Stereochemistry and Chirality
Optical Rotation, Optical Activity, and Specific Rotation
Last updated: May 7th, 2019 |
Optical Rotation, Optical Activity, and Specific Rotation
Here’s a quick summary of what we’ll cover here:
- Molecules that are chiral can rotate the plane of polarized light. The property of rotating the plane of polarized light is called optical activity, and it is a phenomenon that has been known for over 200 years [note]. It is not unique to molecules; some crystalline forms of quartz have it, for example. Many sugars have this property. Perhaps you have heard of dextrose? This sugar, more commonly known as glucose, rotates the plane of polarized light to the right [clockwise, or (+)]. Dextrose is said to be dextrorotatory (from Latin dexter = right)
- Another molecule with this property is fructose, which sometimes goes by another name: levulose, due to the fact that it rotates the plane of polarized light to the left [counterclockwise, or (–)]. Fructose is said to be levorotatory (from Latin laevus = left)
- Optical rotation is the extent (measured in degrees) to which a solution of a molecule will rotate plane-polarized light, as measured by a polarimeter. Optical rotation is dependent on concentration, path length, temperature, and the wavelength of light used, as well as the solvent.
- The specific rotation of a molecule is the rotation in degrees observed upon passing polarized light through a path length of 1 decimetre (dm) at a temperature T. Specific rotation is almost always reported along with the temperature, wavelength of light used, the solvent, and the concentration, since it is sensitive to these factors as well.
For a neat (i.e. undiluted) liquid, at 20°C, the formula is [α]20D = α/ l d , where α is the observed rotation in degrees, l is the length of the column in decimeters, and d is the density at the temperature T.
For a solution, at 20°C, the formula is [α]20D = α/ l c , where c is the concentration.
For example, for (S)-malic acid at a concentration of 5.5 g/ mL in the solvent pyridine at 20°C at a wavelength of 589 nm, the specific rotation is –27° . We can describe this in shorthand as [α]20D –27° (c = 5.5, pyridine). NOTE: As commenter Dr. Fred points out, dissolving 5.5 g of malic acid in 1 mL of pyridine is impossible. For historical reasons, the concentration is given in g/100 mL , and then a correction factor of 100 is applied in the numerator. (See the reference to Vogel in the footnotes).
- Enantiomers have equal and opposite specific rotations, which is why enantiomers are also sometimes called “optical isomers”. The specific rotation of (R)-malic acid is [α]20D +27° (c = 5.5, pyridine), exactly equal and opposite to that of (S)-malic acid.
- A solution containing equal amounts of two enantiomers is known as a racemic mixture. Since the rotations from both enantiomers cancel out (like two equal and opposite vectors) racemic mixtures lack optical activity.
- What is the connection between (R) and (S) and the direction of plane polarized light? For our purposes, there is no simple, straightforward correlation. It can’t be predicted from (R) or (S). It has to be measured. For example, the direction of optical rotation has been known to switch completely upon changing solvent or temperature, malic acid being a prime example. This would certainly not be true if the direction of rotation were a function of the configuration.
That’s the summary. Now let’s tell the full story.
If you’ve been learning about stereochemistry, enantiomers, and diastereomers, the following might sound familiar:
- Diastereomers have different physical properties (i.e. boiling points, melting points, solubilities)
- Enantiomers have identical physical properties* , with one exception: enantiomers rotate plane-polarized light in equal and opposite directions, which is why they are sometimes called “optical isomers”.
*(assuming an achiral environment)
[If you’re unclear on the difference between enantiomers and diastereomers, I’d suggest going back to this post, or watching this brief video which uses cats to explain the differences]
What does that term “optical rotation” mean? Or, for that matter, “optical activity”? You might also have heard of “specific rotation”. What’s that? We’ll cover all of these concepts below.
1. Louis Pasteur’s Discovery of “Left-Handed” and “Right-Handed” Tartaric Acid Crystals
Louis Pasteur is more than just the man whose name was lent to the process of “pasteurization”. He is also the father of organic stereochemistry . In 1848, Pasteur published a study on the recrystallization of various salts of tartaric acid, or “tartrates”, which are found naturally in wine (aka “wine diamonds”).
Of particular interest to Pasteur were the crystalline forms “racemic acid” (from the Latin racemus for “a bunch of grapes”), which at that time was thought to be an isomer of tartaric acid.
At the time, it was known that racemic acid did not turn the plane of polarized light, whereas “tartar”, the most common salt of tartaric acid, rotated plane-polarized light to the right [“dextrorotatory”, or (+) ]
Upon close inspection, Pasteur noticed that the potassium sodium salt of “racemic acid” crystallized in two separate crystal forms which were mirror images of each other. According to rules of crystal morphology, one type was “right handed”, and the other was “left handed” . [Maybe you’ve heard of “left-handed” and “right handed” screws? The process of naming left and right-handed crystals is similar. ]
This was a strange result, since there was no reason to think that crystals that did not themselves rotate plane-polarized light should have any chirality. Pasteur carefully arranged the crystals and discovered that one half of them were right handed and the other half were left handed. Taken into aqueous solution, the right-handed crystals were dextrorotatory (exactly like crystals of “tartar”, from wine) and the left-handed crystals were levorotatory, to precisely the same degree.
From this Pasteur postulated that the two molecules were mirror images of each other – even though it would be years before the absolute structure of tartaric acid was known, and 25 years before Van’t Hoff proposed the tetrahedral shape of carbon as a means of explaining the existence of optical isomers. [Note]
2. The Structure of The Three Isomers Of Tartaric Acid
We now know that what Pasteur called “racemic acid” was not a single compound, but in fact a mixture of two enantiomers of tartrate. Upon crystallization, the [S,S] and [R,R] enantiomers gave different crystals which Pasteur separated mechanically, i.e. by hand. [Note: in the figure below, we show “tartaric acids”; Pasteur did his work on the salts of the conjugate bases, which we call “tartrates”]
In isolation (S,S) tartaric acid rotates plane-polarized light to the left, and (R,R) tartaric acid rotates plane-polarized light to the right. Naturally occurring wine diamonds are (R,R) and thus dextrorotatory.
Thus these are called “optical isomers” in that they differ solely in the direction of their optical rotation.
By the way, Pasteur also studied a third form of tartaric acid that does not rotate plane-polarized light at all. This form was called “meso” (Greek for middle, since the light was rotated neither to the left nor the right). The configuration of the two chiral centers were subsequently determined to be (R,S).
If you’ve covered chirality at all, this term “meso” might be familiar to you. Despite having two chiral enters, “meso” tartaric acid has an internal plane of symmetry and is therefore not a chiral molecule. The name “meso” has come to denote a whole class of compounds that bear chiral centers but are not themselves chiral.
3. Do Molecules With An (R) Configuration always Rotate Plane-Polarized Light To The Right?
Sometimes you might see a molecule that rotates plane-polarized light to the right (dextrorotatory) described as (+) and a molecule that rotates plane-polarized light to the left (levorotatory) as (–).
Hence, we can have (+)-tartaric acid and (–)-tartaric acid, (+)-glucose and (–)-glucose, and (+)-morphine and (–)-morphine – all pairs of enantiomers.
We also noted that (+)-tartaric acid is (R,R) and (–) tartaric acid is (S,S).
All this begs a question. What is the relationship between the direction of optical rotation and the structure of a molecule? Are molecules with an (R) configuration always dextrorotatory, and molecules with an (S) configuration always levorotatory?
No! There is no simple way to predict the direction of rotation based on the structure. If you want to know what direction a molecule rotates polarized light, you just have to measure it.
For example, (S)-2-butanol is dextrorotatory (+)as a pure liquid, while (R)-2-butanol is levorotatory (–). If we wish, we could also describe (S)-2-butanol as (+)-2-butanol, or even (S)-(+)-2-butanol if you prefer.
4. Untangling The Differences Between R and S, D- and L- , d- and l-, and (+)- and (–)-
This of the problems with discussing a relatively old field like organic stereochemistry is that there are many layers of terminology, some obsolete, that must be peeled away.
The Cahn-Ingold-Prelog system [the origin of naming chiral centers (R) and (S) ] is a relatively new development, dating back to 1951.
(R) and (S) describe the absolute stereochemistry of chiral centers, which you can use to draw the molecule if you know the connectivity of a molecule and understand how to apply the system.
The (R,S) system only became possible once the absolute configuration of molecules could be confirmed, which itself only became possible with the development of X-ray crystallography. [Specifically, Bijouvet in 1951 determined the absolute structure of sodium rubidibum (+)-tartrate using the “heavy atom” method.]
Before the (R,S) system, we had the D, L- system, which were based on Emil Fischer’s guess of the absolute structure of (+)-glyceraldehyde, and then applied to other molecules through chemical analogy. [note 1].
For example, the levorotatory (–) form of tartaric acid (S, S) is also sometimes described as D-tartaric acid for reasons we won’t go in to here, and conversely, the dextrorotary form (R, R) is described as L-tartaric acid. You see the terms D– and L– also used for amino acids; the essential amino acids are all L.
To add to the confusion, sometimes lowercase “d” and “l” are used to abbreviate “dextrorotatory” and “levorotatory” respectively in place of (+) and (–). So we have d-tartaric acid, which is (+), and l-tartaric acid, which is (–). If we have a mixture of the two (a racemic mixture) you might see this referred to as dl-tartaric acid. Note that IUPAC has designated these terms as obsolete – use (+)/(–) instead.
5. Polarimetry: The Measurement of Optical Rotation
Let’s briefly delve into what got us into this situation in the first place: the measurement of optical rotation. It has been known since at least the 1810s that certain crystals (e.g. quartz) had chiral forms that rotated plane-polarized light in equal and opposite directions. Furthermore, solutions of glucose and turpentine were measured using this technique and shown to be optically active.
Although the equipment has changed, the technique of polarimetry is no different than it was in Pasteur and Biot’s day. The first step is to pass light through a polarizer, which only allows light with waves aligned in one direction to pass. This polarized light is then transmitted through the material to be studied, in our case a cell containing a solution of the molecule.
At the other end, a second polarizer is rotated a given angle θ until this light is transmitted through the slit. Obviously if the solution is not optically active at all, this angle will be zero.
Here is a diagram of a modern polarimeter. Image source: wikipedia
The technical details of how early scientists obtained polarized light are pretty fascinating. More detail here.
6. Specific Rotation
Now comes the final piece of the puzzle: standardization. It would be useful to have a common standard for optical rotation that allowed us to compare samples collected under slightly different concentrations and path lengths, a little bit like how earned run average (ERA) allows for comparison of performance between pitchers, or goals against average for goalies, or batting average, or quarterback passer rating… you can pick your own sports metaphor.
The term that has been developed for this is specific rotation.
The specific rotation of a molecule is the rotation in degrees observed upon passing polarized light through a path length of 1 decimetre (dm) at a concentration of 1 g/mL.
NOTE: As commenter Dr. Fred points out, in most cases dissolving a whole gram of material into a millilitre of solvent is impractical. In laboratory settings, concentration is measured in g / 100 mL and a correction factor of 100 is applied to the numerator. Values of c from the literature should be assumed to be in g / 100 mL.
For reporting purposes, the specific rotation is usually accompanied by the wavelength (often the D-line of sodium, 589 nm) and the temperature. Here’s an example for D-(+)-glucose.
7. Specific Rotation Sample Problem
Most problems involving specific rotation will ultimately just require a bit of high school algebra. “Plug and chug,” so to speak. Here’s an example:
A sample containing a single enantiomer of fluoxetine (Prozac) is placed in a polarimeter. The observed rotation is 9.06° clockwise. The sample was made by dissolving 1.24 g of fluoxetine in a solution with a total volume of 2.62 mL. The light source was a sodium D line and the temperature was 25° C. The length of the sample tube was 1.25 dm.
You can solve this problem with the following steps.
[α] = [+ 9.06° ] / [(1.24 g/ 2.62 mL)(1.25 dm)]
[α] = +15.3°
Note that we usually just report this number in degrees, although the actual units are degrees cm2 g-1
This post briefly covered some of the main details of optical rotation and specific rotation. In the next post, we’ll explore the relationship between specific rotation and a concept called “enantiomeric excess”.
Questions or comments about this post? Leave one below!
Thanks again to Matt for helping with this post. Hire Matt as your tutor!
Material in this paragraph was adapted from this excellent historical article by crystallographer Howard Flack – highly recommended. In particular, I love Pasteur’s account of demonstrating the resolution of racemic acid to his mentor, Biot: