Freezing-point depression curves

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). 

Figure 1 Time profile of temperature, concentration, and viscosity during freezing of 3% sucrose. Data are calculated assuming that ice crystallization begins at -15°C and that the solution composition follows the equilibrium freezing point depression curve. Viscosities are estimated from a fit of viscosity data over a wide range of composition and temperature to a VTF-type equation (i.e., see [4]). (Data from [7,8].)...

FIGURE 11.2 5 Freezing-point depression curves for xylenes. 

Ethylene glycol Freezing point depression curve for water and ethylene glycol calculated from the AT, = /Clmformula. Despite some differences due to nonideal hehavior, it matches the experimental data fairly well. 

This expression can be modified to apply directly to any of various techniques used to measure the interaction parameter, including membrane and vapor osmometry, freezing point depression, light scattering, viscometry, and inverse gas chromatography [89], A polynomial curve fit is typically used for the concentration dependence of %, while the temperature dependence can usually be fit over a limited temperature range to the form [47]... 

Phase diagrams from freezing point depressions show true compound formations for simpler amides—e.g., water-N-methylacetamide forms a compound at a mole ratio of 2 to 1, water-N,N-dimethylacetamide at 3 to 2 and 3 to 1, and water-N-methylpyrrolidone at 2 to 1. The heats of mixing and heat capacities at 25°C. of a number of water-amide systems were determined. All mixing curves were exothermic and possess maxima at definite mole ratios, while the heat capacities for the most part show distinct curvature changes at the characteristic mole ratios. Both experimental results point to the stability of the particular complexes even at room temperature. This is further supported by absolute viscosity studies over the whole concentration range where large maxima occur at these same mole ratios for disubsti-tuted amides and N-substituted pyrrolidones. 

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... 

Pure solid solvent coexists at equilibrium with its characteristic vapor pressure, determined by the temperature (Section 10.4). Solvent in solution likewise coexists with a certain vapor pressure of solvent. If solid solvent and the solvent in solution are to coexist, they must have the same vapor pressure. This means that the freezing temperature of a solution can be identified as the temperature at which the vapor-pressure curve of the pure solid solvent intersects that of the solution (Fig. 11.12). As solute is added to the solution, the vapor pressure of the solvent falls and the freezing point, the temperature at which the first crystals of pure solvent begin to appear, drops. The difference ATf = T/ — Tf is therefore negative, and a freezing-point depression is observed. 

The dotted line with the open symbols on the right side of the diagram is the freezing curve of ethanol in tire mixture. As one passes downward through this curve, solid ethanol precipitates from the solution. Note that the temperature at which ethanol begins to freeze decreases as the amount of water in the solution increases. Therefore, we see that the addition of impurities decreases the freezing temperature of a substance. This phenomena is known as freezing point depression. 

Figure 12.11 shows that lowering the vapor pressure of the solution shifts the solid-liquid curve to the left. Consequently, this line intersects the horizontal line at a temperature lower than the freezing point of water. The freezing point depression (ATf) is defined as the freezing point of the pure solvent (TJ) minus the freezing point of the solution (Tf) ... 

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