Question

What would be a reason that the specific rotation of enantiomers would differ (only by a degree or so) in magnitude?

Answer 1

Hint: The specific rotation is the property of enantiomers, and can be defined as the change in orientation of plane polarized light. This is measured using a polarimeter in terms of observed optical rotation. Experimental uncertainty causes this difference.

Complete answer:
The formula used for observed optical rotation is given as - $ {\alpha _{obs}} = [\alpha ]_D^{20}cl$ , where, $c$ is the concentration in grams per ml, $l$ is the length of the tube in decimetres, and $ [\alpha ]_D^{20}$ is the specific rotation at ${20^ \circ }C$ using the D line of a sodium light source.

You can see that the value of depends on
- The concentration of the observed rotating solution.
- The length of the polarimeter
- The wavelength of the light source
- The length of the light source
- The length of most polarizers is quite the same. Use the same tube. The wavelength of the light source is a factor, but the sodium D line does not change. This leaves a factor you can control.

If you measure the temperature of the rotation, it will have an effect. Many polarizers are jacketed like condensers, so the water in a thermostatically controlled water bath maintains a constant temperature. The obvious source of uncertainty lies in your measurement of turnover.

Hence, experimental uncertainty is the reason for the difference in magnitude of specific rotation of enantiomers.

Note:
In a full-circle polarimeter, it is difficult to determine when the two halves have exactly the same brightness. Finally, there are significant uncertainties in determining the quality of the sample and making the solution into a specific volume. If all these uncertainties are in the same direction, the calculated specific rotation may change more or less by one degree.