Partial molar volume of the solute

For a dilute solution at high pressure, the variation of activity coefficient with pressure cannot be neglected. But when x2 is small, it is often a good approximation to assume, as above, that the activity coefficient is not significantly affected by composition. If we also assume that v2 the partial molar volume of the solute, is independent of both pressure and composition... 

It is well known that the transfer of nonpolar molecules from nonpolar to polar surroundings results in a decrease in the partial molar volume of the solute. The dimerization studies also show that there is a similar volume decrease when two monomers form a dimer. This volume decrease is of the order of 20 cm3 mol-1. It is difficult to understand how there can be first a volume decrease when the nonpolar molecules are transferred from the nonpolar to the polar environment and then a further volume decrease when two molecules come together and partly reverse the first transfer. It is a little dangerous to speak of the partial reversal of a process we know so little about. It is believed that the hydrophobic hydration is a cooperative phenomenon, in which the exact microstructure of water is very important for the occupied volume. How this microstructure changes when two molecules associate in a hydrophobic interaction is not par-... 

For iodine in methanol solution, the partial molar volume of the solute is essentially constant, independent of concentration, and is equal to 62.3 cm ... 

PI 1.7 Start with equation (11.96) applied to the apparent molar volume V, solve for V, and differentiate to show that V is related to the partial molar volume of the solute by... 

Then, in the limit as x2 goes to zero, with the use of the equation of state for an ideal gas and with the assumption that the partial molar volume of the solute in solution is negligibly small with respect to the molar volume of the gas, Equation (10.159) becomes... 

We see again that Henry s law is a limiting law valid when the molar volume of the gas is large with respect to the partial molar volume of the solute. When the pressure is used as the dependent variable, the applicability of the ideal gas equation of state is also required. 

Equation 11 should be the relationship between retention-solubility and pressure at constant temperature for infinitely dilute solutions. The RHS of eq. 11 consists of three terms, the first term will be a constant whose value depends on the partial molar volume of the solute in the stationary phase. The second term is the solubility of the solute in the supercritical fluid mobile phase. 

The effect of the partial molar volume of the solute in the stationary phase at infinite dilution can be seen in Figure 8. This -stat... 

The composition dependence of the total volume of a solution at constant temperature and pressure is expressed in terms of the partial molar volumes of the solute and the solvent. Since we are concerned with solvation properties, the quantities which we need to discuss are the partial molar volumes in infinite dilution of the solute so that solute-solute interactions make no contribution. In practice, partial molar volumes are obtained indirectly from precise density measurements. The partial molar volumes at infinite dilution of the amino acids are compiled in Table 2 [7]. It is apparent from these data that an approximately linear correlation exists between the partial molar volume and the number of carbon atoms in the backbone. The data indicate volume contributions from the polar head group (NH, COj) and from the CH2 group and to be about... 

Source of Data. There are only a few local density data, and partial molar volumes of solutes at infinite dilution are scarce as well. Only two systems could be identified for which data for the calculation of the correlation volume are available CO2 + naphthalene and CO2 + pyrene. The augmented local density data in these systems were taken from ref 24 and the partial molar volume of the solute at infinite dilution in CO2 + naphthalene system from ref 8. Because the partial molar volume of the solute at infinite dilution for the CO2 + pyrene system was not available, it was taken equal to that for the CO2 + phenanthrene. The density and compressibility of the pure SCR CO2 were taken from refs 1 and 24, respectively, and the solubilities of naphthalene and p)rene in SCR CO2 from refs 28 and 29, respectively. 

The results listed in Tables 1 and 2 also indicate that the sizes of the solvent aggregates predicted from the BN and ML excesses are in agreement with those evaluated from the large negative partial molar volume of the solute at infinite dilution. However, as already noted the BN excesses provide unreasonable results for the aggregate sizes in mixtures far from the... 

The partial molar volume of the solute (component 2) can be expressed in terms of the... 

Examination of literature data has shown that most SC mixtures exhibit the same behavior d COJ naphthalene regarding the partial molar volume of the solute when the mixture moves towards the critical conditions, the partial molar volume of the solute decreases and under certain conditions becomes zero and further becomes negative and at infinite dilution diverges negatively at the critical point of the SCF. A few mixtures, such as COJ ethane, exhibit a different behavior. When the mixture approaches the critical conditions, the partial molar volume of the solute remains positive and at infinite dilution diverges positively at the critical point of the SCF. 

Here V" is the partial molar volume of the solute gas, and 8 and 8b are the solubility parameter values of the solute and the bulk liquid. The solubility parameter is also cohesive-energy density, a measure of the forces between the molecules given by... 

Other molecular properties have been also proposed to model the hydrophobic interactions. The parachor, which is related to the surface tension of a compound (139, 140) represents mainly the intermolecular interactions in a liquid. The Hildebrand-Scott solubility parameter, 6, (141) is related to intermolecular van der Waals forces and the closely related molar attraction constant, F, is obtained by multiplying 6 by the molar volume (142). The partition coefficient between two solvents can be obtained from the solubility parameters and the molar volumes of the solute and the solvents (193). This relationship is based on regular solution theory (194) and the assumption that the partial molar volumes of the solute is not different from its molar volume. Recently this has been criticized and a new derivation was proposed (195) in which the partial molar volumes are taken into account. The molar refractivity, MR, is related to dispersion forces and can be obtained as a sum of the partial molar refractivi-ties assigned to atoms and bonds (140, 143). These parameters have been compared (144) to establish their relative applicability to correlations with biological activity. The conclusion was that logP and molecular refractivity were the best parameters. Parameters obtained from high pressure liquid chromatography (144,... 

The accuracy of equation (43.11) may be tested by plotting the experimental values of V29 the partial molar volume of the solute, at various concentrations against Vc the results should approach a straight line of slope 0.99 in... 

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