Freezing-point, depression tables

It was formulated as [Hg(SCN2H4)2Cl2]1 8 after A. Werner, before P. C. R y s work on the mono-derivative.4 Although this wholly covalent formulation is not impossible, especially in view of the production of mercury (II) sulfide (not oxide) by addition of soda solution,2 it does not fit in with the tables of electrical conductivities and freezing-point depressions (Tables I and II). 

Many chemicals when added to water cause a freezing point depression, as shown in Table 1, and thus are termed antifreezes. The antifreeze properties of these chemicals vary widely as a function of their coUigative, or concentrative, properties. The reduction in freeze point depends both on the chemical itself and the concentration of the chemical in water. The freeze point depression increases as the antifreeze chemical is added to the water, until a characteristic concentration is achieved. Further addition of the antifreeze chemical to water will either result in insolubility or serve to increase the freezing point of the mixture, as illustrated in Figure 1. 

Table 1. Freeze Point Depression of Antifreeze Chemicals ...

If we calculate the H values for various water temperatures, we see results as shown in Table 4.4. The importance of the information content encoded in the H value in these studies is that it is a single-numerical description of the system, water in this case, that can be used to relate to physical property changes occurring at different temperatures. This approach can be used to evaluate a property change such as the freezing point depression. 

The freezing point depression constant for water is known from experiments and can be found in tables Tf = 1.858 ° C kg/mol. To calculate the freezing point, we must first determine the molality of the... 

Table XXVII.—Comparison of Calculated Boiling Point Elevation, Freezing Point Depression, and Osmotic Pressure...

TABLE 8.2. Sodium Chloride Equivalents (E) and Freezing Point Depression (ATI" ") Values of Selected Compounds. 

Step 1 Find the value of freezing point depression of the drug at 1% concentration, AT from Table 8.2. 

Step 1 Freezing point depression (AT ) of 1% atropine solution (from Table 8.2) is 0.07. 

By taking the freezing point constant for water as 1.86 from Table 9-3 and then substituting the values into the equation for freezing point depression, you obtain the change in freezing temperature ... 

We find in Table 21-1 that B freezes at 5.48°C and that the value of Kt js 5.12. The freezing-point depression of this solution is... 

Physical properties of glycerol are shown in Table 1. Glycerol is completely soluble in water and alcohol, slighdy soluble in diethyl ether, ethyl acetate, and dioxane, and insoluble in hydrocarbons (1). Glycerol is seldom seen in the crystallized state because of its tendency to supercool and its pronounced freezing point depression when mixed with water. A mixture of 66.7% glycerol, 33.3% water forms a eutectic mixture with a freezing point of —46.5°C. 

The constant kf is called the freezing-point constant of the solvent it is different for each solvent and must be determined experimentally (Table 8.9). The freezing-point depression for a 0.1 m C12H22011(aq) (sucrose) solution, for instance, is... 

PROBLEM 11.20 Assuming complete dissociation, what is the molality of an aqueous solution of KBr whose freezing point is —2.95°C The molal freezing-point-depression constant of water is given in Table 11.4. 

Due to a cancellation of errors, the equation (without modification) is applicable for aqueous ethylene glycol concentrations to about 0.40 mole fraction (typically for system operation to 233 K). A comparison of results from Hammerschmidt s equation, as well as the prediction by the freezing point depression of water for methanol inhibition is summarized in Table 4.6. 

Table A.5 is the output file for salts in the 4.5- to 5.0-km layer, where the system pressure is 484.5 bars (102 bars km-1 x 4.75 km). The temperature of 268.28 K is the freezing point depression for this particular composition and pressure at 268.27 K, ice forms. The pH of this system is 8.02. The number of independent components is seven. This example deals with lithostatic pressures on solutions dispersed in a regolith, which is fundamentally different from the previous examples (Tables A.2-A.4) that dealt with seawaters.

A few values of Kf and Kb are given in Table 2. For a macromolecular solution, the ideally dilute approximation holds only up to such low molality that freezing-point depression and boiling-point elevation are useless for determining... 

TABLE 2. Freezing-point depression and boiling-point elevation constants... 

Table 18.1 Values for the calculated freezing point depression (FPD) for NaCl, KC1, CaCl2, and...

Table 21.14 Estimating the freezing point depression of various sweeteners73...

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... 

As with the chlorometallate eutectics a model for the effect of HBD on the freezing point depression of the mixture would be beneficial for the design of new liquids. No correlations were observed between the freezing point of the mixtures and the enthalpy of formation or fusion of the pure acids but Table 2.5 shows qualitatively that the larger depressions of freezing point occur with the lower molecular weight HBDs. 

Table 6-2 Freezing Point Depressions of Aqueous Solutions...

Table 3.6 lists Kf and Kb for several solvents. In general, the higher the molar mass of the solvent, the larger the values of Kf and Kb. If the freezing point depression and boiling point elevation constants are known, the molecular weight of the dissolved solute, M2, can be determined ... 

When using NaCl instead of boric acid, follow the same procedure as outlined above. The freezing point depression of 0.38°C should be made up with NaCl. A 1% NaCl solution gives a freezing point depression of 0.58°C (see Table 3.8). One should make a solution of 0.655% NaCl (=1% x 0.38/0.58). The amount of NaCl... 

In Table 1 are given values of the pertinent constants for two common solvents cyclohexane and water. It will be seen that, for freezing-point depressions of about 2 K, omission of the correction term kfATf eads to errors of the order of 1 percent in m or M. 

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