Freezing point law

Range of a process, 114 Rankine s cycle, 113 vapour-pressure equation, 179 Raoult s freezing-point law, 299 ... 

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. 

Raoult s law When a solute is dissolved in a solvent, the vapour pressure of the latter is lowered proportionally to the mole fraction of solute present. Since the lowering of vapour pressure causes an elevation of the boiling point and a depression of the freezing point, Raoult s law also applies and leads to the conclusion that the elevation of boiling point or depression of freezing point is proportional to the weight of the solute and inversely proportional to its molecular weight. Raoult s law is strictly only applicable to ideal solutions since it assumes that there is no chemical interaction between the solute and solvent molecules. 

The fixed points in the lTS-90 are given in Tabie 11.39. Platinum resistance thermometers are recommended for use between 14 K and 1235 K (the freezing point of silver), calibrated against the fixed points. Below 14 K either the vapor pressure of helium or a constant-volume gas thermometer is to be used. Above 1235 K radiometry is to be used in conjunction with the Planck radiation law,... 

This is an expression of Raoult s law which we have used previously. Freezing point depression. A solute which does not form solid solutions with the solvent and is therefore excluded from the solid phase lowers the freezing point of the solvent. It is the chemical potential of the solvent which is lowered by the solute, so the pure solvent reaches the same (lower) value at a lower temperature. At equilibrium... 

In this equation, Pt is the vapor pressure of solvent over the solution, P° is the vapor pressure of the pure solvent at the same temperature, and Xj is the mole fraction of solvent. Note that because Xj in a solution must be less than 1, P must be less than P°. This relationship is called Raoult s law Francois Raoult (1830-1901) carried out a large number of careful experiments on vapor pressures and freezing point lowering. 

Reality Check Actually, the freezing point is somewhat lower, about — 37°C (—35°F), which reminds us that the equation used, ATf = kftn, is a limiting law, strictly valid only in very dilute solution. 

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. 

Above the freezing point of silver, Tgq is defined in terms of a defining fixed point and the Planck radiation law, and optical pyrometers are frequently used as temperature probes. The Comite Consultatif de Thermometrie gives a thorough discussion of the different techniques for approximation of the international temperature scale of 1990 [2, 4],... 

Let the depression of the freezing point be AT, the magnitude of which depends entirely on the amount of solute in the solvent. Re-interpreting Blagden s law gives... 

Raoult s law, osmotic pressure, and freezing point depression calculations use, without conversion, which of the following respective concentration units... 

VAN T HOFF S LAW OF FREEZING-POINT DEPRESSION AND BOILING-POINT ELEVATION... 

It can be observed that g is the ratio between the observed osmotic pressure and the osmotic pressure that would be observed for a completely dissociated electrolyte that follows Henry s law [see Equation (15.47)], hence the name, osmotic coefficient. A similar result can be obtained for the boiling point elevation, the freezing point depression, and the vapor pressure lowering. 

Raoult s law works for small polymers as well as small molecules. Determination of M is based for both ebulliometry (boiling point elevation) and cryometry (freezing point lowering) on the Clausius-Clapeyron equation ... 

For -weak electrolytes the degree of dissociation found by the freezing point method agrees with that found from conductivity within the limits of experimental error and Ostwald s dilution law is obeyed. 

The freezing point of an aqueous solution is governed by the concentration of solutes in the solution. The relationship between the freezing point of a simple aqueous solution and concentration of solute is described by a relation based on Raoult s law ... 

This relationship constitutes the basic definition of the activity. If the solution behaves ideally, a, =x, and Equation (18) define Raoult s law. Those four solution properties that we know as the colligative properties are all based on Equation (12) in each, solvent in solution is in equilibrium with pure solvent in another phase and has the same chemical potential in both phases. This can be solvent vapor in equilibrium with solvent in solution (as in vapor pressure lowering and boiling point elevation) or solvent in solution in equilibrium with pure, solid solvent (as in freezing point depression). Equation (12) also applies to osmotic equilibrium as shown in Figure 3.2. 

The first theoretical basis for calculating the decrease of freezing point according to van t Hoff law as applied to nitric esters was given by Nauckhoff [5]. 

BLAGDEN LAW. The depression of the freezing point of a solution is, for small concentrations, proportional to the concentration of the dissolved substance. 

The vapor pressure of a solvent is lowered on dissolving the solute in it. This lowering for dilute solutions is proportional to die mole fraction of the solute (Raoult s Law). The lowering of the vapor pressure of the solution can be related to the lowering of the freezing point and the elevation of the boiling point. These phenomena serve as a basis for molecular weight determinations. If both components of the solution are volatile, each lowers the vapor pressure of the other and the ratios of the two substances in the liquid and vapor phase are not necessarily the same. Use is made of this fact to separate the two substances by distillation. 

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