Freezing, generally point depression

Freezing point depression follows the colligative laws of thermodynamics at low concentrations added to water. At the same time the boiling point generally will be increased. The freezing point depression can be readily explained from the theory of phase equilibria in thermodynamics. 

Alternatively, potable water can be extracted from seawater by freezing salts, which depress the freezing point of water, remain in the liquid phase. Generally, though, it is more practical to remove the relatively small amount of solutes (typically, 0.02% for river water) from the great excess of water, rather than vice versa. Seawater is an exceptional case, with about 3.5% dissolved solids. Water softening is concerned primarily with removal of Ca2+ and Mg2+, but for some purposes removal of all dissolved solids (deionization or demineralization) is necessary. 

FREEZING-POINT DEPRESSION. The freezing point of a solution is. in general, lower than that of (he pure solvent. The depression is proportional to the active mass of the solute. For dilute (ideal) solutions... 

X V iution), the determination of the molar mass of a solute requires a measurement of mass, volume, temperature, and osmotic pressure. Osmotic pressures are generally large and can be determined quite accurately, thus yielding accurate molar masses. Boiling-point elevations and freezing-point depressions are usually small and not very accurate, so molar mass determinations based on those measures often are not accurate. 

As in the case of freezing point depression, boiling point elevation depends on the carbohydrate profile. In general, the boiling point is increased as the level of conversion increases. Table 21.15 shows the relationship of boiling point to solids content for various sweeteners.76... 

Table 3.6 lists Kf and Kb for several solvents. In general, the higher the molar mass of the solvent, the larger the values of Kf and Kb. If the freezing point depression and boiling point elevation constants are known, the molecular weight of the dissolved solute, M2, can be determined ... 

Starch acetate solutions have so far proved unsatisfactory for molecular weight measurements by either the cryoscopic or ebullioscopic methods. Cryoscopic measurements in phenol or glacial acetic acid have generally given abnormally large freezing point depressions indicative of impossibly low molecular weight values for the starch acetate. 

Derive a general relationship between the osmotic pressure of a dilide solution and its freezing point depression. What form does it take for a very dilute solution ... 

At atmospheric pressure, water will freeze at 0°C. If a solute is added to water, then the mixture will freeze at a lower temperature. This is known as freezing point depression and occurs with any general mixture. Using a model for the activity coefficients, we can quantitatively predict the magnitude of this effect. 

The starting point for the analysis of the freezing-point depression phenomenon is the observation that when a solid freezes out from a mixture, it generally is pure and it is the component that is concentrated in the solution, that is, the pure solvent. [Indeed, this is the basis for zone refining, in which melting and resolidification (or recrystallization) are used to purify metals.] The equilibrium condition when the first crystal of pure solvent forms is... 

General equation for the freezing point depression of a solvent... 

Let us now consider some of the evidence for this general mechanism. Such evidence has, of course, been gathered by study of specific reaction mechanisms. Only some of the most clear-cut cases are cited here. Additional evidence is mentioned when individual mechanisms are discussed in Section 9.4. A good example of studies that have focused on the identity and mode of generation of the electrophile is aromatic nitration. Primarily on the basis of kinetic studies, it has been shown that the active electrophile in nitration is often the nitronium ion, NO2+, which is formed by the reaction of nitric acid with concentrated sulfuric. Several other lines of evidence support the role of the nitronium ion. It can be detected spectroscopically and the freezing-point depression of the solution is consistent with the following equation ... 

---