Isothermic processes Gibbs energy

Whilst every material presents its own problems in crystal growth, which must be solved experimentally, there is a general thermodynamic principle that gives an indication of how difficult the process is likely to be. Since crystal growth takes place reversibly, the Gibbs energy G must be constant and so, under isothermal conditions,... 

The pure species A and B are isothermally compressed (or expanded, depen on the pressure P) to their equilibrium fugacities in the box. The change in Gibbs energy for this process is given by Eq. (15.9), here written for one mole... 

The correct thermodynamic treatment of adsorption processes is possible only on liquid-gas and liquid-liquid interfaces, where the surface energy or the surface tension of the liquid can precisely be determined. For these systems, the Gibbs adsorption isotherm can be applied. For example on a liquid-liquid interface,... 

The successive Legendre transformations of E yield a state function, G, for which the natural variables p and T, are both intensive properties (independent of the size of the system). Furthermore, for dp = 0 and dT = 0 (isobaric, isothermal system), the state of the system is characterized by dG. This is clearly convenient for chemical applications under atmospheric pressure, constant-temperature conditions (or at any other isobaric, isothermal conditions). Then, in place of equation (21) for internal energy variation, we state the conditions for irreversible or reversible processes in terms of the Gibbs energy as... 

One mole of an ideal gas expands isothermally until its volume is doubled. What is the change in Gibbs energy, AG, for the process ... 

There are other forms of the Gibbs-Helmholtz equation which are more frequently employed these deal with changes in the free energy, heat content, etc., accompanying an appreciable process. The process may be chemical or physical in nature the only restriction is that it takes place in a closed system, i.e., one of constant mass, which is in equilibrium with the external pressure. For the initial and final states, indicated by the subscripts 1 and 2, respectively, of an isothermal process, equation (25.8) becomes... 

Finally, some formulas and stability constants of (hypothetical) surface species (or Gibbs energies of adsorption) are reported in Tables 4.1-4.4. These quantities belong to adsorption models proposed by the authors of cited publications, but they are not sufficient to calculate the uptake curves or adsorption isotherms when the model involves an electrostatic factor. Adsorption models themselves are not discussed in the present chapter, their terminology is explained in detail in Chapter 5, In contrast with the directly measured quantities that represent the sorption properties at specific experimental conditions, the model parameters characterize the sorption process over a wide range of experimental conditions, although the match between experimental and theoretically calculated quantities was not always... 

As in the case of fluid interfaces, the question of whether the adsorption of proteins onto solids is reversible or irreversible is very important for correct estimation of physicochemical characteristics of the process. In a reversible process, dilution of sorbate in the bulk phase should lead to spontaneous desorption of some portion of adsorbed molecules up to elimination of a transient difference in the chemical potential of the sorbate at the interface and in the solution the ascending and descending branches of the isotherm must overlap at all values of Cb. Only in this case the isotherm represents thermodynamic equilibrium, and the equilibrium constant Kads and the standard Gibbs energy of adsorption AG°ads = A/7°ads - rAS°ads can be determined. 

Direction of corrosion process is determined by thermodynamic properties of the system. The reactivity is determined by the change in isobaric-isothermal potential or Gibbs energy... 

For isothermal steady-flow processes, the reversible work is given by the accumulated difference in Gibbs energy between inlets and outlets. 

The positive value indicates that work must be done on the mixture to achieve an isobaric separation. In a real isothermal-isobaric separation of ideal gases, more than this minimum amount of work would be needed, because a real process would be irreversible. Moreover, when separating real mixtures (whose components have inter-molecular forces), the total minimum work would not be given by (4.1.47). However, it could still be determined from O using (4.1.46), provided a reliable model were available for the Gibbs energy of the mixture and each pure. Expressions for G of real mixtures would be more complicated than the ideal-gas expression (4.1.47) but such expressions could be obtained from model equations of state. 

For both idealities, when material is added, the volume must expand to keep P constant and we must add heat to keep T constant. If we mole-fraction average the work given in (6.3.1), we obtain the change in Gibbs energy on mixing, g , which is the reversible isothermal-isobaric work involved in forming a mixture from its pure components cf. 3.7.4 in which we consider the reverse process. 

To obtain a physical interpretation for the residual Gibbs energy, we start with an ideal-gas mixture confined to a closed vessel. As the process, we consider the reversible isothermal-isobaric conversion of the ideal-gas molecules into real ones. Although this process is hypothetical, it is a mathematically well-defined operation in statistical mechanics the process amounts to a "turning on" of intermolecular forces. We first want to obtain an expression for the work, but since the process involves a change in molecular identities, we must start with the general energy balance (3.6.3). For a system with no inlets and no outlets, (3.6.3) becomes... 

To obtain a physical interpretation for the excess Gibbs energy, we consider a Lewis-Randall ideal solution confined to a closed vessel, and we determine the reversible isothermal-isobaric work involved in converting the ideal solution into a real mixture. Again this is a hypothetical process all intermolecular forces are initially the same (but they are nonzero), and the process changes the forces into those of real molecules. 

The processes of cohesion and adhesion are schematically depicted in Figure 5.5a and b. Cohesion involves the merging of two volumes of a (or P) into one volume in an environment of its vapor. Then, in view of Equation 5.6, the Gibbs energy of cohesion in phase a is defined as the reverse of the isothermal isobaric work per nnit cross-sectional area, indicated by the subscript a, to reversibly separate two volumes of a. 

In words, this equation says that the change in the Gibbs energy is directly proportional to the change in area of a liquid. If we consider an isothermal, isobaric process (that is, dp = 0 and dT = 0 these conditions are necessary when you consider the natural variable expression in equation 22.7), the process is spontaneous if AG is negative. Because surface tension must be a positive number, this implies that AA for a spontaneous process must be negative a spontaneous process must occur with a corresponding decrease in surface area. 

The Gibbs equations derived for fiee, S/L, and S/G interfaces provide a uniform picture of physical adsorption however, they eannot give information on the structure of energy [i.e., we do not know how many and what kind of physieal parameters or quantities influenee the energy (heat) processes connected with the adsorption]. As it is well known these heat proeesses ean be exactly measured in a thermostat of approximately infinite eapacity. This thermostat eontains the adsorbate and the adsorptive, both in a state of equilibrium. We take only the isotherm proeesses into account [i.e., those in whieh the heat released during the adsorption process is absorbed by the thermostat at eonstant temperature dT = 0) or, by eonverse processes (desorption), the heat is transferred fi om the thermostat to the adsorbate, also at eonstant temperature]. Under these conditions, let <7n -mol adsorptive be adsorbed by the adsorbent and, during this process, an... 

The energy change for any equimolar process occurring at constant temperature is a work process. If the isothermal, equimolar process is carried out reversibly at constant pressure, the work is Gibbs free energy. If the isothermal process is carried out reversibly at constant volume, the work is Helmholtz free energy. 

---