Freezing-point lowering

In this equation, Pt is the vapor pressure of solvent over the solution, P° is the vapor pressure of the pure solvent at the same temperature, and Xj is the mole fraction of solvent. Note that because Xj in a solution must be less than 1, P must be less than P°. This relationship is called Raoult s law Francois Raoult (1830-1901) carried out a large number of careful experiments on vapor pressures and freezing point lowering. 

Boiling Point Elevation and Freezing Point Lowering... 

When a solution is cooled, it does not begin to freeze until a temperature below the freezing point of the pure solvent is reached. The freezing point lowering, A Tf, is defined to be a positive quantity ... 

The freezing point lowering, like the boiling point elevation, is a direct result of the lowering of the solvent vapor pressure by the solute. Notice from Figure 10.8 that the freezing point of the solution is the temperature at which the solvent in solution has the same vapor pressure as the pure solid solvent. This implies that it is pure solvent (e.g., ice) that separates when the solution freezes. 

Boiling point elevation and freezing point lowering, like vapor pressure lowerings are colligative properties. They are directly proportional to solute concentration, generally expressed as molality, m. The relevant equations are... 

Effects of vapor pressure lowering. Because a nonvolatile solute lowers the vepor pressure of a solvent, the boiling point of a solution will be higher and the freezing point lower than the corresponding values for the pure solvent Water solutions freeze below 0°C at point A and boil above 100°C at point B. 

Strategy First (1) calculate the number of moles of C2H602 (MM = 62.07 g/mol). Then (2) apply the defining equation to calculate the molality. Finally (3), use the equation ATf = (1.86°C/m) X molality to find the freezing point lowering. 

You take advantage of freezing point lowering when you add antifreeze to your automobile radiator in winter. Ethylene glycol, HO(CH2)2OH, is the solute commonly used. It has a... 

To calculate the freezing point lowering of an electrolyte in water, we use the general equation... 

Table 10.3 Freezing Point Lowerings of Solutions A 7V Observed (°C) / (Calc from A TV) ... 

The data in Table 10.3 suggest that the situation is not as simple as this discussion implies. The observed freezing point lowerings of NaQ and MgS04 are smaller than would be predicted with t = 2. For example, 0.50 m solutions of NaCl and MgS04 freeze at —1.68 and —0.995°C, respectively the predicted freezing point is — 1.86°C. Only in very dilute solution does the multiplier i approach the predicted value of 2. 

Freezing point lowering (or other colligative properties) can be used to determine the extent of dissociation of a weak electrolyte in water. The procedure followed is illustrated in Example 10.11. 

Fractional crystallization, 413 Freezing point lowering, 325, 393 Freon, 362 Frequency of light, 246 relation to wave length, 251 Fructose, 423 Fumaric acid, 428 properties, 308 structure, 316... 

Freezing point methods are often applied to the measurement of activities of electrolytes in dilute aqueous solution because the freezing point lowering, 6= T — T, can be determined with high accuracy, and the solute does not dissolve in the solid to any appreciable extent. Equations can be derivedgg relating a to 9 instead of T and T. The detailed expressions can be found in the literature.16... 

Notwithstanding the fact that the crystalloids present are dissolved in the case of mayonnaise 2 in some 28% more water than for mayonnaise 1, the breaking temperature of mayonnaise 2 is some 12° F. lower than that of mayonnaise 1. Obviously, were it simply a matter of freezing point lowering, the difference would have to be in the reverse direction. 

The freezing point lowering of sulfuric acid by acetic anhydride and by benzoic anhydride also corresponds to -factors of four.201 Two explanations are possible in this case, but conductivity measurements favor the second one 202... 

In Table 8.2, it is observed that 1% solution of sodium chloride has a freezing point lowering of 0.58. Therefore, one can also express the proportion as ... 

Know how to use the appropriate colligative properties equation to calculate the amount of vapor-pressure lowering, freezing-point lowering, van t Hoff factor, etc. 

Raoult s law works for small polymers as well as small molecules. Determination of M is based for both ebulliometry (boiling point elevation) and cryometry (freezing point lowering) on the Clausius-Clapeyron equation ... 

According to modem theory, many strong electrolytes are completely dissociated in dilute solutions. The freezing-point lowering, however, does not indicate complete dissociation. For NaCl, the depression is not quite twice the amount calculated on the basis of the number of moles of NaCl added. In the solution, the ions attract one another to some extent therefore they do not behave as completely independent particles, as they would if they were nonelectrolytes. From the colligative properties, therefore, we can compute only the "apparent degree of dissociation" of a strong electrolyte in solution. 

This we can use to compute the value of a from the freezing-point lowering. As mentioned previously, we find that a solution of 1 mole of NaCl in 1 kg of H20 freezes at -3.50°C. Here n = 1, so we have m = 1 + a moles/kg of water. Applying Equation 21-2, we obtain... 

N204 (c). By direct measurement, Ramsay2 found F= —2.96 10, while data on the freezing point lowering yield —3.10. These values are in accord with the heat of sublimation calculated by Russ.1 See also Egerton.1... 

POCl3 (c). Oddo1 computed the heat of fusion to be —3.21,7, from data on the freezing point lowering. 

LiN03 3H20 (c). Morgan and Benson1 found, from measurement of the constant of the freezing point lowering, F28-9= —8.7. This gives, at 18°, F= — 8.4, which is equivalent to S3. 

Na2S (liq.). Friedrich1 gave F — —1.65,920 from the freezing point lowering constant. 

Na2C03 (liq.). Sackur1 determined the heat of fusion from freezing point lowering data. 

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