The freezing point law

Let us consider the crystallization curve (or the freezing curve) of a dilute solution. We define the depression of freezing point d) of the solvent by 

Expanding in powers of djTl, and neglecting terms higher than the second order in 

For very dilute solutions it is sufficient to retain only the term in djT. Then, by employing the osmotic coefficient defined by (20.9) we find that (c/. 20.55) 

Analogous formulae are readily derived relating the lowering of freezing point to the molar concentrations and the molalities m of the solute species, by substituting (20.47) or (20.51) into (22.10). 

If a solution is both very dilute and ideal, we have, in terms of molalities (cf. 20.51) 

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Note that the assumption is made that the solid phase obtained on freezing the solution is pure solvent if a crystalline solution is formed, as sometimes occurs, the freezing-point law does not hold. 

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