Entropy molar properties

The systems of interest in chemical technology are usually comprised of fluids not appreciably influenced by surface, gravitational, electrical, or magnetic effects. For such homogeneous fluids, molar or specific volume, V, is observed to be a function of temperature, T, pressure, P, and composition. This observation leads to the basic postulate that macroscopic properties of homogeneous PPIT systems at internal equiUbrium can be expressed as functions of temperature, pressure, and composition only. Thus the internal energy and the entropy are functions of temperature, pressure, and composition. These molar or unit mass properties, represented by the symbols U, and S, are independent of system size and are intensive. Total system properties, J and S do depend on system size and are extensive. Thus, if the system contains n moles of fluid, = nAf, where Af is a molar property. Temperature... 

P rtl IMol r Properties. The properties of individual components in a mixture or solution play an important role in solution thermodynamics. These properties, which represent molar derivatives of such extensive quantities as Gibbs free energy and entropy, are called partial molar properties. For example, in a Hquid mixture of ethanol and water, the partial molar volume of ethanol and the partial molar volume of water have values that are, in general, quite different from the volumes of pure ethanol and pure water at the same temperature and pressure (21). If the mixture is an ideal solution, the partial molar volume of a component in solution is the same as the molar volume of the pure material at the same temperature and pressure. 

Chapter 4 presents the Third Law, demonstrates its usefulness in generating absolute entropies, and describes its implications and limitations in real systems. Chapter 5 develops the concept of the chemical potential and its importance as a criterion for equilibrium. Partial molar properties are defined and described, and their relationship through the Gibbs-Duhem equation is presented. 

In open systems consisting of several components the thermodynamic properties of each component depend on the overall composition in addition to T and p. Chemical thermodynamics in such systems relies on the partial molar properties of the components. The partial molar Gibbs energy at constantp, Tand rij (eq. 1.77) has been given a special name due to its great importance the chemical potential. The corresponding partial molar enthalpy, entropy and volume under the same conditions are defined as... 

Partial molar availability, 24 692 Partial molar entropy, of an ideal gas mixture, 24 673—674 Partial molar Gibbs energy, 24 672, 678 Partial molar properties, of mixtures, 24 667-668... 

Figure 6J Excess partial molar properties of jadeite component in NaAlSi206-KAlSi206 molten mixture. (A) Excess partial molar entropy. (B) Excess partial molar enthalpy. Reprinted from Eraser et al. (1983), Bulletin Mineralogique, 106, 111-117, with permission from Masson S.A., Paris, Erance.

The two primary reference works on inorganic thermochemistry in aqueous solution are the National Bureau of Standards tables (323) and Bard, Parsons, and Jordan s revision (30) (referred to herein as Standard Potentials) of Latimer s Oxidation Potentials (195). These two works have rather little to say about free radicals. Most inorganic free radicals are transient species in aqueous solution. Assignment of thermodynamic properties to these species requires, nevertheless, that they have sufficient lifetimes to be vibrationally at equilibrium with the solvent. Such equilibration occurs rapidly enough that, on the time scale at which these species are usually observed (nanoseconds to milliseconds), it is appropriate to discuss their thermodynamics. The field is still in its infancy of the various thermodynamic parameters, experiments have primarily yielded free energies and reduction potentials. Enthalpies, entropies, molar volumes, and their derivative functions are available if at all in only a very small subset. 

Tliis equation defines the partial molar property of species i in solution, where the generic symbol Mt may standfor the partial molar internal energy t/, the partial molar enthalpy //, the partial molar entropy 5,, the partial molar Gibbs energy G,, etc. It is a response function, representing the change of total prope ity n M due to additionat constant T and f of a differential amount of species i to a finite amount of solution. 

Equation 41 shows that the chemical potential is a partial molar property. We will need other partial molar quantities (e.g., those for volume, enthalpy, and entropy) in dealing with pressure and temperature effects on energetics of reactions. 

Gibbs-Duhem Relationship The partial molar properties of a multicomponent phase cannot be varied independently (the mole fractions, jc, = ,/E of the components total unity). For example, for the chemical potentials, /i, the Gibbs-Duhem relationship is En, dni = 0 (for details, see e.g., Atkirs, 1990 Blandamer, 1992 Denbigh, 1971). Similar constraints apply to the partial molar volumes, enthalpies, entropies, and heat capacities. For pure substances, the partial molar property is equal to the molar property. For example, the chemical potential of a pure solid or liquid is its energy per mole. For gaseous, liquid, or solid solutions, X, = X,(ny), that is, the chemical potentials and partial molar volumes of the species depend on the mole fractions. 

The fundamental thermodynamic properties that arise in connection with the first and second laws of thermodynamics are internal energy and entropy. These properties together with the two laws for which they are essential apply to all types of systems. However, different types of systems are characterized by different sets of measurable coordinates or variables. The type of system most commonly encountered in chemical technology is one for which the primary characteristic variables are temperature T, pressure P, molar volume V, and composition, not all of which are necessarily independent. Such systems are usually made up of fluids (liquid or gas) and are called PVT systems. 

This simply shows that there is a physical relationship between different quantities that one can measure in a gas system, so that gas pressure can be expressed as a function of gas volume, temperature and number of moles, n. In general, some relationships come from the specific properties of a material and some follow from physical laws that are independent of the material (such as the laws of thermodynamics). There are two different kinds of thermodynamic variables intensive variables (those that do not depend on the size and amount of the system, like temperature, pressure, density, electrostatic potential, electric field, magnetic field and molar properties) and extensive variables (those that scale linearly with the size and amount of the system, like mass, volume, number of molecules, internal energy, enthalpy and entropy). Extensive variables are additive whereas intensive variables are not. 

Lowercase roman letters usually denote molar properties of a phase. Thus, g, A. s, and v are the molar Gibbs energy, molar enthalpy, molar entropy, and molar volume. Whan it is essentia] to distinguish between a molar property of a mixture nod that of a pure component, we identify the pure-component property by a subscript. For example, ft, is the molar enthalpy of pure i. Total properties are usually designated by capilal letters, Thus H is the total enthalpy of a mixture it is related to the molar mixture enihelpy A by H nh. where n is the total number of moles in the mixture. 

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. 

Comparing this with eqs. rQ.2c l (q.26 and (Q.27) for the volume, enthalpy and entropy of the ideal mixture we identify the respective partial molar properties as... 

The first thing we come across when looking at real data is that quite often the data are reported as apparent molar volumes, enthalpies, entropies or heat capacities. If we call component 1 the solvent (usually water in our cases), component 2 the solute (say, NaCl), Z and Z the total and molar forms of any of these properties, then apparent molar properties are defined as... 

Keywords Aqueous systems bibliography biochemical systems enthalpy data entropy data equilibrium data excess properties Gibbs energy data heat capacHy data partial molar properties review articles thermochemistry thermodynamics. 

There is an advantage in using the constant surface pressure standard state since it yields molar properties (enthalpies and entropies of adsorption) analogous to those associated with phase changes evaluated from the Clapeyron equation [80]. The use of the standard state with constant surface concentration provides differential quantities for the enthalpy and entropy changes which are not directly comparable with those calculated using the methods of statistical thermodynamics. The values of AS calculated by these two standard states differ only by the gas constant, B, and are readily interconverted. 

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