Experiment 09 · Theory
Specific Rotation
A sugar solution looks like water and behaves like water in almost every way you could test by eye. Send plane polarized light through it and something else happens: the plane the light vibrates in comes out turned through an angle. How far it turns depends on how much sugar is dissolved in it, which is why a polarimeter can weigh out sugar without touching the solution.
Polarization of light
Light is a transverse electromagnetic wave, so its electric field vibrates at right angles to the direction it travels in. In ordinary light those vibrations point every possible way around the line of travel, changing from one instant to the next. That is unpolarized light.
Restrict the vibrations to a single plane containing the direction of travel and the light is plane polarized. The plane holding the direction of vibration is the plane of polarization. A Nicol prism or a Polaroid sheet will do the restricting: it passes light vibrating along one particular direction and absorbs the rest.
Optical activity
Put certain substances in the path of plane polarized light and they turn the plane about the direction of travel through a definite angle. The property is called optical activity and the substances are called optically active.
The cause is molecular. A chiral molecule has no plane of symmetry, so it cannot be laid over its own mirror image. Plane polarized light can be treated as two circularly polarized components turning in opposite senses, and a chiral medium presents a slightly different refractive index to each of them. One component falls behind the other, and when they recombine the plane of vibration has swung round.
| Kind | Direction of rotation | Examples |
|---|---|---|
| Dextrorotatory (d) | Clockwise, to an observer facing the oncoming light | Cane sugar solution, quartz cut one way |
| Levorotatory (l) | Anticlockwise, to the same observer | Fructose solution, turpentine oil |
Cane sugar is dextrorotatory, so every reading in this experiment moves the same way along the scale and the angle grows with the concentration.
Specific rotation
The angle a solution turns the plane through is not a property of the substance on its own. It depends on how concentrated the solution is, how far the light has to travel through it, the wavelength of that light and the temperature. To describe the substance rather than the sample, all of that is divided out and what remains is the specific rotation.
Specific rotation is the rotation in degrees produced by a solution of unit concentration, one gram per millilitre, over a path length of one decimetre, at a stated temperature and wavelength.
Rearranged, that says θ = [α] l C, which is Biot's law: the rotation is proportional to the length of the column and to the concentration of the solution. Both proportionalities are worth having. Fix the concentration and the angle tells you the path length; fix the path length and the angle tells you the concentration, which is how a sugar refinery uses one.
The tube in this experiment is 20 cm long, so l is 2 dm, and the chart writes the same formula with the tube measured in centimetres instead:
The half-shade polarimeter
A polarimeter is a monochromatic source, a lens to gather its light into a parallel beam, a polarizer to make that light plane polarized, the half-shade device, a glass tube to hold the solution, and an analyzer on a graduated circle with a telescope behind it. Both polarizer and analyzer are Nicol prisms. The analyzer is the one that turns, and the circle is what the angle is read from. The telescope is there so the two halves of the field are seen sharply enough to be compared.
The half-shade device is the part that makes the measurement possible. It is a semicircular quartz plate joined along a diameter to a semicircular glass plate. The quartz half is cut to act as a half-wave plate and turns the plane of polarization of the light crossing it; the glass half leaves the plane alone. Light leaving the two halves is therefore polarized in two planes inclined at a small angle to each other, and the field of view is split down the middle into two halves that can be compared.
How a reading is taken
- Light from the sodium lamp passes the polarizer and comes out plane polarized.
- It crosses the half-shade plate and emerges as two beams polarized in slightly different planes, one from each half.
- With the tube full of distilled water, the analyzer is turned until the two halves of the field look equally illuminated. That setting is the analyzer bisecting the angle between the two planes, and the scale reading there is θ1, the zero of the instrument.
- The tube is refilled with the sugar solution. Both beams have their planes turned through the same angle θ, the match is spoiled, and one half of the field goes brighter than the other.
- The analyzer is turned again until the halves match. The new reading is θ2, and θ2 − θ1 is the rotation the solution produced.
There are two settings 90° apart where the halves match. At one of them both are bright and at the other both are equally faint (dull bright). The faint setting is the one to use. Near extinction a small turn of the analyzer changes the brightness of each half by a much larger fraction, so the position where they stop differing is pinned down far more tightly.
Getting the specific rotation out of it
Each concentration gives one value of θ, and dividing it by l × C gives one value of S. Taking four concentrations and averaging is the analytical result.
The graph is the better route. Plot θ up the y-axis against C along the x-axis and Biot's law says the points lie on a straight line through the origin. Its slope is θ/C, and dividing the slope by the length of the column in decimetres gives S. A slope drawn through four points is less at the mercy of any single misread setting than four separate divisions are, and the line passing through the origin is itself a check that nothing systematic has gone wrong.