Freezing point depression is a colligative property meaning that the amount of change in the freezing point depends only on the number of particles dissolved in the solution. The freezing point depression does not care what the particles are; it is only concerned with how many are there. Because of this, the measurement of the change in freezing point between a pure solvent, and a solvent with a known amount of substance in it gives an accurate, and absolute, value of the number of molecules dissolved in the solution. Knowing the mass of the solute and the freezing point of the pure solvent provides enough information to accurately calculate the Molecules per unit mass of the solute.
Each solvent has its own freezing point and with it, its own molal freezing – point constant. The molal freezing point constant is the depression in degrees Centigrade of the solvent when 1 mole of solute is dissolved in 1 kilogram of the solvent (Chemical Technician's Ready Reference Handbook, pg 435). Freezing point constants are published values available for most pure solvents.
Many people, including me way back when, do freezing point the hard way. By this I mean that we fabricated our own apparatus with test tubes, glass thermometers, a piece of wire, and an acetone plus dry ice bath. We placed our sample into the tube, immersed the thermometer with the wire looped around it then sticking out as a handle, and then froze the solution in the dry ice acetone mixture. Once frozen, we removed our apparatus and painstakenly plotted the rise in temperature moving the wire up and down to keep the temperature constant. With this plot we estimated freezing point the best we could, cleaned our device, and went on to the next sample. The process was slow, kind of fun, but fairly inacurate and not very cost effective for a commercial lab.
Enter the cryoscope; an instrument that does all this, automatically and on small samples at that. With microliter size samples up to a milliliter or so, a cryoscope accurately measures freezing point depression to thousandths of a degree centigrade on a calibrated, basically push button instrument. A single value is returned from which molecular weight is easily calculated. Hazardous solvents, such as benzene, can readily be used with little risk of analyst exposure.