Partial molar volume absolute value

Fig. 13. Absolute partial molar volumes, Vab8°, of [Ln(H20) P in aqueous LnCl3 solutions (301) (closed circles), compared with the calculated Vabs° values (4, 42) for [Ln(H20)8]3+ and [Ln(H20)9]3 indicated by the upper and lower solid curves, respectively. Interchange rate constants, kj (298 K) (310), for the substitution of S042 on [Ln(H20) ]3+ are shown as open squares, and water exchange rate constants, fcn2o (298 K) (311, 312), for [Ln(H20)8]3+ are shown as open circles. 

The absolute partial molar volumes, V° for [Ln(H20)n]3+ in LnCU, calculated value of V° for 8 and 9 coordinate ions, rate constants for substitution by sulphate, water exchange, and activation volumes are shown for lanthanide series in Fig. 8.40. It is clear from the figure the nine coordination is valid from La to Nd, 8 coordination from Dy to Lu and intermediate between 8 and 9 for Pm to Tb. This type of change in coordination number causes further confusion in distinguishing inner sphere from outer sphere. 

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. 

It is clear that from the integrated form of Equation (4) the volume of reaction can be obtained if the equilibrium constant can be determined over a range of pressure. If the volume of activation is not experimentally accessible for one of the directions of the reaction, A V can be used to calculate its value. Under certain conditions and with suitable properties of reactants and/or products it may be possible to determine their partial molar volumes, hence allowing development of a volume profile on an absolute volume basis, as noted above. Even if A V can be determined either from the pressure dependence of the equilibrium constant and/or from use of Equation (5), it may be possible to confirm its value by determination of the partial molar volumes from density measurements. The conditions for conducting successful determinations of partial molar volumes are rather stringent and will be described in Section 2. The method depends on measuring the density, d, of several solutions of different concentrations of the reactant or product. The following equation is used to obtain... 

Note that in contrast to the partial molar volume, this quantity is not a relative one. This follows from the fact that the absolute value of the partial molar enthalpy cannot be determined. In a thermodynamic system with constant T and P, the isobaric heat capacity can be regarded as the measure of the enthalpy fluctuations of the system ... 

It is important to note that few simplifications have been considered in application of Henry s law (sometime also called Henry-Dalton s law) the validity of the ideal gas equation, ideal diluted solution and that the partial molar volume of the dissolve gas is negligible compared with that in the gas phase. However, the range of its validity in the climate system is appreciable. It is clear that during heterogeneous nucleation (CCN to cloud droplet formation) Henry s law is not valid. Absolute values of solubility cannot be found from thermodynamic considerations. Nevertheless, general rules are valid for all gases ... 

A simpler version of the same principle uses the language of the mixture-model approach to liquid water. Within this approach, the principle states that there exists a range of temperatures and pressures at which there are non-negligible concentrations of two species one characterized by large partial molar volume and large absolute value of the partial molar enthalpy, and a second characterized by a smaller partial molar volume and smaller absolute value of the partial molar enthalpy. In order to obtain the outstanding properties of water, one also needs to assume that the concentrations of these two species are of comparable magnitude (see Sec. 2.3 for details). 

Zana and Yeager (1966) measured the individual or absolute ionic partial molar volumes of ions at room temperature using the ultrasonic vibration potentials and they could assign values for the V° of some ions with an error of 2 cm moT, while the uncertainty was higher for others. Thus, for at 22°C they found Vh+ = -5.4 cm mol". ... 

The absolute value of the partial molar volumes at infinite dilution of an ion of charge z, at 25 °C can be calculated from the conventional one by means of. 

A similar procedure may be used to obtain the partial molar volumes from measurements of the volume change on mixing, i.e. from the density of the mixture. In this instance the absolute values of the volumes, and V2, of the pure components are known, and it is therefore possible to obtain the absolute values of the partial molar volumes. In some mixtures it may occur that the partial molar volume of a particular component is negative, implying that an... 

We described methods for obtaining values for V,-, Cpi, and S but did not apply the methods to //, and G, (or w), since absolute values of Gm and Hm cannot be obtained. We did describe a procedure for obtaining the volume difference V,— Vf using equations (5.40). (5.41) and (5.42),r where V is the volume of the pure substance, and indicated that equations of the same form can be used to obtain //, - Hf. We will return to this method later in this chapter as we describe ways for measuring relative partial molar enthalpies. 

At infinite dilution, the standard molar volumes of the cations and anions are additive and conventional values V,"", based on V ( ", aq) " =0cm -mol" at all temperatures, have been listed by Millero [78] at several temperatures (0,25, 50, and 75°C). Some of the 25°C values have since been revised [55]. The absolute standard partial ionic molar volumes are V (1, aq) = V " aq) and the tempera-... 

The absolute values of some partial molar quantities, such as the volume, can be determined experimentally. Other absolute values, however, cannot be these include partial molar enthalpies, free enthalpies, and free entropies. However, their changes are measurable. 

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