Fundamental equation of chemical thermodynamics

Equations (3)-(6) display a certain degree of symmetry and have been called the fundamental equations of chemical thermodynamics [2]. They are very useful in providing general relations between thermodynamic properties. For example, from equation (6) it follows that... 

This is sometimes called the fundamental equation of chemical thermodynamics. juf may be thought of as the increase in the free energy of the system when one mole of component i is added to an infinitely large quantity of the mixture so that it does not significantly change the overall composition. Chemical potential is an intensive property and can be regarded as providing the force which drives chemical systems to equilibrium. Consider a chemical i distributed between two phases a and / as illustrated in Fig. 4.5. Let its chemical potential be /q(a) and juf(/l) in these phases. At constant T and P if we transfer dnf moles of i from to / ,... 

We make use of the fundamental equation of chemical thermodynamics to obtain... 

This equation is known as the fundamental equation of chemical thermodynamics. It can also be considered as the fundamental equation of the thermodynamics of crystal growth. It is applied for both (physical) phase and (chemical) reaction equihbria. 

An attempt to make this application prompted the appearance of The Thermodynamics of Soil Solutions (Oxford University Press, 1981). Besides its evident purpose, to demonstrate the use of chemical thermodynamics, this book carried a leitmotif on the fundamental limitations of chemical thermodynamics for describing natural soils. These limitations referred especially to the influence of kinetics on stability, to the accuracy of thermodynamic data, and to the impossibility of deducing molecular mechanisms. The problem of mechanisms vis-a-vis thermodynamics cannot be expressed better than in the words of M. L. McGlashan 2 what can we learn from thermodynamic equations about the microscopic or molecular explanation of macroscopic changes Nothing whatever. What is a thermodynamic theory (The phrase is used in the titles of many papers published in reputable chemical journals.) There is no such thing. What then is the use of thermodynamic equations to the chemist They are indeed useful, but only by virtue of their use for the calculation of some desired quantity which has not been measured, or which is difficult to measure, from others which have been measured, or which are easier to measure. This point cannot be stated often enough. 

Calculation of equilibrium conversions is based on the fundamental equations of chemical-reaction equilibrium, which in application require data for the standard Gibbs energy of reaction. The basic equations are developed in Secs. 15.1 through 15.4. These provide the relationship between the standard Gibbs energy change of reaction and the equilibrium constant. Evaluation of the equilibrium constant from thermodynamic data is considered in Sec. 15.5. Application of this information to the calculation of equilibrium conversions for single reactions is taken up in Sec. 15.7. In Sec. 15.8, the phase role is reconsidered finally, multireaction equilibrium is treated in Sec. I5.9.t... 

In the first equation of eq 9.4, p(Af) is the continuous version of the partial molar chemical potential and corresponds to the usual thermodynamic expression provided as the second equation of eq 9.4. The integral relates to the total range of the characterization variable M. In principle, knowing G and calculating 6G according to eq 9.3 the comparison of eqs 9.3 and 9.4 leads to the partial molar quantities p M). Based on the previously outlined principles the well-known fundamental equations of usual thermodynamics may be translated into continuous thermodynamics to give the basic equations... 

Equation (4.5-3) is called the Gibbs equation or the fundamental relation of chemical thermodynamics. We could also choose to write... 

In the broadest sense, thermodynamics is concerned with mathematical relationships that describe equiUbrium conditions as well as transformations of energy from one form to another. Many chemical properties and parameters of engineering significance have origins in the mathematical expressions of the first and second laws and accompanying definitions. Particularly important are those fundamental equations which connect thermodynamic state functions to real-world, measurable properties such as pressure, volume, temperature, and heat capacity (1 3) (see also Thermodynamic properties). 

This volume begins as Chapter 11 in the two-volume set. This Chapter summarizes the fundamental relationships that form the basis of the discipline of chemical thermodynamics. This chapter can serve as a review of the fundamental thermodynamic equations that are necessary for the more sophisticated applications described in the remainder of this book. This level of review may be all that is necessary for the practising scientist who has been away from the field for some time. For those who need more, references are given to the sections in Principles and Applications where the equations are derived. This is the only place that this volume refers back to the earlier one. 

In treating the fundamental equations of thermodynamics, chemical potentials of species are always used, but in making calculations when T and P are independent variables, chemical potentials are replaced by Gibbs energies of formation AfG . Therefore, we will use equation 3.1-10 in the form... 

When the pH is specified, we enter into a whole new world of thermodynamics because there is a complete set of new thermodynamic properties, called transformed properties, new fundamental equations, new Maxwell equations, new Gibbs-Helmholtz equations, and a new Gibbs-Duhem equation. These new equations are similar to those in chemical thermodynamics, which were discussed in the preceding chapter, but they deal with properties of reactants (sums of species) rather than species. The fundamental equations for transformed thermodynamic potentials include additional terms for hydrogen ions, and perhaps metal ions. The transformed thermodynamic properties of reactants in biochemical reactions are connected with the thermodynamic properties of species in chemical reactions by equations given here. 

Not all the chemical potentials (and therefore, the activity coeflicients) in a mixture are independent of each other. They are all related to one another through the Gibbs-Duhem equation. To derive this equation, we start with tlie fundamental equation of thermodynamics for the Gibbs free energy, which can be written as... 

Equation (13-33) is the fundamental equation for the thermodynamic study of galvanic cells. The chemical potential of component i in phase a is related to the corresponding activity by the equation... 

The changes in the states of entropy-elastic bodies described in the previous section can be expressed quantitatively by phenomenological thermodynamics, starting with one of the fundamental equations in thermodynamics. The relationship of interest here relates the pressure p with the internal energy (7, the volume F, and the thermodynamic temperature T (see textbooks of chemical thermodynamics) ... 

Equations (67a)-(67d) show the particular role of partial molar Gibbs energies Gi. By their definition, quantities G/ are both partial molar quantities and chemical potentials as defined by the fundamental equation of thermodynamics ... 

The estimates of constants are refined by methods of sequential planning of precise experiments. If necessary, additional chemical investigations are executed in order to come to conclusions about the most probable mechanism. Fishtik and Datta [57,58] have shown that the fundamental equations of thermodynamics have the property of being decomposed into a linear sum of contributions associated with a unique class of reactions referred to as response reactions. This property can also be used for the discrimination among reaction mechanisms. 

The equations (2 40) (2 43) form the basis of chemical thermodynamics. The first of them may be regarded as the fundamental relation which contains the physical information embodied in the properties of 17, T and S, whilst the other three are derived from it by virtue of the definitions of H, A and O and contain no additional information. At this stage it may also be noted that the most convenient choice of the independent variables in the solving of thermodynamic problems is determined by the structure of the above equations. Thus... 

Walther Hermann Nemst (1864-1941) was a German physical chemist who is known for his theories behind the calculation of chemical affinity as embodied in the third law of thermodynamics, for which he won the 1920 Nobel Prize in Chemistry. Nemst also made fundamental contributions to the theory of electrolyte solutions. He is most known for developing the Nernst equation, one of the most fundamental equations of equilibrium electrochemistry. 

A mechanical system, typified by a pendulum, can oscillate around a position of final equilibrium. Chemical systems cannot do so, because of the fundamental law of thermodynamics that at all times AG > 0 when the system is not at equilibrium. There is nonetheless the occasional chemical system in which intermediates oscillate in concentration during the course of the reaction. Products, too, are formed at oscillating rates. This striking phenomenon of oscillatory behavior can be shown to occur when there are dual sets of solutions to the steady-state equations. The full mathematical treatment of this phenomenon and of instability will not be given, but a simplified version will be presented. With two sets of steady-state concentrations for the intermediates, no sooner is one set established than the consequent other changes cause the system to pass quickly to the other set, and vice versa. In effect, this establishes a chemical feedback loop. 

Even though the van der Waals equation is not as accurate for describing the properties of real gases as empirical models such as the virial equation, it has been and still is a fundamental and important model in statistical mechanics and chemical thermodynamics. In this book, the van der Waals equation of state will be used further to discuss the stability of fluid phases in Chapter 5. 

Formal thermodynamics does not rest on KMT or other molecular assumptions (hence, their relegation to sidebar status in this book). Nevertheless, thermodynamic studies are highly valued for their ability to provide fundamental insights into the intermolecular forces that underlie chemical phenomena. Indeed, the most successful advances in thermodynamic theory and practice are often inspired by molecular insights, and the productive interplay between microscopic and macroscopic domains should be emphasized in a pedagogically useful presentation of thermodynamic principles. Accordingly, we discuss equations of state in terms of their ability to suggest improvements over the KMT ideal gas picture of intermolecular interactions. 

In order to better understand the physical nature of the chemical potential jxt of a chemical substance, let us first review the major mathematical features of the Gibbsian thermodynamics formalism. The starting point is the Gibbs fundamental equation for the internal energy function... 

PHYSICAL CHEMISTRY. Application of the concepts and laws of physics to chemical phenomena in order to describe in quantitative (mathematical) terms a vast amount of empirical (observational) information. A selection of only the most important concepts of physical chemistiy would include the electron wave equation and the quantum mechanical interpretation of atomic and molecular structure, the study of the subatomic fundamental particles of matter. Application of thermodynamics to heats of formation of compounds and the heats of chemical reaction, the theory of rate processes and chemical equilibria, orbital theory and chemical bonding. surface chemistry (including catalysis and finely divided particles) die principles of electrochemistry and ionization. Although physical chemistry is closely related to both inorganic and organic chemistry, it is considered a separate discipline. See also Inorganic Chemistry and Organic Chemistry. 

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