In measuring optical rotation, plane-polarized light travels down a long tube containing the sample.  If it is a liquid, the sample may be placed in the tube as a pure liquid (its is sometimes called a neat sample).  Usually, the sample is dissolved in a solvent and the resulting solution is placed in the tube.

There are important factors affecting the outcome of the experiment.

• Optical rotation depends on the number of molecules encountered by the light during the experiment.

• Two factors can be controlled in the experiment and must be accounted for when comparing an experimental result to a reported value.

FigureSC7.1.  The effect of concentration on optical rotation.

• The more concentrated the sample (the more molecules per unit volume), the more molecules will be encountered.

• Concentrated solutions and neat samples will have higher optical rotations than dilute solutions.

• The value of the optical rotation must be corrected for concentration.

FigureSC7.2.  The effect of path length on optical rotation.

• The longer the path of light through a solution of molecules, the more molecules will be encountered by the light, and the greater the optical rotation.
• The value of the optical rotation must be corrected for the length of the cell used to hold the sample.

In summary:

[a] = a / (c x l)

• a is the measured optical rotation.
• c is the sample concentration in grams per deciliter (1 dL = 10 mL). 
• That is, c = m / V (m = mass in g, V = volume in dL).
• l is the cell length in decimeters (1 dm = 10 cm = 100 mm)
• The square brackets mean the optical rotation has been corrected for these variables.

Problem SC7.1.  A pure sample of the naturally-occurring, chiral compound A (0.250 g) is dissolved in acetone (2.0 mL) and the solution is placed in a 0.5 dm cell.  Three polarimetry readings are recorded with the sample:  0.775^o, 0.806^o, 0.682^o.

a) What is [a]?

b) What would be the [a] value of the opposite enantiomer?

Problem SC7.2.  A pure sample of the (+) enantiomer of compound B shows [a] = 32^o.  What would be the observed a if  a solution of the sample was made by dissolving 0.150 g in 1.0 mL of dichloromethane and was then placed in a 0.5 dm cell?