Partial molar compressibility

Equation 163, written as liu = (f- / RT, clearly shows that In (j) is a partial molar property with respect to GR/ RT. MultipHcation of equation 175 by n and differentiation with respect to at constant 7, P, and in accord with equation 116 yields, after reduction, equation 179 (constant 7, .x), where Z, is the partial molar compressibility factor. This equation is the partial-property analogue of equation 178. 

Further deviatives yield the partial molar compressibility, Iq, and the partial molar heat capacity, These quantities are required to calculate chemical potentials at higher pressures and over a wider range of temperatures, respectively. 

If instead AV° is a function of pressure, we may define the standard partial molar compressibility which for single species i equals... 

Table 6.10 shows that the partial molar volumes and particularly the isentropic partial molar compressibilities at infinite dilution are significantly higher in the micellar environment than in water. As far as the partial molar volume is concerned, the increment per CH2 group is reasonably constant. The values are 15.9 cmVmol in water and 16.8 cmVmol in the micelles. This can be compared to a CH2 group value of 16.1 in octane and 16.2 in heptane and 16.8 for the molar volume of pure alcohols. It means that as far as the volume of a CH2 group in the micelle is concerned, pure alcohol is the best comparison. 

Partial Molar Volumes and Isentropic Partial Molar Compressibilities of Alcohols at Infinite Dilution in Aqueous Surfactant Solutions at 298.15 K (volumes in cm /mol, compressibilities in cm /mol/bar)... 

If we look at the absolute values of partial molar volumes and compressibilites of alcohols solubilized in micelles, it appears that for the lower alcohols, up to heptanol, volumes and compressibilities exhibit lower values in SDS than in carboxylates. It also appears that the partial molar compressibilities of these alcohols are higher than the molar compressibility of the pure alcohols when solubilized in the carboxylate micelles and lower when solubilized in SDS. 

In cationic micelles the partial molar compressibility is generally slightly higher than for the anionic ones. There are two possible explanations for the differences in partial molar compressibility for an alcohol in the various micellar systems. It is possible that the micellar structure is slightly different and that it is easier to compress a carboxylate micelle around an alcohol molecule than it is for a dodecylsulfate micelle. However, the partial molar compressibility of a surfactant molecule... 

Here, quantity 2, is a partial molar compressibility factor evaluated at constant temperature and total volume ... 

Here, pis molar density, and is a partial molar compressibility factor given by... 

This very extensive (99 pages) chapter (no. 2 in Volume II) contains a general discussion of the effects of temperature and pressure on activity coefficients for both binary and mixed electrolyte solutions. Properties of interest are the partial molar volume, expansibility, compressibility, heat capacity, and enthalpy. There is also an excellent discussion of methods of estimating partial molar properties in mixed electrolyte solutions. There are 226 references to the literature. Tables of data are presented for Debye-HUckel limiting law slopes for the afJ parent molar volume, enthalpy, heat capacity, expansibility, and compressibility as a function of temperature parameters for the partial molar volumes of 30 aqueous electrolyes at 25 °C parameters for the partial molar expansibility of ten electrolytes at 25 C parameters for the partial molar compressibilities of 33 electrolytes at 25 °C values of the activity coefficients of aqueous NaCl solutions at 25 C as a function of pressure (up to 1000 bars) parameters for the partial molar enthalpies of 59 electrolytes at 25 C parameters for the partial molar heat capacities of 140 electrolytes at 25 °C and tables giving compositions and the partial molar properties of average seawater. 

There are several thermodynamic properties that are very useful for investigating solute-water interactions in aqueous solution. The partial molar compressibility of the solute is one such property. This quantity is particularly sensitive to the nature and extent of the intermolecular interactions between the solute and the solvent [74M, 94C1] and, as such, can be used to characterize the hydration of solutes in aqueous solution. The importance of compressibility measurements as a means to characterize the hydration of proteins and their constituent groups has been recognized and as a consequence of this, new results on biological compounds have been reported in recent years. In addition to this emphasis on hydration, compressibility measurements of proteins in aqueous solution are also of some importance in the study of the dynamics of globular proteins since the volume fluctuation of a protein is related to its isothermal coefficient of compressibility [76C],... 

It is generally difficult to calculate precise values of partial molar compressibilities from a direct determination of the derivative (3Vi/3p)x. A more convenient method is to determine the apparent molar compressibility from which the partial molar property can be derived. The apparent molar isothermal compressibility of a solute in a solution is given by the equation... 

In a recent study of the a, co-amino acids, Chalikian et al. [93C] determined apparent molar quantities over the concentration range 1 - 3 mg mL Within the limits of the experimental errors, the results obtained were considered to be the same as partial molar compressibilities at infinite dilution. 

Kharakoz [9IK] analyzed the partial molar compressibilities for the amino acids using an additive function of contributions of atomic groups Ki... 

There have been few studies undertaken to obtain partial molar compressibilities of peptides in aqueous solution. The available data are presented in Table 8. Most of the K3 2data for peptides in aqueous solution have been obtained in our own studies. 

The partial molar compressibilities at 25°C for members of the series of oligoglycines, (gly)n, have been determined in several studies [8711, 91H1, 94C2]. This homologous series is of some interest... 

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