Freezing-point measurements

This section explains how we can evaluate — fX for a solution of a given composition at a given T and p from the freezing point of the solution combined with additional data obtained from calorimetric measurements. 

Consider a binary solution of solvent A and solute B. We assume that when this solution is cooled at constant pressure and composition, the solid that first appears is pure A. For example, for a dilute aqueous solution the solid would be ice. The temperature at which solid A first appears is Tf, the freezing point of the solution. This temperature is lower than the freezing point T of the pure solvent, a consequence of the lowering of /za by the presence of the solute. Both Tf and T can be measured experimentally. 

Let T be a temperature of interest that is equal to or greater than T. We wish to determine the value of /Xa(1 7 0 /t-A(sln, T ), where /r (l, T ) refers to pure liquid solvent and /XA(sln, T ) refers to the solution. 

Thermodynamics and Chemistry, second edition, version 3 2011 by Howard DeVfoe. Latesi version sn.chem.umd.edu/thermobook 

For convenience of notation, this book will use Asoi.aT/ to denote the molar enthalpy difference i/A(sln) - H (s). Aso, aH is the molar differential enthalpy of solution of solid A in the solution at constant T and p. The first integral on the right side of Eq. 12.2.3 requires knowledge of Aso1,a7/ over a temperature range, but the only temperature at which it is practical to measure this quantity calorimetrically is at the equilibrium transition temperature Tf. It is usually sufficient to assume Asoi.aT/ is a linear function of T  

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In carrying out a molar mass determination by freezing point depression, we must choose a solvent in which the solute is readily soluble. Usually, several such solvents are available. Of these, we tend to pick one that has the largest kf. This makes ATf large and thus reduces the percent error in the freezing point measurement From this point of view, cyclohexane or other organic solvents are better choices than water, because their kf values are larger. 

The ionisation may be attributed to the great tendency of the free hydrogen ions H+ to combine with water molecules to form hydroxonium ions. Hydrochloric and nitric acids are almost completely dissociated in aqueous solution in accordance with the above equations this is readily demonstrated by freezing-point measurements and by other methods. 

Boiling point measurements of sufficient accuracy to obtain reliable activities are not easy to make. It is difficult to ensure that equilibrium conditions are achieved in the still. As a result, boiling point measurements, unlike freezing point measurements, are not often used to determine these quantities. 

For a detailed discussion of the calculation of activities (and excess Gibbs free energies) from freezing point measurements, see R. L. Snow. J. B. Ott. J. R. Goates. K. N. Marsh, S. O Shea, and R. N. Stokes. "(Solid + Liquid) and (Vapor + Liquid) Phase Equilibria and Excess Enthalpies for (Benzene + //-Tetradecane), (Benzene + //-Hexadecane). (Cyclohexane + //-Tetradecane), and (Cyclohexane +//-Hexadecane) at 293.15, 298.15, and... 

From a thermodynamic standpoint, freezing point measurements and isopiestic measurements are similar since both yield directly the activity of the solvent. When done carefully, freezing point data can generate activity coefficient values at concentrations down to 0.001 molal. During the first half of this century, much activity coefficient data was obtained from freezing point measurements. However, the popularity of this technique has decreased and is seldom used for aqueous solutions at the present time. 

Because of the compound s thermal instability, the enthalpy of fusion of peroxydode-canoic acid (perlauric acid) was indirectly determined from freezing point measurements in various solutions. The resulting value, 46.3 0.8 kJmol, is 10 kJmol larger than... 

Purity — 95% min (Freezing point of 11.23 C min) calculated in accordance with Method D1016, from the experimentally determined freezing point, measured by Method D1015 A2.3 Specifications for Isopropanol 91% ... 

Clarification by removal of casein with such agents as calcium chloride, acetic acid, cooper sulfate, or rennin has often been employed to obtain a serum more suitable for refractometric measurements. Obviously the composition, and hence the refractive index, of such sera will depend on the method of preparation. Furthermore, some of the serum proteins may be precipitated with the casein by some of the agents used, particularly if the milk has been heated. Refractive index measurements of such sera are not generally considered as satisfactory as freezing point measurements for detection of added water (David and MacDonald 1953 Munchberg and Narbutas 1937 Schuler 1938 Tell-mann 1933 Vleeschauwer and Waeyenberge 1941). Menefee and Overman (1939) reported a close relation between total solids in evaporated and condensed products and the refractive index of serum prepared therefrom by the copper sulfate method. Of course, a different proportionality constant would hold for each type of product. 

The freezing point measurement, standard method for the detennination of styrene assay until the 1970s, has been largely replaced by gas chromatography. Color is measured spectrophotometrically and registered on the APILA or the platinum-cobalt scale. 

Hydrate isomerism is quite analogous to ionization isomerism. The compound Cr(H20)5Ci2+ (C1 )2 H20 contains one Cr—Cl bond and five Cr—O bonds per complex whereas its isomer, Cr(H20)4Clt C1 2H20, has two Cr—Cl bonds and only four Cr—O bonds per complex. The first of these yields three ions per gram-atom of chromium when dissolved in water (as may be checked by freezing-point measurements), whereas the second yields but two ions per complex. Those water molecules not directly coordinated to chromium are probably present as lattice water. ... 

The Li sigmatropic shifts in 68, 72 and 74 are much faster than in 70. X-ray crystallography shows all four compounds to be internally solvated. Only 68 is a dimer both in the solid and in solution as determined from freezing point measurements the other three are monomers in the solid as well as in solution. Neither 68 nor 72 exhibited 13C—6Li (or 7Li) spin coupling down to 150 K. 

This molality in can be calculated from the observed AT using Eq. (10-20). Thus freezing-point measurements on weak electrolyte solutions of known molality m enable the determination of a. 

Fig. 51. Test of Debye-Hiickel equation by freezing-point measurements in cyclohexanol (Schreiner and Frivold)...

Hence, as for carbonic acid, being undissociated, i = i, and for acid calcium carbonate from freezing-point measurements i = -56, we expect and find... 

Durrant first prepared the potassium salt, to which he assigned the formula [K2Co(C204)2(H20)2]20, from cobalt-(II) oxalate, potassium oxalate, and hydrogen peroxide. Percival and Wardlaw, from freezing-point measurements, subsequently suggested that the compound is a binuclear complex containing five ions ... 

The cryoscopic method was used in Hantzsch s original work 53, 54) and was later developed by Hammett and Deyrup 56) and by Gillespie et al. 48). Sulfuric acid freezes at 10.371 C and has a relatively large molal freezing-point depression or cryoscopic constant fc = 6.12 32). It is thus a convenient solvent for cryoscopic measurements provided that adequate precautions are taken to prevent absorption of water from the atmosphere. From freezing-point measurements the number, v, of moles of particles (ions and molecules) produced by one mole of any solute may be obtained. Some examples are given in Table IV. 

For freezing-point measurements made in 100% sulphuric acid v is given by the expression... 

To evaluate from freezing point measurements it is thus necessary to have a knowledge of e. If this is not known then we can do no more than calculate an apparent osmotic coefficient (j>a, which is calculated as though the substance 2 were not dissociated (e = 0) or a coefficient cf)a by assuming complete dissociation (e = 1). These are related by the equations... 

ACTIVITY COEFFICIENTS OF SODIUM CHLOBIDE FROM FREEZING POINT MEASUREMENTS... 

The amount of reliable data available for the purpose of correcting activity coefficients obtained from freezing point measurements is not large. The freezing point method has thus been mainly used for the study of dilute solutions. 

As a result of freezing point measurements carried out with vanous amalgams, Richards and Daniels have shown that the compound Tl2Hg6 exists, its composition corresponding roughly to 29 per cent of thallium The compound melts at 14 90 C Owing to dissociation one would scarcely expect the existence of this compound to affect senously the e m f values, especially m the more dilute region The deviations from the osmotic expression can scarcely be attributed therefore to this compound... 

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