Measurements of Freezing Points

Perhaps the method of most general applicability for determining activities of nonelectrolytes in solutions is the one based on measurements of the lowering of the freezing point of a solution. As measurements are made of the properties of the solvent, activities of the solute are calculated by methods described in the preceding section. 

Elaborate procedures have been developed for obtaining activity coefficients from freezing-point and thermochemical data. However, to avoid duplication, the details will not be outlined here, because a completely general discussion, which is applicable to solutions of electrolytes as well as to nonelectrolytes, is presented in Chapter 21 of the Third Edition of this book [6]. 

The data in Table 17.2 for the partial pressures (in mm Hg) of toluene and of acetic acid at 69.94 °C have been taken from Ref. 7. For the purposes of this exercise, assume that the partial pressure of each component is identical with 

TABLE 17.2. Partial Pressures of Toluene and Acetic Acid at 69.94°C 

Xi (Toluene) X2 (Acetic Acid) Pi/(mm Hg) (Toluene) P2/(mm Hg) (Acetic Acid) 

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Another method that has proved extremely useful in obtaining information about the nature of solutes in sulfuric acid solution is the measurement of freezing point depressions. The freezing point constant (k) for sulfuric acid is 6.12 kg °C mol-1. For idea) solutions, the depression of the freezing point is given by... 

The only examples of asymmetric Claisen rearrangements catalyzed by a chiral aluminum catalyst are those published by Yamamoto and coworkers [24-27]. The Claisen rearrangement of allyl vinyl ethers of type 91 (Sch. 13) can proceed via either of the two enantiomeric chair transition states 92 or 94. If a chiral Lewis acid is used to activate the process, the transition states become diastereomeric and preferential formation of one enantiomer of the product is possible. This is complicated because coordination of a chiral Lewis acid to the ether oxygen of allyl vinyl ether produces a new chiral center as indicated in 96 and asymmetric induction might occur from a substituent on aluminum to the oxygen and then from the oxygen to the C-3 carbon in the product. In their initial report, Maruoka, Banno, and Yamamoto found that a catalyst prepared from the 3,3 -disilyl-substituted BINOL 97 and trimethylaluminum was effective in this transformation [24]. The catalyst 98 was shown to be monomeric by measurement of freezing point depression. 

Table 14-3 lists actual and ideal values of i for solutions of some strong electrolytes, based on measurements of freezing point depressions. 

Determination of Electrolytic Dissociation and Degree of Hydrolysis by Measurements of Freezing Point and Boiling Point... 

To determine the osmotic coefficient of aqueous solutions of hydrogen chloride from measurements of freezing point. 

In the next section we shall discuss the physical properties and structure of the more important of the organic solvents mentioned in later chapters. In Chapter 2, the thermodynamic properties of solutions are discussed. Firstly, C. M. Criss discusses solubility and calorimetric measurements. In planning new work with unfamiliar solvents the extent of solubility of compounds is a primary consideration. Viscosity is also considered under this heading since although it is a transport property it is often used in the same way as thermodynamic measurements, to infer structural properties. An important technique for obtaining thermodynamic quantities of certain solutions is cryoscopy, the measurement of freezing point depressions, and this is discussed by R. Garnsey and J. E. Prue. Measurement of the e.m.f.s of suitable cells... 

It is given by At = K(Cm, where Q is the molar concentration of dissolved solute and KfisA constant (the cryoscopic constant) for the solvent used. Measurements of freezing-point depression (using a Beckmann thermometer) can be used for finding relative molecular masses of unknown substances. 

The number average molecular weight determines the colligative properties (i.e., those which depend only on the number of dissolved molecules) of polymer solutions. Measurements of freezing point depression (cryoscopy) or... 

Valentin, J. L. Fernandez-Torrres, A. Posadas, P. Marco-Fernandez, A. Rodriguez, A. Gonzalez, L., Measurements of Freezing-Point Depression to Evaluate Rubber Network Structure. Crosslinking of Natural Rubber witb Dicumyl Peroxide. J. Polym. Sci., PartB Polym. Phys. 2007,45,544-556. 

Over the small ranges of temperature which are usually encountered in the measurement of freezing-point depression, Ac, may usuaUy be assumed constant. The integration of (8 44) therefore gives... 

The general procedure described in this section for evaluating y requires knowledge of the osmotic coefficient (pm as a function of molality, (pm is commonly evaluated by the isopiestic method (Sec. 9.6.4) or from measurements of freezing-point depression (Sec. 12.2). 

His first measurements of freezing-point depressions appeared in 1878. He pointed out the advantages of determining the molar mass of a substance from the freezing point of its dilute solution, and gave specific examples of this procedure. He was the first to show experimentally that the freezing-point depression of a dilute aqueous solution of an electrolyte is proportional to the number of ions per solute formula unit (Eq. 12.4.12). 

Since Kf has a larger value than Kb (because Afus,A77 is smaller than Avap,A77), the measurement of freezing-point depression is more useful than that of boiling-point elevation for estimating the molahty of a dilute solution. 

Media formulations do not generally specify the osmotic pressure instead, the number of dissolved particles is given as osmolarity or osmolality. Osmolality is the number of moles of particles per kilogram of solution whereas osmolarity is the number of moles per liter of solution. One mole of particles is an osmole, abbreviated as Osm. Animal cell culture media have an osmolality of 280 to 320 mOsm kg to conform to the osmolality of serum (290 mOsm kg ). Osmolality is not easily calculated especially when a medium has many components and the degree of dissociation is not known. In such cases, osmolality is estimated from measurements of freezing point depression and other colligative properties (i.e., those dependent on the concentration of dissolved particles). In cell culture media, sodium chloride is used for adjusting osmolality to the requisite value. 

For the measurement of freezing-points, a thermometer calibrated at the National Physical Laboratory and of the range 99-5 -l30 5 Celsius as specified in B.S. 593 1954 (Laboratory Thermometers) under the schedule A.130/100, is used. To facilitate temperature readings, by interpolation, to 0 02 , a magnifying device is attached to the thermometer. 

Due to the fact that freezing point temperature and vapor pressure of a substance vary with interfacial curvature in a pore, the determination of pore size and pore size distribution can be achieved by observing solid-liquid or liquid-vapor transition in pores. Thermoporometry is a technique involving the measurement of freezing point depression of a liquid in membrane pores using a sensitive differential scanning calorimetry (Table 15.3e). The principle of thermoporometry is described by Gibbs-Thomson equation [174] ... 

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