Transfer partial molar volume

For the mechanistic interpretation of activation volume data for nonsymmetrical electron-transfer reactions, it is essential to have information on the overall volume change that can occur during such a process. This can be calculated from the partial molar volumes of reactant and product species, when these are available, or can be determined from density measurements. Efforts have in recent years focused on the electrochemical determination of reaction volume data from the pressure dependence of the redox potential. Tregloan and coworkers (139, 140) have demonstrated how such techniques can reveal information on the magnitude of intrinsic and solvational volume changes associated with electron-transfer reactions of transition... 

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-... 

The partial molar volumes at infinite dilution of the amides show a consistent volume decrease for the amides on transfer into the aqueous phase, which becomes greater with increasing size of the substituents and amounts to about 2.5 cc. per mole per pair of methylenic groups in the case of the acetamide series. This value may be compared with that found in the alcohol series (6), where a more negative value of about 2.5 cc. per mole per methylenic group is found, and also to similar de-... 

The kinetic effect on (1/72—1/7)) is proportional to (Amagnetic field as shown in Fig. 7.23. From the temperature and pressure dependence, the kinetic parameters presented in Table 7.13 were obtained. The two activation parameters, namely the entropy and the volumes of activation, are negative and also are of the same magnitude for all the lanthanide ions. These activation parameters imply a common water exchange mechanism for all the lanthanides studied and possibly an associative activation path of exchange. The activation volume, AV of —6.0 cm3 mol-1 probably reflects the difference between a large negative contribution due to the transfer of a water molecule electrostricted in the second coordination sphere to the first coordination sphere and a positive contribution due to the difference in partial molar volumes of N + 1 coordinated transition state and N coordinated aquo lanthanide ion. It should be noted that the latter difference (in partial molar volumes of Fn(H20)w+i and Fn(H20)jv is due to the increase in Fn-O bond distance (Fig. 7.16). 

Several factors can affect this enhanced mass transfer. First, as Debenedetti and Reid ( pointed out, the very low kinematic viscosities in conjunction with very high buoyant forces serve to enhance natural convection at the same Reynolds number. This is accentuated by large density differences that can occur as naphthalene dissolves in the C02 It is possible to have very large, negative partial molar volumes (i.e., -2000 cc/mole) for a solute at conditions near the critical point (Eckert et al., (23)) which causes the fluid density to depend strongly on composition. At 35 0 and 100 atm, naphthalene s partial molar volume at infinite dilution is approximately -300 cc/mol. This can cause a significantly higher fluid... 

Electrochemical methods have also been adopted for application of high pressure [41-43] (see Chapter 5). Correlations emerging from these investigations have valuable application in the interpretation of partial molar volume changes associated with electron transfer reactions (see Sect. 1.3.4). A potential future interest is in reactions carried out at elevated pressures in a suprercritical fluid medium in view of this a special optical cell has been developed for studying organometallic reactions initiated by flash photolysis in supercritical fluids [20] (see Chapters 12 to 14). 

Probably the most systematic and complete study on the influence of temperature on water transfer has been performed on mammalian red cells [10,20,28]. The dependence on temperature of both the tracer diffusional permeability coefficient (cotho) 3 nd the hydraulic conductivity (Lp) of water in human and dog red-cell membranes have been studied. The apparent activation energies calculated from these results for both processes are given in Table 2. The values for the apparent activation energies for water self-diffusion and for water transport in a lipid bilayer are also included in the table. For dog red cells, the value of 4.9 kcal/mol is not significantly different from that of 4.6-4.8 kcal/mol for the apparent activation energy of the water diffusion coefficient ( >,) in free solution. Furthermore, it can be shown that the product L — THOV )rt, where is the partial molar volume of water and the viscosity of water remains virtually independent of temperature for dog, hut not for the human red-cell membrane [20]. The similarity of the transmembrane diffusion with bulk water diffusion and the invariance of the... 

Fluid phase interactions - Second virial coefficients Solution interactions - Partial molar volumes - Solubilities Surface interactions - Adsorption isotherms Diffusion coefficients Mass transfer coefficients Molecular masses... 

Although a number of methods have been proposed to determine the cmc of surfactants, such as electrical conductance [4, 5], transference number [6, 7], dye absorption [8-10], solubilization [11-15], surface tension [16, 17], partial molar volume [18, 19],... 

Tabulated are single-ion entropies of about 110 diatomic and polyatomic ions in water Gibbs energies, enthalpies, and entropies of hydration of monatomic ions at 25 C partial molar volumes of about 120 common ions at 25 C ionic partial molar heat capacities of ions Gibbs energies of transfer of inorganic electrolytes from HjO to 020 and calorimetrically determined enthalpies of solution of salts in H2O and 020. 

Tabulated are the equivalent conductances, transference numbers, activity coefficients, densities and partial molar volumes, apparent molar compressibilities, heats of solution and dilution for the rare earth salts in aqueous solution at 25 "C. 

Recent applications of the theory have been made for calculating the contribution the formation of a cavity gives to the free energy of transfer of a series of isomeric ketones(134), or various other solutes(132), from H2O to D2O, for the studies of solubility of many apolar gases in water and other polar solvents(135), for comparing the experimental thermodynamic data for the solution of rare gases(51), or some perfluorocarbon gases(136), in water at various temperatures with data calculated by means of the SPT. In a tentative made to extend the theory at aqueous solutions where solute-solute interactions have to be considered and hydrophobic interactions are operative, it has been shown that the dependence of the partial molar volumes and enthalpies of hard-sphere solutes in water on concentration and temperature are due to the anomalous trends the 63/6P and 63/6T (3 coefficient of isothermal compressibility) of pure water present, rather than to the solute structural effects(137). 

Thermodynamic properties of ions in nonaqueous solvents are described in terms of the transfer from water as the source solvent to nonaqueous solvents as the targets of this transfer. These properties include the standard molar Gibbs energies of transfer (Table 4.2), enthalpies of transfer (Table 4.3), entropies of transfer (Table 4.4) and heat capacities of transfer (Table 4.5) as well as the standard partial molar volumes (Table 4.6) and the solvation numbers of the ions in non-aqueous solvents (Table 4.10). The transfer properties together with the properties of the aqueous ions yield the corresponding properties of ions in the nonaqueous solvents. 

Equation 9.138 is an overall conservation equation, expressing perhaps conservation of volume. It shows how the velocity v changes as a result of an electrode reaction and the changing composition of the solution. Equation 9.139 is a material balance for the electrolyte. Both equations simplify considerably with assumptions of constant transference numbers and partial molar volumes. Equations 9.122, 9.125, and 9.138 can then be combined and integrated to relate the velocity to the current density... 

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