine that we have 70% of (+)-2-butanol and 30% of (-)-2-butanol.
11. What is the enantiomeric excess of a mixture of 80% dextrorotatory enantiomer and 20% levorotatory?
12. What is the enantiomeric excess of a mixture of 1.2 grams of levorotatory enantiomer and 0.8 grams of dextrorotatory?
13. What percentage of the dextrorotatory enantiomer is in a sample that is 50% enantiomeric excess of the d-enantiomer?
Answers
10. We cannot tell from the (R) or (S) designation only. Just because the Cahn-Ingold-Prelog arrow is clockwise or to the right for (R), it has no bearing on if the compound is d or l. The experiment needs to be performed. (R)-2-bromobutane is levorotatory with a specific rotation of -23.1°.
11. 60% e.e. of dextrorotatory.
12. 20% e.e. of levorotatory.
13. 75% e.e. of d-enantiomer (25% of l-enantiomer)