Extensive thermodynamic properties chemical potential

A curious example is that of the distribution of benzene in water benzene will initially spread on water, then as the water becomes saturated with benzene, it will round up into lenses. Virtually all of the thermodynamics of a system will be affected by the presence of the surface. A system containing a surface may be considered as being made up of three parts two bulk phases and the interface separating them. Any extensive thermodynamic property will be apportioned among these parts. For example, in a two-phase multicomponent system, the extra amount of an i component that can be accom-mondated in the system due to the presence of the interface ( ) may be expressed as Qi Qii where is the total number of molecules of i in the whole system, Vj and Vjj are the volumes of phases I and II, respectively, and Q and Qn are the concentrations of i in phases I and II, respectively. The surface (excess) concentration of i is defined as Fj = A, where A is the surface area. At equilibrium, the chemical potential of any component is the same in each bulk phase and at the surface. The Gibbs adsorption equation, which is one of the most widely used expression in surface and colloid science is shown in Eq. (2) ... 

Partial molar quantity Increase in any extensive thermodynamic property of a system at constant pressme and temperature when 1 mol of component Y, is added to an infinite amount of the system. The chemical potential of component Y, is also the partial molar Gibbs energy of compound Y,. 

That is, we set AG° y,(H+, aq) = 0. Then the thermodynamic properties of anions can be found by measuring the chemical potentials of ionic solutions containing H" " in combination with different anions, and then using Eq. (4.1.3b). The anionic chemical potentials so determined can be employed as secondary standards in solutions containing different cations, and this matching process is continued as needed. Extensive tabulations constructed in this manner are available. However, this convention becomes null and void in processes where H" ions are transported across the phase boundaries of the aqueous solutions. 

In this part of the paper we examine the thermodynamic properties of hydrated ionomers. By strongly hydrated we mean that we are beyond the state of solvation shells, where V, the number of water molecules per cation, is a small number ("v A to 6). In a strongly hydrated sample, the water molecules are considered to be free, and make a concentrated solution with the cations (the counter ions) and eventually with some mobile anions (the coions). This subject has already been extensively studied because of its practical importance (1-4). From the following discussion, we shall see that some of the usual classical laws are no longer valid. For instance, the variation of the chemical potential of water with the concentration of cations may no longer hold. 

Fluctuations in thermodynamics automatically imply the existence of an underlying structure that has created them. We know that such structure is comprised of molecules, and that their large number allows statistical studies, which, in turn, allow one to relate various statistical moments to macroscopic thermodynamic quantities. One of the purposes of the statistical theory of liquids (STL) is to provide such relations for liquids (Frisch and Lebowitz 1964 Gray and Gubbins 1984 Hansen and McDonald 2006). In such theories, many macroscopic quantities appear as limits at zero wave number of the Fourier transforms of statistical correlation functions. For example, the Kirkwood-Buff theory allows one to relate integrals of the pair density correlation functions to various thermo-physical properties such as the isothermal compressibility, the partial molar volumes, and the density derivatives of the chemical potentials (Kirkwood and Buff 1951). If one wants a connection between detailed correlations and integrated moments, one may ask about the nature of the wave-number dependence of these quantities. It turns out that the statistical theory of liquids allows an answer to such a question very precisely, which leads to new types of questions. The Ornstein-Zemike equation (Hansen and McDonald 2006), which is an exact equation of the STL, introduces the concept of correlation length which relates to the spatial extension of the density and/or concentration (the latter in the case of mixtures) fluctuations. This quantity cannot be accessed from pure... 

The basic thermodynamic functions are internal energy U, enthalpy H, entropy S, and Gibbs free energy G. These are extensive properties of a thermodynamic system and they are first order homogenous functions of the components of the system. Pressure and temperature are intensive properties of the system and they are zero-order homogenous functions of the components of the system. Electrochemical potentials are the driving force in an electrochemical system. The electrochemical potential comprises chemical potential and electrostatic potential in the following relation. 

Phases in thermodynamic systems are then macroscopic homogeneous parts with distinct physical properties. For example, densities of extensive thermodynamical variables, such as particle number N of the fth species, enthalpy U, volume V, entropy S, and possible order parameters, such as the nematic order parameter for a liquid crystalline polymer etc, differ in such coexisting phases. In equilibrium, intensive thermodynamic variables, namely T,p, and the chemical potentials pi have to be the same in all phases. Coexisting phases are separated by well-defined interfaces (the width and internal structure of such interfaces play an important role in the kinetics of the phase transformation (1) and in other... 

Inaccuracy of the model with regard to the simulated system is reflected by the fact that under the same values of the temperature and of the chemical potentials the extensive characteristics of the model, U , S , and differ from the eorresponding eharacteristics of the box, Uf, Sf, and Thermodynamic relations for the exeess phase may be obtained by subtracting the extensive properties of the box and of the model. Subliaction of Eq. (1) from Eq. (3) and, correspondingly, of Eq. (2) from Eq. (4) gives... 

Contrary to the bulk liquid phase which is homogeneous in three directions in space, has a characteristic composition, and is also autonomous (i.e., its extensive properties depend only on the intensive variables characterising this phase such as the temperature T, the pressure P, and the chemical potentials of the solvent /ri and the solute /u-2), the formal thermodynamic description of a Solid-Liquid interface presents a serious difficulty. In the interfacial region, the density a> of any extensive quantity changes continuously throughout the thickness (Fig. 6.1a). 

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