# Cryoscopy

Under cryoscopy (from ancient Greek κρύος kryos "cold" and σκοπεῖν skopein "look") refers to a method for determination of the molar mass of substances by measuring the freezing point depression .

## Basic procedure

The freezing point of a solvent is lowered by adding soluble or miscible substances. The lowering of the freezing point in dilute solutions depends linearly on the molal concentration of the added substance: ${\ displaystyle \ Delta T}$ ${\ displaystyle {\ frac {n} {m _ {\ mathrm {L}}}}}$

${\ displaystyle \ Delta T = E_ {n} \ cdot {\ frac {n} {m _ {\ mathrm {L}}}}}$

With

• the cryoscopic constant of the solvent as a proportionality factor${\ displaystyle E_ {n}}$
• the amount of substance in the solute${\ displaystyle n}$
• the mass of the solvent.${\ displaystyle m _ {\ mathrm {L}}}$

The change in temperature only depends on the number of dissolved particles, not on their type. The lowering of the freezing point is therefore one of the colligative properties .

The following applies to the amount of dissolved substance:

${\ displaystyle n = {\ frac {m} {M}}}$

With

• the molar mass of the solute${\ displaystyle M}$
• the mass of the sample added, where: (diluted solution).${\ displaystyle m}$${\ displaystyle m \ ll m _ {\ mathrm {L}} \ Leftrightarrow {\ frac {m} {m _ {\ mathrm {L}}}} <{\ frac {1} {10}}}$

If you insert into the first equation and solve for the molar mass, you get: ${\ displaystyle n}$

${\ displaystyle M = {\ frac {m \ cdot E_ {n}} {m_ {L} \ cdot \ Delta T}}}$

The molar mass of the dissolved substance can therefore be deduced from the mass of the added sample and the resulting depression of the freezing point.

To determine the temperature difference - if necessary, in a cold mixture - first the freezing temperature of the pure solvent and then that of the solution is determined, e.g. B. with the help of the Beckmann thermometer . To do this, the temperature profile in the vicinity of the freezing point is usually determined and plotted graphically. ${\ displaystyle \ Delta T}$

With the cryoscopic determination, the possible dissociation of the added substance must be taken into account, e.g. B. Acetic acid dissociates into acetate and hydronium ions ; the dissociation effectively increases the number of particles and thus the amount of substance . In addition, in the case of concentrated solutions, the changed effective concentration must be replaced by the chemical activity of the particles . There are limits to this method for high molecular weight substances and colloidal solutions. ${\ displaystyle n}$${\ displaystyle \ left ({\ frac {m} {m _ {\ mathrm {L}}}} \ geq {\ frac {1} {10}} \ right)}$

## Procedure according to Rast

Camphor has a cryoscopic constant that is particularly large in terms of amount: -39.7 K · kg / mol. Therefore, the lowering of the freezing point of solutions in camphor is relatively large and therefore easier to measure. Since molten camphor is also a good solvent for many substances, it is particularly suitable for determining molar mass. Because cryoscopy was developed by the physical chemist Karl Rast with camphor as the solvent and with small amounts of substance, such a cryoscopic molar mass determination is called the " Rast method ". Karl Rast wrote about the advantages of the method: “A solvent has now been found in camphor [...] that opens up the possibility of using an ordinary thermometer divided into whole degrees instead of the Beckmann thermometer and taking the measurement in a melting point apparatus; Due to the minimal amounts required for this, the method takes on the character of a micro-method. ”These advantages led to camphor becoming the most frequently used solvent for determining the molar mass of newly obtained substances. The method is only suitable for substances that are not yet decomposed at the relatively high melting point of camphor (179 ° C).

## Analogous application: Ebullioscopy

The principle of increasing the boiling point , which is analogous to lowering the freezing point, also allows conclusions to be drawn about the molar mass of substances contained in solutions:

${\ displaystyle M = {\ frac {m \ cdot E_ {s}} {m_ {L} \ cdot \ Delta T}}}$

However, this procedure, called ebullioscopy , is somewhat less precise than cryoscopy because the ebullioscopy constants are smaller than the cryoscopic ones. Examples: ${\ displaystyle E_ {s}}$

${\ displaystyle E_ {s}}$ ${\ displaystyle E_ {n}}$
water 0.515 K kg / mol -1.86 K · kg / mol
Camphor 6.1 K kg / mol -39.7 K · kg / mol

• Osmometry , d. H. the determination of the concentration or the molar mass from the osmotic pressure. The concentration determined in this way was also called osmolarity .

## literature

• Gerhard Jander , Ewald Blasius: Textbook of analytical and preparative inorganic chemistry . 16th edition. S. Hirzel Verlag, Stuttgart 2006, ISBN 3-7776-1388-6 (EA Stuttgart 1952).
• Udo R. Kunze: Basics of quantitative analysis . 6th edition. Wiley-VCH, Weinheim 2009, ISBN 978-3-527-32075-2 (EA Stuttgart 1980).
• Wolfgang Gottwald, Werner Puff, Andreas Stieglitz: Physico-chemical internship . VCH, Weinheim 1986, ISBN 3-527-26498-1 , p. 28 ff.
• G. Amarell: Molecular weight determination with the Beckmann thermometer . In: GIT Labor-Fachzeitschrift , 1961, October, (also published as a special print).