Depression of the freezing-point

In the second application discussed above, the concentration of the solutes is normally small and is close to unity. If the solution is ideal at the particular mole fraction it will continue to be so a fortiori over the range of mole fractions up to the pure solvent. This makes possible the integration of (8 43) to give the depression of the freezing-point, allowing only for the temperature variation of Li over the curve MP of Fig. 36. 

It is to be noted that (8 43) applies strictly under conditions of constant total pressure, as when the solution is under the pressure of the atmosphere. Under the same conditions the temperature coefiS-cient of Li is given by 

Over the small ranges of temperature which are usually encountered in the measurement of freezing-point depression, Ac, may usuaUy be assumed constant. The integration of (8 44) therefore gives 

Integrating from x = 1 to the particular mole fraction x at which the freezing-point depression is to be calculated. 

A less accurate integration can be carried out by neglecting the temperature coefficient of the enthalpy of melting, equivalent to putting ACp=0. In place of (8-47) we obtain 

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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. 

III. Depression of the Freezing-point of Camphor (Rast s Method). 

The depression of the freezing point of sulphuric acid by the addition of nitric acid has historically been the subject of confusion. Hantzsch suggested that, because sulphuric acid is the stronger acid, the following equilibria might exist in these solutions ... 

In an electrolyte solution, each formula unit contributes two or more ions. Sodium chloride, for instance, dissolves to give Na+ and Cl ions, and both kinds of ions contribute to the depression of the freezing point. The cations and anions contribute nearly independently in very dilute solutions, and so the total solute molality is twice the molality of NaCl formula units. In place of Eq. 5a we write... 

The question asks for the freezing point of a solution. The phrase to prevent the waterfrom freezing reveals that we are dealing with depression of the freezing point of water. Equation describes this process for a dilute solution A Zf —. A coolant solution is quite concentrated, so this equation... 

The hydrate-formation temperamre can be reduced by the addition of antifreeze agents such as methanol, glycols [1430], or brines. The depression of the freezing point is given by... 

Hydrate control is not included in this chapter, but is discussed in Chapter 13 because of the relative importance and difference in chemical mechanism. Many chemicals added to water will result in a depression of the freezing point. The practical application is restricted, however, because of some other unwanted effects, such as corrosion, destruction of rubber sealings in engine parts, or economic aspects. 

Depression of the Freezing Point in a Mixture of Ethylene glycol-Water... 

Ethylene glycol is not as active in depression of the freezing point as methanol, but it has a very low vapor pressure evaporation loss in a coolant system is due more to the evaporation of water than to the evaporazation of ethylene glycol. Furthermore, the flammability problem is literally eliminated. 1 1 mixtures of ethylene glycol and water do not exhibit a flash point at all. 

The depression of the freezing point of a solvent due to the presence of a dissolved solute is an example of a colligative property, that is, a property of a dilute solution that depends on the number of dissolved particles and not on the identity of the particles. Water has a freezing point depression constant, Kf, of 1.86 K kg mol-1. In other words, for every mole of nonvolatile solute dissolved in a kilogram of water, the freezing point of water is lowered by 1.86°C. The change in freezing point, A T, can be calculated from the equation... 

In some systems the acylium ion is formed reverisbly and to a detectable extent while in others, to be discussed in the next chapter, it is a hypothetical intermediate. The first evidence for a stable acylium ion was the fourfold depression of the freezing point of sulfuric acid by mesitoic acid.176 The presence of the acylium ion in the sulfuric acid solutions of carboxylic acids with fourfold depressed freezing points is confirmed chemically by the high yield of ester obtained on pouring the... 

This depression of the freezing point occurs in just the same way as the lower melting point of an impure sample, as discussed previously. This determination of the depression of the freezing point is termed crysoscopy. 

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... 

The presence of the u- and 7r-modifieations of sulphur dissolved in molten A-sulphur naturally causes a depression of the freezing-point of the latter, and from the magnitude of this effect it has been possible to demonstrate the probability of a molecular weight corresponding to S6 for the dark brown p.-allotrope, a result which is of especial interest as correlating this form of liquid sulphur with the hexatomic sulphur believed to occur in sulphur vapour (see before).3... 

The colligative properties of solutions are those properties that depend upon the number of dissolved molecules or ions, irrespective of their kind. They are the lowering of the vapor pressure, the depression of the freezing point, the elevation of the boiling point, and the osmotic pressure. These properties may be used in determining molecular weights of dissolved substances. 

The freezing point of milk, like that of any aqueous system, depends on the concentration of water-soluble components. The mathematical relationship between depression of the freezing point and concentration of the solute was determined by Raoult (1884) and is expressed in the equation... 

Properties of Aqueous Solutions of Arsenic Acid.—The system As,Oj-H20 has been investigated 11 by determining the solubility curves of the (1, 4)- and the (3, 5)-hydrates, and also the curve for the depression of the freezing point of water. The data obtained are given in the following table and are graphically represented in fig. 10. 

BECKMANN METHOD. A method of measuring elevation of the boiling point or depression of the freezing point of a solution, It may be used to measure concentration if the nature of the solute is known, or the molecular weight of the solute if the volume concentration is known. 

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

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