Solid freezing point depression

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... 

For a solution with a liquid as solvent, the temperature at which it freezes to a solid is slightly lower than the freezing point of the pure solvent. This phenomenon is known as freezing point depression and is related in a simple manner to the concentration of the solute. The lowering of the freezing point is given hy... 

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. 

In each hatched two-phase region, the lever rule (Section 7.3.2) can be used as usual to determine the relative amounts of the two phases at opposite ends of the tie-line. However, the quantity of precipitated solid a and/or /3 is usually of less interest than the composition of the melt, so the principal focus is on the two liquidus lines that meet at the eutectic point. These liquidus lines are also called solubility curves or freezing-point depression curves, in that they map both the saturation-solubility limits (horizontal variations) as well as the freezing-point depression of the liquid (vertical variations). 

A similar explanation accounts for freezing-point depression. We know that liquid and solid phases are in equilibrium at the freezing point, so the free-energy difference between the phases (AGfusion) is zero. 

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... 

The collected urine is centrifuged to remove solid debris and analyzed by standard methods for sodium, potassium and chloride (Durst and Siggard-Andersen, 1999, Scott et al. 1999). Osmolality is also measured with an osmometer (the freezing point depression type of instrument is recommended (Scott et al. 1999). 

Another consequence of lowering of vapour pressure is that the freezing point of the solution is lower than that of the pure solvent. The freezing point of a solution is the temperature at which the solution exists in equilibrium with solid solvent. In such an equilibrium, the solvent must have the same vapour pressure in both solid and liquid states. Consequently, the freezing point is the temperature at which the vapour pressure curves of the solvent and solution intersect the sublimation curve of the solid solvent that is, points C and D, respectively, in Fig. 2.8. The freezing point depression is T-To = ATf. An expression for freezing... 

This phase diagram shows how temperature and pressure affect the solid, liquid, and gas phases of a pure solvent (solid lines) and a solution (dashed lines). The difference between the solid and dashed lines corresponds to vapor pressure lowering (AP), boiling point elevation (AT[,), and freezing point depression (ATf). 

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