Gibbs energy activity concept

In many cases the CALPHAD method is applied to systems where there is solubility between the various components which make up the system, whether it is in the solid, liquid or gaseous state. Such a system is called a solution, and the separate elements (i.e., Al, Fe...) and/or molecules (i.e., NaCl, CuS...) which make up the solution are defined as the components. The model description of solutions (or solution phases) is absolutely fundamental to the CALPHAD process and is dealt with in more detail in chapter S. The present chapter will discuss concepts such as ideal mixing energies, excess Gibbs energies, activities, etc. 

We can estimate the activity coefficients by using the excess Gibbs energy models. Based on the local composition concept, the Wilson, NRTL, and UNIQUAC models for excess Gibbs energy provide relations for activity coefficient... 

The activity concept arises from the dependence of the Gibbs free energy on the pressure of a pure substance or on the composition of a solution, regardless of the phase of the system. The discussion just before Equation 14.3 shows that the change in Gibbs free energy when a gas is taken from a reference state to any pressure P is given by... 

It should be stressed that the single ion activities and activity coefficients can be introduced only formally. The reason is that due to the electro-neutrality we cannot differentiate the Gibbs energy of the system according to the amount of cations keeping the amount of the anions constant. The concept of the chemical potential of a single ion seems to be thus somewhat dubious. 

The proposed approach leads directly to practical results such as the prediction—based upon the chemical potential—of whether or not a reaction runs spontaneously. Moreover, the chemical potential is key in dealing with physicochemical problems. Based upon this central concept, it is possible to explore many other fields. The dependence of the chemical potential upon temperature, pressure, and concentration is the gateway to the deduction of the mass action law, the calculation of equilibrium constants, solubilities, and many other data, the construction of phase diagrams, and so on. It is simple to expand the concept to colligative phenomena, diffusion processes, surface effects, electrochemical processes, etc. Furthermore, the same tools allow us to solve problems even at the atomic and molecular level, which are usually treated by quantum statistical methods. This approach allows us to eliminate many thermodynamic quantities that are traditionally used such as enthalpy H, Gibbs energy G, activity a, etc. The usage of these quantities is not excluded but superfluous in most cases. An optimized calculus results in short calculations, which are intuitively predictable and can be easily verified. 

In 1983 Samec, Marecek, and Homolka introduced the concept of the Br0nsted relationship between the standard Gibbs energy of activation for ion transfer and the standard Gibbs trans-... 

The behaviour of most metallurgically important solutions could be described by certain simple laws. These laws and several other pertinent aspects of solution behaviour are described in this section. The laws of Raoult, Henry and Sievert are presented first. Next, certain parameters such as activity, activity coefficient, chemical potential, and relative partial and integral molar free energies, which are essential for thermodynamic detailing of solution behaviour, are defined. This is followed by a discussion on the Gibbs-Duhem equation and ideal and nonideal solutions. The special case of nonideal solutions, termed as a regular solution, is then presented wherein the concept of excess thermodynamic functions has been used. 

A macroscopic thermodynamic understanding of the preexponential factor was greatly advanced by the work of Kohnstamm and Scheffer [5], who introduced the concept of the Gibbs free energy of activation. A complementary molecular understanding came from the collision theory approach of McC Lewis [6], which is rather remarkable for its simplicity. If a collision between molecules A and B is defined as the two molecules coming within (rA-hrs), the sum of the radii, then each molecule of A with relative velocity vab will sweep out a cylinder of length vab Z and cross section n rp -h re). The mean relative velocity, vab, had been calculated 50 years earlier by Maxwell and Boltzmann [7] ... 

In Eqs. (127) and (128) /fa is the equilibrium constants of the chemical reaction and and are the activities at equilibrium concentrations of the reactants. Using the concept of standard reaction enthalpies, standard Gibbs reaction energies, and standard entropies (Section III), the quantities h (P T) can be calculated with the help of tabulated standard values (at 25°C and 1 atm) and Cp or U functions. Phase transitions on the path of integration must... 

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