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Specific Rotation |
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Calculating Specific Rotation Specific rotation, [a], can be accurately determined from net optical rotation measurements by using a gaussian peak model and having knowledge of the injected mass of the optically active enantiomer. We have included in the web site a tutorial that demonstrates this technique using phenylalanine as an example. You can download the example's worksheet by clicking on its Hyperlink, either here or from the tutorial. This technique is applicable to HPLC, SFC, CE or FIA when a symmetrical peak is observed. The basic equation for specific rotation is given below :
In this equation, R is the enantiomer's peak height in degrees, using the Faraday effect. c is the concentration of the optically active material in the detector's flow cell at the time of maximum peak height. The concentration can be detemined as follows :
To simplify the process, the bracketed term can also be obtained from standard tabulations of a normal distribution. Thus, with knowledge of the flow cell dimensions, the mass of the sample injected and a normal distribution table, [a ] can be determined at previously unavailable levels of precision, accuracy and sensitivity. An Example Here we present, as an example, the calculation of specific rotation for an observed gaussian peak using the PDR-Chiral Detector. An injection of 0.01 mg of an optically active enantiomer produced an observed rotation of -838 mdegrees with a peak width at half-height of 0.19 minutes. First,
we calculate the peak volume by multiplying the flow rate times the peak width
at half-height. Next, we divide the peak volume
by 2.354 to calculate the standard deviation. Then transform the standard deviation into the gaussian probability variable "z" by dividing one-half the flow cell volume (56 ml) by the standard deviation.[e.g. (56 ml x 0.5) / 82.1 ml = 0.3409] Next, we use a standard, normal distribution table to convert the gaussian probability variable to the gaussian probability factor. [e.g. 0.3665] However, many tabulations are one-sided and you will need to multiply the gaussian probability factor by 2 to calculate the gaussian fraction "under the curve" from +z to �z. Furthermore, many tabulations give the excluded area. While this may be more appropriate for probability analysis, we must subtract the product from 1 to get the included area. For example, the above
calculated gaussian probability factor of 0.3665 will yield a gaussian fraction
of 0.267. Next, calculate the observed rotation from the sample's peak height. Note that the PDR-Chiral Detector is calibrated to 40,000 microdegrees per volt. As a convenient internal reference, the CAL 1 peak is �100 microdegrees, and the CAL 2 peak is +1000 microdegrees. Finally, the specific rotation ([a]) is then calculated from the observed rotation (- 838 mdegrees), the flow cell volume (56 ml), the flow cell length (0.517 dm), the injected mass (1x10-5 g) and the gaussian fraction (.267) according to the equation below.
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