Question

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

Answer 1

The usual reason is experimental uncertainty.

Explanation:

The formula for observed optical rotation is

`α_"obs" = [α]_D^20cl`

where `c` is the concentration in grams per millilitre, `l` is the length of the tube in decimetres, and `[α_"D"^20]` is the specific rotation at 20 °C using the D line of a sodium light source.

You can see that the value of `[α]` depends on

• the observed rotation
• the concentration of the solution
• the length of the polarimeter tube
• the temperature
• the wavelength of the light source

Most polarimeter tubes are quite consistent in length, and you probably used the same tube for both measurements, anyway.

The wavelength of the light source is a factor, but the sodium D line doesn't vary.

That leaves factors that you can control

If the temperature was different when you measured the rotations, that would have an effect.

Many polarimeter tubes are jacketed like a condenser, so that water from a thermostatically controlled water bath keeps the temperature constant. Was yours?

Obvious sources of uncertainty are in your measurement of the rotation.

In a full-circle polarimeter, it is difficult to decide when the two halves have exactly the same brightness.

Finally there are the obvious uncertainties in determining the mass of the sample and in making the solution to a specific volume.

If all these uncertainties happen to be in the same direction, the calculated specific rotations could vary by a degree or so.