Coefficient partial molal volumes

Matteoli, E. and L. Lepori. 1990. The ternary system water + 1-propanol + urea at 298.15 K. Activity coefficients, partial molal volumes and Kirkwood-Buff integrals. Journal of Molecular Liquids. 47, 89. 

Coefficient expressing the effect of concentration of gas on its activity coefficient, kg H20/mole Coefficient expressing the effect of change of partial molal volume of electrolyte (with temperature) on the salting-out coefficient, kg H20/cm3. Salt concentration, mol/2. 

When the Krichevsky-Kasarnowsky equation fails it may be because of either changing activity coefficient of the solute gas with composition, changing partial molal volume of the gas with pressure, or both. The Krichevsky-Ilinskaya equation takes into account the variation in the activity coefficient of the solute gas with mole fraction by means of a two-suffix Margules equation. 

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 these equations is the partial molal free energy (chemical potential) and Vj the partial molal volume. The Mj are the molecular weights, c is the concentration in moles per liter, p is the mass density, and z, is the mole fraction of species i. The D are the multicomponent diffusion coefficients, and the are the multicomponent thermal diffusion coefficients. The first contribution to the mass flux—that due to the concentration gradients—is seen to depend in a complicated way on the chemical potentials of all the components present. It is shown in the next section how this expression reduces to the usual expressions for the mass flux in two-component systems. The pressure diffusion contribution to the mass flux is quite small and has thus far been studied only slightly it is considered in Sec. IV,A,6. The forced diffusion term is important in ionic systems (C3, Chapter 18 K4) if gravity is the only external force, then this term vanishes identically. The thermal diffusion term is impor-... 

An admittedly extreme but dramatic example is provided by the study of supercritical solutions. At H2O densities of about 0.3 g/cc the partial molal volume of NaCl in steam above the critical temperature of water (374 C) can reach values of —5000 cc/mole The coefficient of compressibility of steam at this temperature and density is about 20 times greater than for H2O at 25°C. Data from S. W. Benson et al., J. Chem, Phys., 21, 2208 (1953). 

Water solubility (g/100 g, 25 C) P -COjH P -nhJ pK side chain Partial molal volumes (cm mol", 25°C) Molal activity coefficients in water, 25°C ... 

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. 

The osmotic pressure of a sucrose solution is 148.5 atm at 20°C. The concentration is 1.43 kg sucrose/kg water, corresponding to a mol fraction 0.0700 of sucrose. The partial molal volume of water is approx 0.018 L/g mol. Accordingly, the activity coefficient of the water is... 

Thermodynamic activities of ionic species in aqueous solutions with ionic strength (I) < 0.01 molal (m) commonly are calculated using the ion-pair model (3), which is valid also for solutions with I < 0.1 m. In dominantly NaCl solutions, the ion-pair model can be used for I < 3 m with appropriate adjustments to the activity coefficients (4). The specific ion interaction model ( may be more appropriate for solutions of high ionic strengths. The effect of pressure on the thermodynamic activities of single ions in this model can be estimated from the stoichiometric partial molal volume and compressibility data (]) However, a complete data set for all the ion-interaction parameters is not yet available for this model to be used in complex geochemical solutions. 

Standard molal volumes of minerals together with the coefficients of isobaric expansion and isothermal compressibility are available in several compilations (8,9). Standard partial molal volumes of uncomplexed ions are available at 25°C and 1 atm. (1) however, data are sparse for the coefficients of isobaric expansion and isothermal compressibility. 

Wavelength of maximum absorption Extinction coefficient at 7200A. Width at half-height Oscillator strength Diffusion Constant Equivalent Conductance Effective Collision Radius Ion Atmosphere Relaxation Time at /x = 0.24M Partial Molal Volume Standard Free Energy of Solvation G (e m), y-Radiation Yield Lifetime with respect to H30+ at pH 7 Lifetime with respect to H20... 

Thus we thought it necessary to measure the solute activity (or activity coefficient), namely the mean activity (or activity coefficient) of polyelectrolytes. Our subsequent study was extended to the partial molal volume of polyelectrolytes, which is a pressure derivative of the mean activity coefficient. By this volumetric property, the solvait-solute interactions in polyelectrolyte solutions, which could be discussed only qualitatively on the basis of the mean activity coefficient data, were considered in a quantitative way. Furthermore, the catalytic action of polyelectrolytes in ionic reactions was studied and discussed in terms of the activity coefficient data. 

The partial molal volume (F ) at zero concentration was determined by extrapolation of The F was found to increase with rising temperature, and the temperature coefficients for tetrabutylammonium salts of polyacrylic add, polyethylenesulfonic add, and polystyrenesulfonic acid were in the range of 0.2 0.3 ml/monomole-deg 80), which are in a rough agreement with those found for tetrabutylammonium bromide [0.2 0.5 ml/mole deg] (S5). The values were discu d in terms of the partial molal voluine of macroions (Fj ) and g enions (F, )... 

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