Partial molal volume measurements

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. 

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]. 

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. ... 

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... 

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... 

In the work presented here, these processes have been studied primarily by calorimetry. Planned measurements of partial specific heat and partial molal volume will give additional thermodynamic data on the structure of micellar systems. Heat capacity measurements will allow "simple" extrapolation of measured enthalpy terms to higher temperatures. In addition, a direct measure of the effect of temperature variation is of interest for solution structure studies. Partial molal volume measurements give information on the packing of surfactant monomers and micelles within the water structure. The effect of cosurfactants on the partial molal volume will be of particular interest. 

The comparison studies of decyl and dodecyl sulfonates show the strong dependence of the enthalpy terms on chain length. The cmc for the decyl salt is considerably higher under all conditions than the dodecyl salt. The planned heat capacity and partial molal volume measurements will be of interest in this comparison. 

Of course the partial molal volume of Haq is not directly measurable. This parameter could be measured for the solutes Ho and He by determining densities of solutions, but no record of such observations has been found. The entry for V° of Haq in Table I is simply the volume of a sphere of radius 1.0 A. (the volume containing 99% of the electronic charge distribution). The ideas of Nemethy and Scheraga (6) on hydro-phobic bonding suggest that even this small estimate may be somewhat too large. 

The partial molal volume (Vh) of dissolved hydrogen is about 0.30 nm atom for aU metals in which it has been measured [43]. A number of measurements have been made on a-iron, and the overall results indicate a value of 0.33 nm atom , or 2.0 cm mol [38, 44, 45]. 

Density measurements, like solubilities, have also frequently been obtained for purposes other than calculating thermodynamic properties, and consequently many of these are not useful for evaluating partial molal volumes. There are, however, some excellent recent measurements in this area which have been used to evaluate partial molal volumes. Since Millero has thoroughly examined all volume data for electrolytes in both aqueous and non-aqueous solutions in a recent review, only some of the more interesting results, from a structural point of view, will be included here. 

Although density measurements of varying degrees of accuracy have been reported for ethanolic solutions, standard state partial molal volumes in ethanol have been evaluated for only a few electrolytes. Vosburgh, Connell and Butler reported for LiCl in water and a series of alcohols, including ethanol. They observed that the salt had a much smaller value of F in the alcohols than in water, and that for all the systems studied it was smallest in ethanol. Sobkowski and Mine have reported for HCl in water and the three lower alcohols and also observe F to be smaller in the alcohols than in water, but it is smallest in methanol rather than ethanol. Lee and Hyne have reported F° at 50.25°C for the tetraalkylammonium chlorides in ethanol-water mixtures up to 0.4 mol fraction of ethanol. With the tetramethyl and tetraethyl salts, the volumes are all very positive in water but decrease rapidly with an increase in alcohol content and appear to be at a minimum around 0.3 to 0.4 mol fraction of ethanol. The higher tetraalkyl salts are not entirely consistent with this pattern. 

In an attempt to correlate gross structure of solute-water with packing and stereochemistry, the partial molal volumes and isentropic partial molal compressibilities were measured for sugars, uronic acids, and some di- and trisaccharides in water at 25 C. Attempts to systematize the results were unsuccessful. In a different approach, the structural transitions at saturation temperature using Arrhenius plots of results obtained by conductance measurements on electrolyte-sucrose-water solution were determined. These transitions were postulated to be due to the ability of the sucrose to form intermolecular hydrogen bonds with the solvent, so that at saturation temperature it was considered to have entered the total structure of the solution. ... 

Generally, the values of h differ somewhat with different methods of calculation, but they consistently show an increase in h of 10-20% throughout the lanthanide series (Bertha and Choppin 1969). Thus, hydration numbers range from 9.0-11.0 and 12.8-13.9 as calculated from partial molal volumes (Padova 1967) and conductivity (Choppin and Graffeo 1965) measurements. Under similar experimental conditions, the relative values of h for An (III) ions and Eu(III) indicate that actinide ions are more... 

Partial molal volumes are d( t( rminable from experiment by a variety of methods, the most commonly used one involving the computation of the apparent molal olume, pure solvent. The quantity

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This method involves the accurate measurement of the density of the solution and the determination of the surfactant concentration. Any change in the partial molal volume of surfactant will be reflected in the density of the solution. As with all of the other methods, very careful measurement procedures and precise temperature control are required in order to obtain reliable data. This method can be used for any type of surfactant in aqueous, as well as non-aqueous, systems. 

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