Thermodynamics partial mass property

Partial Molar Properties Consider a homogeneous fluid solution comprised of any number of chemical species. For such a PVT system let the symbol M represent the molar (or unit-mass) value of any extensive thermodynamic property of the solution, where M may stand in turn for U, H, S, and so on. A total-system property is then nM, where n = Xi/i, and i is the index identifying chemical species. One might expect the solution propei fy M to be related solely to the properties M, of the pure chemical species which comprise the solution. However, no such generally vahd relation is known, and the connection must be establi ed experimentally for eveiy specific system. 

Interest here centers on solntions their molar (or nnit-mass) properties are therefore representedby the plain symbol M. Partial properties are denotedby an overbar, with a subscript to identify the species the symbol is therefore M. In addition, properties of the individnal species as they exist in the pure state at the T and P of the solution are identified by only a subscript, and the symbol is Mi. In snmmary, the three kinds of properties nsed in solntion thermodynamics are distingnishedby the following symbolism ... 

In 2.4 we presented differential forms of the thermodynamic stuff equations for overall mass, energy, and entropy flows through open systems. Usually, such systems, together with their inlet and outlet streams, will be mixtures of any number of components. Individual components can contribute in different ways to mass, energy, and entropy flows, so here we generalize the stuff equations to show explicitly the contributions from individual components these generalized forms contain partial molar properties introduced in 3.4. 

Such salt effects are of practical importance in stagemise separation processes and in pollution abatement. Certain salts increase the solubility by more than an order of. magnitude (salting-in), and also change the solvent selectivity for various solutes others decrease the solubility (salting-out) (4, 6, 7, 10) Partial molal properties of the dissolved gas are also profoundly affected by the addition of salt. Thermodynamic properties of gas-electrolyte solution are also an important consideration in the design and operation of fuel cells, where mass transfer of... 

The experimental results are briefly discussed in terms of thermodynamic and mass transport properties in the glassy polymer mixture. The aim of the discussion is to highlight peculiarities of solubility and difiusivity in polymeric systems below the glass transition temperature and to consider possible interpretations. The focus is on the effect of swelling on the thermodynamic and transport properties in glasses. Indeed, it is well known that, contrary to the case of rubbery systems, the solute partial specific... 

This type of defect equilibrium treatment has been used extensively to model the defect chemistry and non-stoichiometry of inorganic substances and has the great advantage that it easily takes several simultaneous defect equilibria into account [22], On the other hand, the way the mass action laws are normally used they are focused on partial thermodynamic properties and not on the integral Gibbs energy. The latter is often preferred in other types of thermodynamic analyses. In such cases the following solid solution approach is an alternative. 

Note, however, that EM is not determined by the thermodynamic equilibrium potentials Ef and E2 but by the kinetics of the respective reactions, i.e. by the respective anodic and cathodic component curves in Fig. 13(a) with the condition indicated by eqn. (190). These curves may be altered by mass transport conditions, surface area and, specific properties and consequently the mixed potential EM may be susceptible to those kinetic factors, unlike the equilibrium potential of each partial electrode reaction which is fixed by thermodynamics and the activities in the bulk solution. 

Partial Molar Quantities. — The thermodynamic functions, such as heat content, free energy, etc., encountered in electrochemistry have the property of depending on the temperature, pressure and volume, i.e., the state of the system, and on the amounts of the various constituents present. For a given mass, the temperature, pressure and volume are not independent variables, and so it is, in general, sufficient to express the function in terms of two of these factors, e.g., temperature and pressure. If X represents any such extensive property, i.e., one whose magnitude is determined by the state of the system and the amounts, e.g., number of moles, of the constituents, then the partial molar value of that property, for any constituent i of the system, is defined by... 

When taking these partial derivatives it must be remembered that, in general, the molar densities, the mass transfer coefficients, and thermodynamic properties are functions of temperature, pressure, and composition. In addition, H is a function of the molar fluxes. We have ignored most of these dependencies in deriving the expressions given above. The important exception is the dependence of the K values on temperature and composition that cannot be ignored. The derivatives of the K values with respect to the vapor mole fractions are zero in this case since the model used to evaluate the K values is independent of the vapor composition. 

Table V-2 Re-evaluated second and third law enthalpy of formation of Se2(g) at 298.15 K as obtained from mass spectrometric investigations and determinations of the magnetic susceptibility of selenium gas. The last column contains the values evaluated by Gronvold, Drowart, and Westrum [84GRO/DRO] from the cited references. The value attributed to [84GRO/DRO] in the first column was evaluated from the measurements of Tobisawa [60TOB] who did not originally evaluate partial pressures or thermodynamic properties.

The partial pressures of the species in gaseous aluminium-selenium mixtures were determined in the temperature range 1232 to 1352 K using mass spectrometry and Knud-sen effusion cells. The measured ion intensities were converted to partial pressures by normalising the ion intensity of Al(g) in equilibrium with Al(l) to the known total vapour pressure. The derived thermodynamic quantities were recalculated by the review using the selected thermodynamic properties of Se2(g), the CODATA [89COX/WAG] properties of Al(g), and the entropies and heat capacity expressions of the aluminium selenides given in Sections V.8.2.1.1 to V.8.2.1.3. The results are summarised in Table A-59. 

The experimental data for the partial solubility of perfluoro-n-heptane in various solvents has been plotted as a function of both mole fraction and volume ftaction in Fig. 11.2-3. It is of interest to notice that these solubility data are almost symmeuic functions of the volume fraction and nonsymmetric functions of the mole fraction. Such behavior has also been found with other thermodynamic mixture properties these observations suggest the use of volume fractions, rather than mole fractions or mass fractions, as the appropriate concentration variables for describing nonideal mixture behavior. Indeed, this is the reason that volume fractions have been used in both the regular solution model and the Wohl expansion of Eq. 94-8 for liquid mixtures. 

SID/AKI] Sidorov, L. N., Akishin, P. A., Shol ts, V. B., Korenev, Y. M., Mass-spectrometric study of the thermodynamic properties of the sodium fluoride-zirconium tetrafluoride system. III. Temperature variation of the partial pressures and the thermodynamic properties of the condensed phase, Russ. J. Phys. C/zew., 39, (1965), 1146-1150. Cited on page 150. 

It is possible to subdivide the properties used to describe a thermodynamic system (e.g., T, P, V,U,...) into two main classes termed intensive and extensive variables. This distinction is quite important since the two classes of variables are often treated in significantly different fashion. For present purposes, extensive properties are defined as those that depend on the mass of the system considered, such as volume and total energy content, indeed all the total system properties (Z) mentioned above. On the other hand, intensive properties do not depend on the mass of the system, an obvious example being density. For example, the density of two grams of water is the same as that of one gram at the same P, T, though the volume is double. Other common intensive variables include temperature, pressure, concentration, viscosity and all molar (Z) and partial molar (Z, defined below) quantities. ... 

The fundamentals of liquid/liquid extraction are provided by the thermodynamic theory of equilibrium. Two immiscible liquid partial systems 1 and 2 are in equilibrium when all mass-, energy-, and impulse-transfer processes have come to a stop, that is, when the chemical potential, temperature, and pressure are the same in both phases. If Equation (2.3.4-1) is set up for a component E in phase 1 or 2, then the chemical potential describes the state of the pure component E with the properties of the ideal dilute solution ... 

The partial pressures of Cu in the system Cu-Fe-Pt in the temperature range 1240 to 1360°C have been measured by the Knudsen effusion technique and the thermodynamic properties of this system at 1300°C have been derived [1989Par]. The activities of Fe in solid solutions at 1300°C were calculated by Gibbs-Duhem integration of the Cu activities. The experimental alloys were prepared from Cu (99.999 mass%), Fe (99.999 mass%) and Pt (99.99 mass%) by induction melting in an alumina cmcible under an Ar atmosphere. The alloy buttons were then homogenized in a H2 atmosphere for 5 to 30 days at 900 to 1300°C. 

---