Specific property molar volume

Temperature, pressure, and composition are thermodynamic coordinates representing conditions imposed upon or exhibited by the system, andtne functional dependence of the thermodynamic properties on these conditions is determined by experiment. This is quite direct for molar or specific volume which can be measured, and leads immediately to the conclusion that there exists an equation of. state relating molar volume to temperature, pressure, and composition for any particular homogeneous PVT system. The equation of state is a primaiy tool in apphcations of thermodyuamics. 

In order to draw the property - composition diagram, coordinates are usually chosen so that the ideal system values correspond with the additive law regarding concentration [313]. It is known, for instance, that in an ideal system, molar volume changes additively with the concentration, and is expressed in molar fractions or molar percentages, whereas specific volume changes linearly with the concentration, and is expressed in mass fractions or mass percentages. 

This chapter presents new information about the physical properties of humic acid fractions from the Okefenokee Swamp, Georgia. Specialized techniques of fluorescence depolarization spectroscopy and phase-shift fluorometry allow the nondestructive determination of molar volume and shape in aqueous solutions. The techniques also provide sufficient data to make a reliable estimate of the number of different fluorophores in the molecule their respective excitation and emission spectra, and their phase-resolved emission spectra. These measurements are possible even in instances where two fluorophores have nearly identical emission specta. The general theoretical background of each method is presented first, followed by the specific results of our measurements. Parts of the theoretical treatment of depolarization and phase-shift fluorometry given here are more fully expanded upon in (5,9-ll). Recent work and reviews of these techniques are given by Warner and McGown (72). 

The major differences between behavior profiles of organic chemicals in the environment are attributable to their physical-chemical properties. The key properties are recognized as solubility in water, vapor pressure, the three partition coefficients between air, water and octanol, dissociation constant in water (when relevant) and susceptibility to degradation or transformation reactions. Other essential molecular descriptors are molar mass and molar volume, with properties such as critical temperature and pressure and molecular area being occasionally useful for specific purposes. A useful source of information and estimation methods on these properties is the handbook by Boethling and Mackay (2000). 

Finally, the thermodynamic properties of a system considered as variables may be classified as either intensive or extensive variables. The distinction between these two types of variables is best understood in terms of an operation. We consider a system in some fixed state and divide this system into two or more parts without changing any other properties of the system. Those variables whose value remains the same in this operation are called intensive variables. Such variables are the temperature, pressure, concentration variables, and specific and molar quantities. Those variables whose values are changed because of the operation are known as extensive variables. Such variables are the volume and the amount of substance (number of moles) of the components forming the system. 

The partial molar properties are not measured directly per se, but are readily derivable from experimental measurements. For example, the volumes or heat capacities of definite quantities of solution of known composition are measured. These data are then expressed in terms of an intensive quantity—such as the specific volume or heat capacity, or the molar volume or heat capacity—as a function of some composition variable. The problem then arises of determining the partial molar quantity from these functions. The intensive quantity must first be converted to an extensive quantity, then the differentiation must be performed. Two general methods are possible (1) the composition variables may be expressed in terms of the mole numbers before the differentiation and reintroduced after the differentiation or (2) expressions for the partial molar quantities may be obtained in terms of the derivatives of the intensive quantity with respect to the composition variables. In the remainder of this section several examples are given with emphasis on the second method. Multicomponent systems are used throughout the section in order to obtain general relations. 

The physical property monitors of ASPEN provide very complete flexibility in computing physical properties. Quite often a user may need to compute a property in one area of a process with high accuracy, which is expensive in computer time, and then compromise the accuracy in another area, in order to save computer time. In ASPEN, the user can do this by specifying the method or "property route", as it is called. The property route is the detailed specification of how to calculate one of the ten major properties for a given vapor, liquid, or solid phase of a pure component or mixture. Properties that can be calculated are enthalpy, entropy, free energy, molar volume, equilibrium ratio, fugacity coefficient, viscosity, thermal conductivity, diffusion coefficient, and thermal conductivity. 

A maybe a volume, a specific heat, etc. B is an expansion property B/,4R usually is nearly constant. As an example, the molar volume in the glassy state was expressed (Chap. 4) as ... 

Both MC and MD simulations have been used to calculate thermodynamic properties, most often the internal energy U, the virial pVYMgT, and the specific heat at constant volume Cy. Some of the rigid molecule models, e.g., the TIPS4 potential, were parameterized in part to give the correct molar volume at 300 K and zero pressure. As with the radial distribution functions, it is found that there is a reasonable variation between predicted values of these properties and that no one potential is clearly superior. 

Hiis condensation or contraction is the cause of the highly negative partial molar volumes, which become more pronounced as the isothermal compressibility increases. These clusters are bound by van der Waals forces and are thus very different from other types of aggregates such as clathrates which are bound by specific chemical forces. Their size can reach values on the order of 100 molecules, which means that they extend over many coordination shells. While the partial molar volume, a macroscopic property, provides evidence of clustering, more detailed information has been obtained recently using spectroscopic techniques which probe solute-solvent interactions directly. 

The specific surface area and the pore size distribution of sorbents and catalysts are of central importance for their properties. For most cases it is sufficient to use the BET theory for the determination, although it will face limitations at very low surface areas and in the presence of micropores. The most successfully used gas is N2 but, for low surface area materials, the use of a more easily condensable gas, such as Ar, has advantages. It is strongly recommended, however, that these methods be calibrated against a weU-known sample, as the packing density of the various gases cannot be extrapolated directly from their molar volumes. The concept of surface area is not applicable for micropores, i.e., when the pore size and the size of the sorbed molecule approach each other. 

Crystallographic Properties [1.1,1.6]. Besides amorphous tungsten, three modifications (a-, P-, and y-tungsten) are known. Table 1.8 provides crystallographic parameters and related data, such as density, molar volume, and specific volume. 

Consider first of all the volume of the solution. The volume of any solution may be estimated from the mass of each component and its density. Volume is an extensive property, since its value depends on the total amount of solution. A quantity of more fundamental interest is the specific volume, Cg, that is, the volume per gram. It is simply the reciprocal of the density. This is an intensive quantity, since its value does not depend on the size of the solution, only on its composition, temperature, and pressure. From the point of view of chemists, an even better way to describe this property is in terms of the molar volume, that is, the volume per mole of solution. For a two-component solution, the molar volume Fjj, is related to the density as follows ... 

For each extensive property, there is a corresponding partial molar and partial specific property. Consider any thermodynamic extensive property, such as volume, free energy, entropy, energy content, etc., the value of which, for a homogeneous system, is completely determined by the state of the system e.g., the temperature, pressure, and the amounts of the various constituents present. Thus, denoting by Y any extensive thermodynamic property, it can be represented by... 

The molecular weight per repeat unit (M) is useful in calculating many properties. For example, it can be used to obtain densities and specific volumes from the molar volumes listed in Chapter 3, specific heat capacities from the molar heat capacities listed in Chapter 4, the numbers of repeat units between crosslinks from Mc values, and the number of repeat units between entanglements from Me values. Table A. 1 lists the values of M for many polymers, in units of g/mole, and in alphabetical order by the polymer name. 

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