ΔTF = TF (pure solvent) - TF (solution) = TF (water) - TF (wine)
KF = cryoscopic constant, for water = 1.853 K·kg/mol
m = molality (mol solute per kg of solvent)
i = van 't Hoff factor (number of solute particles per mol), for alcohol i = 1.
Molar mass (g/mol) of alcohol (ethanol), CH3–CH2–OH
= 2 x 12.0107 + 5 x 1.00794 + 15.9994 = 46.06844 g/mol
For ice wine of 6% of alcohol, per 100g of wine
the mole of ethanol = 6/46.06844 = 0.13024
the mass of water = 0.094 kg
molality, m = 0.13024/0.094 = 1.38553
TF (wine) = 0 (=-273K) - 1.853 x 1.386 x 1 = -2.568°C
Freeze distillation
A process of enriching a solution by partially freezing it and removing frozen material that is poorer in the dissolved material than is the liquid portion left behind. Such enrichment parallels enrichment by true distillation, where the evaporated and recondensed portion is richer than the liquid portion left behind. Freeze distillation is a kind of partial crystallization of liquid.
The best-known freeze-distilled beverages are applejack and ice beer. Ice wine is the result of a similar process, but in this case, the freezing happens before the fermentation, and thus it is sugar, not alcohol, that gets concentrated.
However, thermodynamics (eutectic system) shown that,
- unless the removal of solid material carries away liquid, the degree of concentration will depend on the final temperature rather than on the number of cycles of removing solid material and chilling
- even if temperatures somewhat below the freezing point of ethyl alcohol are achieved, there will still be alcohol and water mixed as a liquid, and
- at some still lower temperature, the remaining alcohol-and-water solution will freeze without an alcohol-poor solid being separable
Notes:
1. Ethanol also called ethyl alcohol, drinking alcohol, or grain alcohol, is a straight-chain alcohol. Its molecular formula is C2H5OH. Ethanol is often abbreviated as EtOH, using the common organic chemistry notation of representing the ethyl group (C2H5) with Et. Freezing point is -114°C and boiling point is 78°C.
2. Colligative property - consider solvent freezes to a very nearly pure crystal. This typically occurs simply because the solute molecules do not fit well in the crystal, i.e. substituting a solute for a solvent molecule in the crystal has high enthalpy. For dilute solution, the freezing point depression depends solely on the concentration of solute particles, not on their individual properties. The explanation for the freezing point depression is then simply that as solvent molecules leave the liquid and join the solid they leave behind a smaller volume of liquid in which the solute particles can roam. The resulting reduced entropy of the solute particles thus is independent of their properties.
3. This approximation ceases to hold when the concentration becomes large enough for solute-solute interactions to become important. In that regime, the freezing point depression depends on particular properties of the solute other than its concentration.
4. Through the procedure called cryoscopy, a known constant can be used to calculate an unknown molar mass.
5. van 't Hoff factor is a measure of the effect of a solute upon colligative properties, such as vapor pressure, osmotic pressure and freezing point depression. i = the actual number of particles in solution after dissociation ÷ the number of formula units initially dissolved in solution. Means the number of particles per formula unit of the solute when a solution is dilute. For ideal solutions, i is essentially 1 for most non-electrolytes dissolved in water, e.g., Glucose in water. For most ionic compounds dissolved in water, the van 't Hoff factor is equal to the number of discrete ions in a formula unit of the substance, e.g., i=2 for NaCl.
