Partial molar free enthalpy

The driving force for the transport of all particles is a change in the electrochemical potential /i, which is related to the partial molar free enthalpy /i, and the electric potential 0 as follows ... 

Since an ion has an electric charge, the partial molar free enthalpy gt of an ion i consists not only of the chemical potential ju, but also of the electrostatic energy zfffy of the ion where z, is the ionic valence, F is the Faraday constant, and is the electrostatic inner potential of the solution. This partial molar free enthalpy gt defines the electrochemical potential rj of an ion in an electrolyte solution as shown in Eq. 8.38 ... 

Charged particles such as ions and electrons play an important role in what is called electrochemical processes. We shall now discuss the energy level of ions and electrons in an electrochemical system. The partial molar free enthalpy (partial molar Gibbs energy) of a charged particle i, as described in the foregoing chapter (section 8.7), is represented by the electrochemical potential r)t shown in Eq. 9.1 ... 

H = qp, heat content F = wp, work function G/N = /r, partial molar free enthalpy... 

The chemical potential or the partial molar free enthalpy (5G/5wi) of the... 

The combination of eqns. (11) and (7) allows the formulation of an alternative expression of the second law, it introduces the partial molar free enthalpy, g., (also termed Gibbs free energy) ... 

However, the concept of current flow is only applicable to aqueous systems. In the gaseous phase of air, electron exchange occurs within the transition state of two molecular entities, basically in a wider sense of charge transfer complexes. Any substance in a specified phase has an electrochemical potential consisting of the chemical potential Pi (partial molar free enthalpy) and a specified electric potential ... 

It was shown before that the phase equilibrium of a single component system can be described by the free enthalpy G. The partial molar free enthalpy G, is... 

Solvation processes occurring in a solvent mixture, i.e., the interactions between the solvent and the solute, are even more involved than the interactions between the solvent components themselves. Padova [Pa 68] stated that it is the partial molar free enthalpy of solvation of the components that determines which of the components of the solvent mixture will solvate the dissolved ion. Naturally, this is true in general, but it hardly gives a factual basis for the interpretation of the special interactions. 

Standard partial molar free enthalpies, enthalpies, and entropies of vaporization from infinitely dilute solutions in Apiezon M were calculated from retention volumes determined over a range of temperatures data are listed for many organic and a few MR4 compounds (M = Si, Ge, and Sn), including Ge(C2H5)4 [29]. Apiezon L and two polar stationary phases were used in similar studies on a variety of MRr,R4 n compounds, yielding relative molar enthalpies and entropies of solution at 100°C referred to Si(CH3)4 as the standard [43]. Retention volumes and heats of solutions on two stationary phases have also been compared for M(C2H5)4 and M(C2H5)3H compounds with M = Si, Ge, and Sn [38]. 

The description of phase equilibria makes use of the partial molar free enthalpies, i, called also chemical potentials. For one-component phase equilibria the same formalism is used, just that the enthalpies, G, can be used directly. The first case treated is the freezing point lowering of component 1 (solvent) due to the presence of a component 2 (solute). It is assumed that there is complete solubility in the liquid phase (solution, s) and no solubility in the crystalline phase (c). The chemical potentials of the solvent in solution, crystals, and in the pure liquid (o) are shown in Fig. 2.26. At equilibrium, ft of component 1 must be equal in both phases as shown by Eq. (1). A similar set of equations can be written for component 2. By subtracting j,i° from both sides of Eq. (1), the more easily discussed mixing (left-hand side, LHS) and crystallization (right-hand side, RHS) are equated as Eq. (2). 

Chemical Potential (partial molar free enthalpy)-. An expression for the change of the free enthalpy of a system, which consists of a mixture, if 1 mole of the mixture component / is added to an infinite amount of the mixture. 

This equation is similar to equation m - 3, only two terms have been added which describe the change in number of moles of both components. The chemical potential of a component i, which is the partial molar free enthalpy, is defined as... 

The quantities Xa, Xb, etc, are called the partial molar quantities. The partial molar free enthalpy is also called the chemical potential and given the letter jx. In general, the partial molar quantities are not additive, but the following relationship can be derived between two different components (easily generalized for multicomponent systems)... 

The temperature of the transition between two different phase structures is thermodynamically defined by the equality of their partial molar free enthalpies Ml and M2- Figure 13a illustrates the so-called ideal solution in a plot of the vapor pressure Pi as a function of concentration in terms of the mole fraction xi (Raoult s law, Xi Po= Pi, where Po is the vapor pressure of the pure solvent 1). In this ideal case, only the entropy of mixing, ASi = —RT In xi, changes the chemical potential of the solvent, mi > from its pure state, mi°, as expressed by... 

Chemical potential and partial molar free enthalpy We are going to prove the following theorem ... 

G, G,, [G] free enthalpy, partial molar free enthalpy of /, generalized free enthalpy. 

A chemical potential is an intensive partial molar quantity. Its value does not depend on the sample mass since, by definition, a molar quantity concerns one mole. The chemical potential is also called the partial molar free enthalpy G, ... 

The chemical potentials or partial molar free enthalpies are defined by the following partial derivative ... 

The quantities va and vb are called partial molar volumes. In this sense p.i is the partial molar free enthalpy of component i. 

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