5.8: The Polarimetry Experiment

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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 (it 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.

Diagrams of two tubes, A and B, with black dots distributed randomly throughout their interiors. Both tubes are split with dashed lines. A has five black dots in it, while B has ten black dots. — Figure \(\PageIndex{1}\): 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.

Diagrams of two tubes, A and B, with black dots distributed randomly throughout their interiors. Both tubes are split with dashed lines and have the same concentration of black dots; however, tube A is twice as long as tube B. — Figure \(\PageIndex{2}\): 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:

\[[\alpha] = \frac{\alpha}{c \times l} \nonumber\]

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.

Exercise \(\PageIndex{1}\)

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?

Answer a:

\[[a] = \frac{a}{(c)(l)} \nonumber\]

\[c = (\frac{0.250g}{2mL})(\frac{10mL}{1 dL}) = 1.25 \frac{g}{dL} \nonumber\]

\[a = \frac{0.775 ^{o} + 0.806^{o} + 0.682^{o}}{3} = 0.754 ^{o} \nonumber\]

\[[a] = \frac{a}{(c)(l)} = \frac{0.754^{o}}{(1.25 \frac{g}{dL})(0.5dm)} = + 1.21 ^{o} \nonumber\]

Answer b:

-1.21^o

Exercise \(\PageIndex{2}\)

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?

Answer

\[[a] = \frac{a}{(c)(l)} \nonumber\]

\[[a] = 32^{o} \nonumber\]

\[c = (\frac{0.150g}{1mL})(\frac{10mL}{1dL}) = 1.5 \frac{g}{dL} \nonumber\]

\[[a] = \frac{a}{(c)(l)} = 32^{o} = \frac{a}{(1.5 \frac{g}{dL})(0.5 dm} \nonumber\]

Solve for a.

\[a = + 24^{o} \nonumber\]