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  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    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 \(\PageIndex{1}\): 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.
    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.


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

    • \(\alpha\) 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.

    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: 0.775o, 0.806o, 0.682o.

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


    Exercise \(\PageIndex{2}\)

    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?



    This page titled Polarimetry is shared under a CC BY-NC 3.0 license and was authored, remixed, and/or curated by Chris Schaller.

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