Lowering of freezing point

The lowering of freezing point and the generation of osmotic pressure both depend on the total concentration of solute particles. Therefore, by using the colligative property to determine the amount of solute present, and knowing its mass, we can infer its molar mass. 

Effects of Chemical Composition on Melting (Equation of Lowering of Freezing Point)... 

Equation 6.56 is known as the equation of lowering of freezing point and is valid for solid mixtures crystallizing from multicomponent melts. Like the Clausius-Clapeyron equation, it tells us how the system behaves, with changing T, to maintain equilibrium on the univariant curve. However, whereas in the Clausius-Clapeyron equation equilibrium is maintained with concomitant changes in 7) here it is maintained by appropriately varying the activity of the component of interest in the melt and in the solid mixture. 

The quasi-ideality of several other molten systems with constant amounts of silica may be deduced by applying the lowering of freezing point equation. A very... 

Substituting equations 6.59, 6.60, 6.61, and 6.62 into the lowering of freezing point equation, we obtain... 

Ficj. XVII-9.—Gibbs free energy as function of eoncentration, for lowering of freezing point. 

ACTIVITY OF SOLVENT AND SOLUTE FROM LOWERING OF FREEZING POINT DATA... 

Debye, P. and Huckel, E. Theory of electrolytes I Lowering of freezing point and related... 

Lowering of freezing-points of solutions.— Let us see, from an example, the importance of this law. 

X63. In general, a modification which leaves invariable the composition of each phase cannot be imposed upon a system whose variance exceeds 1, page 195.—164. In general, the equilibrium of a system whose variance exceeds 1 is stable, 196.—X65. Displacement of equilibrium by variation of pressure, 196.—x66. Various applications, 197.—X67. Case of combination without contraction, 198.— x68. —Experimental verifications hydriodic acid, 198.—X69. Sele-nic acid, 199.—170. Variation of the solubility of a salt with pressure, 200.—X7X. Displacement of equilibrium by variation of the temperature, 202.—X7a. Lowering of freezing points of solvents, 208.—... 

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). 

In very dilute solutions, the lowering of freezing point 6 is given by cf. 22.10-22.12),... 

Lowering of freezing point = AT = (freezing point of solvent) - (freezing point of solution) = Kfm... 

IV —The Relation between Osmotic Pressure P and the lowering of Freezing Point AT of the Solvent due to the presence of the Solute We imagine a cycle very similar to the previous one carried out Consider two vessels (Fig as) I and II Vessel I contains solvent (water, say) m equilibrium with ice at the freezing point To The vessel II contains an aqueous solution which is also m equilibrium with ice at the temperature T lower than To by the amount AT. The osmotic pressure in II isP... 

This expression has exactly the same form as that obtained for the rise of boiling point It is the thermodynamical basis of the Raoult generalisation regarding the concentration of a solution and the lowering of freezing point... 

The Fourth Method—The lowering of freezing point. The LpAT... 

For the special case in which x is chosen equal to M and V = ice, it is evident that AT = 1863° This is the so-called Molecular depression of freezing point For 1 mole dissolved in 1 liter of water, the lowering of freezing point is evidently 1 863° C This agrees excellently with that found by Raoult Note, however, that Raoult s definition of molecular lowering refers to x mole dissolved in 1 gram of solvent, and similarly for the molecular rise of boiling point... 

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