Measurements partial molal

The partial molal volumes of gases in water are needed to apply the Krichevsky-Kasarnowsky and the Krichevsky-Ilinskaya equations. A survey of the available experimentally measured partial molal volumes is given in Table VII. The results of Tiepel and Gubbins (2 ) seem especially reliable. The recent results of Popov and Drakin 26) usually appear to be much too high, possibly because of Popov and Drakin depended on literature solubility values for the concentration to be used in their calculation of the partial molal volume from the density data. 

One should always remember that it is difficult to proceed from thermodynamic measurements to molecular properties. This is particularly true in multicomponent systems. That is, water-water and water-protein interactions are inextricably mixed with protein-protein interactions when one measures partial molal quantities. Assumptions and experiments beyond those yielding thermodynamic information are needed to determine what is happening at the molecular level. The major cause... 

Since the saturated solutions of AgT and AgCl are both very dilute, it is of interest to examine their partial molal entropies, to see whether we can make a comparison between the values of the unitary terms. As mentioned above, the heat of precipitation of silver iodide was found by calorimetric measurement to be 1.16 electron-volts per ion pair, or 26,710 cal/mole. Dividing this by the temperature, we find for the entropy of solution of the crystal in the saturated solution the value... 

Let us now ask how this value could be used as a basis from which to measure the local disturbance of the water structure that will be caused by each ionic field. The electrostriction round each ion may lead to a local increase in the density of the solvent. As an example, let us first consider the following imaginary case let us suppose that in the neighborhood of each ion the density is such that 101 water molecules occupy the volume initially occupied by 100 molecules and that more distant molecules are not appreciably affected. In this case the local increase in density would exactly compensate for the 36.0 cm1 increment in volume per mole of KF. The volume of the solution would be the same as that of the initial pure solvent, and the partial molal volume of KF at infinite dilution would be zero. Moreover, if we had supposed that in the vicinity of each ion 101 molecules occupy rather less than the volume initially occupied by 100 molecules, the partial molal volume of the solute would in this case have a negative value. 

Interesting is a comparison of the volumes occupied by individual complexes in solution and in the solid state. The partial molal volumes can be obtained from precise measurements of the solution densities of the complexes as a function of concentration [177]. These values may be subsequently compared with the unit cell volumes per complex molecule derived from the crystal structure. For Fe[HB(pz)3]2, the apparent molal volume in tetrahydrofuran solution was determined as 340.9 em mol Taking into account that the complex in solution forms an equilibrium between 86% LS and 14% HS isomers and employing the volume difference between the two spin states AF° = 23.6 cm mol S the volume of the LS isomer was calculated as 337.6 cm mol This value agrees closely with the volume of 337.3 cm mol for the completely LS complex in solid Fe[HB(pz)3]2 [105]. 

Calcium-sodium-chloride-type brines (which typically occur in deep-well-injection zones) require sophisticated electrolyte models to calculate their thermodynamic properties. Many parameters for characterizing the partial molal properties of the dissolved constituents in such brines have not been determined. (Molality is a measure of the relative number of solute and solvent particles in a solution and is expressed as the number of gram-molecular weights of solute in 1000 g of solvent.) Precise modeling is limited to relatively low salinities (where many parameters are unnecessary) or to chemically simple systems operating near 25°C. 

We have been actively developing two types of calorimeters which will operate at elevated temperatures and pressures. One type is a heat of mixing calorimeter to measure enthalpies of dilution in order to obtain differences in partial molal enthalpy... 

In kinetics, similar relationships apply, but the volume of activation AV can be determined only from the pressure dependence of the rate coefficient k, since the partial molal volumes V of transition states are not directly measurable. Conversely, however, equation 4 can yield values of V. ... 

When performing the chemical analysis of an aqueous solution, we obtain a set of values representing the bulk concentration of dissolved components, but we do not discriminate the various forms of solutes in which a given species is partitioned. For instance, we can measure the total molal amount of calcium or fluorine mp, but this value is the sum of all partial molalities of ionic and... 

In connection with Vaslow s measurements (150) of the apparent molal volumes of the alkali metal chlorides in solutions, we call attention to the earlier measurements by Halasey on the temperature dependence of the partial molal volumes. These measurements suggest (31) that the... 

An experimental measure of the interaction of a solute species with a given solvent medium is afforded by the partial molal heat of solution, AHs. For a stable species this is obtained directly by calorimetry or indirectly from the temperature coefficient of the Henry s law constant. The difference in the value of AHs between the two solvents is termed the enthalpy of transfer, denoted by 8AHtI. Combining enthalpies of transfer for the reactants, 8AHft, with transfer enthalpies of activation, 8AH t, using equation (1)... 

Probably the most significant comparisons which can be made are of values of properties determined from calorimetric measurements with values calculated from adsorption isotherms. Two general methods are available for the comparison of values of enthalpies determined from experiments of the two types. One involves two differentiations The change in the partial molal enthalpy, AH2, of X2, for Process 4, is determined from the differentiation with respect to n2/n1 of the integral heat of adsorption measured in a series of calorimetric experiments of the type represented by Equation 1. The values of the differential heats of adsorption (heats corresponding to the differential Process 4) are compared with values determined from the temperature variation of AG2/T for a series of values of n2/n in Process 4. This type of comparison has been made successfully by several groups of authors (3, 5, 10). 

If the quantity of adsorbent should be increased by the addition of more material in the same state of subdivision, we could measure changes in volume, in heat capacity, and in certain other extensive properties which can be directly observed. We could differentiate any one of these properties with respect to the number of moles of adsorbent (whether the system contains one, two, or more components) to obtain a partial molal property. The partial molal property so obtained would be the weighted average for interior and exterior adsorbent and is in harmony with Equations 9 and 11. 

Adsorption isotherms for the system BaS04-H20 at three temperatures have been obtained. Thermodynamic study of these data reveals that part of the free energy decrease in the adsorption process involves changes in the partial molal free energy of the adsorbent. From the three isotherms differential and integral heats of adsorption were derived and compared with new calorimetric determinations of the same thermodynamic functions. In both kinds of measurements exactly the same system and exactly the same materials were used. 

Similarly, although there is a maximum difference in cadmium partial molal free energy of a little less than 2 kcal. per mole between the extrapolated upper structure, a, of Figure 1 and the most stable observed microphases, the difference in total molal free energy is less than 10 cal. per mole. (The calculation is based on the path 133 to 209 with assumed two-phase equilibrium pressures of cadmium. This path closes on microphase H.) The difference in these two values emphasizes that the vapor pressure measurements have reflected the concentration and bonding of cadmium species which are minor fractions of the total cadmium present and which did not much alter the average bonding of the system. 

Actually this is an almost trivial category, siru e, when measurable, it might usually be expected that the reverse rea( tions to groups 1 and 2 would belong to group 3. The only requirement r this is that the over-all partial molal volume change in reaction AFr be less than AF" ". This condition usually obtains. 

In Chapter 8, Zuyi Tao, in order to provide a better understanding of the ion-exchange behavior of amino acids, has compiled their particular acid-base properties, their solubility in water, their partial molal volumes, and their molal activity coefficients in water at 25 C. This information has been used in Gibbs-Donnan-based equations to facilitate a better understanding of the mechanism of amino acid uptake by ion exchangers at low and high solution concentration levels. Measurement of distribution coefficients and separation factors are also described. The eventual resolution of thermodynamic ion-exchange functions (AG, AH, and AS) is provided for the reader. 

There are several studies that have been successful in determining the dissolution rate at conditions near seawater saturation. Acker et al. (1987) was able to employ very precise determinations of pH to measure the rate of dissolution of a single pteropod shell at different pressures from 15 atm to 300 atm. Because his measurements were at different pressures and is a function of pressure, he was able to determine whether the rate constant is indeed a function of K p. He found that Equation (9) fit his data better than (10), suggesting that the constant is not pressure dependent and the former is a more accurate universal rate law. An exponent oin= 1.9 was obtained for this surface-controlled dissolution reaction and a partial molal volume. Ay, of —39 cm mol (very close to the mean of the values determined in laboratory experiments for calcite) best fit the data. 

This provides a means of finding the partial molal volumes as illustrated in Fig. 1.19.1, one measures the molar volume of the solution at a set of X2 values. At the particular value X2 = b a tangent to the curve is drawn. The points of intersection of this tangent at X2 = 0, 1 yields the desired quantities Vi and V2 respectively. 

Since G is not as readily measured as V, methods other than those discussed above for specifying partial molal volumes must be introduced to determine the chemical potentials. These procedures will be taken up at a later stage. 

To determine the in situ properties of the carbonate system in the ocean, it is necessaiy to determine the effect of pressure on the thermodynamic constants. This correction can be made in two ways (1) using direct measurements of the constants and (2) using partial molal volume and compressibility data (Mil-lero, 1979). The two methods are in good agreement (Millero, 1979) when comparisons are made for the carbonate system. The effect of pressure on the dissociation constants of acids (A ,) can be made from (Millero, 1979) equations... 

Charles (1954) has compared the entropy of ethylenediamine-tetraacetate (EDTA) complex formation for several elements, including zinc, and finds the entropy change to be a linear function of the partial molal entropy of the complexed metal. In Fig. 10, the entropy changes in the formation of ammonia (Williams, 1954), ethylenediamiue (En) (Davies et al., 1954), and EDTA (Charles, 1954) complexes of Zn, Cu, and Cd are plotted as a reciprocal of the ionic radius minus a term containing the molecular weight (Powell and Latimer, 1951), as a measure of the partial molal entropy of the cations. The AS° values plotted are for the reaction ... 

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