# 2.4: Polarimetry

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.

Figure 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:

$[\alpha] = \dfrac{\alpha}{c l}$

• $$\alpha$$ 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: 0.775o, 0.806o, 0.682o.

1. What is [a]?
2. What would be the [a] value of the opposite enantiomer?
##### Problem SC7.2.

A pure sample of the (+) enantiomer of compound B shows [a] = 32o. 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?