Chemical equilibria thermodynamics internal

With the discussion of the free-energy function G in this chapter, all of the thermodynamic functions needed for chemical equilibrium and kinetic calculations have been introduced. Chapter 8 discussed methods for estimating the internal energy E, entropy S, heat capacity Cv, and enthalpy H. These techniques are very useful when the needed information is not available from experiment. 

Equilibrium thermodynamics is the most important, most tangible result of classical thermodynamics. It is a monumental collection of relations between state properties such as temperature, pressure, composition, volume, internal energy, and so forth. It has impressed, maybe more so overwhelmed, many to the extent that most were left confused and hesitant, if not to say paralyzed, to apply its main results. The most characteristic thing that can be said about equilibrium thermodynamics is that it deals with transitions between well-defined states, equilibrium states, while there is a strict absence of macroscopic flows of energy and mass and of driving forces, potential differences, such as difference in pressure, temperature, or chemical potential. It allows, however, for nonequilibrium situations that are inherently unstable, out of equilibrium, but kinetically inhibited to change. The driving force is there, but the flow is effectively zero. 

The difficulties of experimentally determining the speciation of actinides present at very low concentrations in natural waters have encouraged the use of computer simulations, based on thermodynamic data, as a means of predicting their speciation and hence their environmental behaviour. The use of modelling techniques to describe the speciation, sorption, solubility and kinetics of inorganic systems in aqueous media has been reviewed in the papers given at an international conference in 1978. Both chemical equilibrium models, exemplified by computer programs such as MINEQL and SOLMNQ, and dynamic reaction path models, exemplified by EQ6, have been developed. Application of the equilibrium models to radioactive waste disposal... 

Now, the macroscopic behavior of all systems, whether in equilibrium or nonequilibrium states, is classically described in terms of the thermodynamic variables pressure P, temperature T, specific volume V (volume per mole), specific internal energy U (energy per mole), specific entropy S (entropy per mole), concentration or chemical potential /r, and velocity v. In nonequilibrium states, these variables change with respect to space and/or time, and the subject matter is called nonequilibrium thermodynamics. When these variables do not change with respect to space or time, their prediction falls vmder the subject matter of equilibrium thermodynamics. As a matter of notation, we would indicate a nonequilibrium variable such as entropy hy (r,t), where r is a vector that locates a particular region in space (locator vector) and t is the time, whereas the equilibrium notation would simply be . 

For later purposes we need a few further basic relations of equilibrium thermodynamics. Let us therefore restrict ourselves in this section to thermodynamic systems which are in external equilibrium with respect to a coupling to bath system as well as in internal equilibrium with respect to chemical reactions. 

The basis of our approach is the notion of local equilibrium. For a very large class of systems that are not in thermodynamic equilibrium, thermodynamic quantities such as temperature, concentration, pressure and internal energy remain well-defined concepts locally, i.e. one could meaningfully formulate a thermodynamic description of a system in which intensive variables such as temperature and pressure are" well defined in each elemental volume, and extensive variables such as entropy and internal energy are replaced by their corresponding densities. Thus, thermodynamic variables can be considered as functions of position and time. This is the assumption of local equilibrium. There are systems in which this assumption is not a good approximation but they are exceptional. In most hydrodynamic and chemical systems, local equilibrium is an excellent approximation. Modem computer simulations of molecular dynamics have shown that if initially the system is in such a state that... 

The purpose of the chapter dealing with equilibrium thermodynamics of the perfect solid (Chapter 4) is to elaborate, on the one hand, simple expressions for the thermodynamic functions of the chemical ground state and, on the other hand, to make the reader familiar with questions of internal and external equilibria, not least with the intention to provide the equipment to deal with the thermodynamics of defect formation. (The major portion of the free enthalpy at absolute zero consists of bonding energy, while the temperature dependence is largely determined by the vibration properties.)... 

Equation (3.48) describes the rate of forward reaction at chemical equilibrium between reactants and products. It is assumed in TST that Eq. (3.48) also describes the rate in the forward direction even if the system is not at equilibrium, i.e., when net forward reaction occurs. One condition for this is that the reactants are in internal thermodynamic equilibrium, so that their states are populated according to the Boltzmann distribution law. If this is true, Eq. (3.48) is unaffected by the extent to which the reverse reaction is occurring (Smith, 1980). 

Chemical reaction equilibrium calculations are structured around another thermodynamic term called tlie free energy. Tliis so-callcd free energy G is a property that also cannot be defined easily without sonic basic grounding in tlicmiodynamics. However, no such attempt is made here, and the interested reader is directed to tlie literature. " Note that free energy has the same units as entlialpy and internal energy and may be on a mole or total mass basis. Some key equations and information is provided below. 

It is reasonable to expeet that models in ehemistry should be capable of giving thermodynamic quantities to chemical accuracy. In this text, the phrase thermodynamic quantities means enthalpy changes A//, internal energy changes AU, heat capacities C, and so on, for gas-phase reactions. Where necessary, the gases are assumed ideal. The calculation of equilibrium constants and transport properties is also of great interest, but I don t have the space to deal with them in this text. Also, the term chemical accuracy means that we should be able to calculate the usual thermodynamic quantities to the same accuracy that an experimentalist would measure them ( 10kJmol ). 

In Chapter 1 we described the fundamental thermodynamic properties internal energy U and entropy S. They are the subjects of the First and Second Laws of Thermodynamics. These laws not only provide the mathematical relationships we need to calculate changes in U, S, H,A, and G, but also allow us to predict spontaneity and the point of equilibrium in a chemical process. The mathematical relationships provided by the laws are numerous, and we want to move ahead now to develop these equations.1... 

Ilya Prigogine, the founding editor of Advances in Chemical Physics, died May 25, 2003. He was born in Moscow, fled Russia with his family in 1921, and, after brief periods in Lithuania and Germany, settled in Belgium, which was his home for 80 years. His many profound contributions to the theory of irreversible processes included extensions of both macroscopic thermodynamic analysis and statistical mechanical analysis of time-dependent processes and the approach to equilibrium. While sometimes controversial, these contributions were uniformly of outstanding intellectual merit and always addressed to the most fundamental issues they earned him international repute and the Nobel Prize in Chemistry in 1977. Arguably equally important was his creation of a school of theoretical chemical physics centered at the University of Brussels, as well as the mentoring of numerous creative and productive scientists. 

Parameters describing a particular thermodynamic equilibrium system are derived from experimental quantities obtained by a variety of methods, for example, calorimetry, potentio-metry, and solubility studies. In the ideal case, critical examination of well-studied systems reveals high-quality experimental data that lead to a unique set of thermodynamic constants, which are internally consistent, not only formally, but also from a chemical point of view. In the course of our reviews, however, we encountered several cases of conflicting experimental data that resisted any attempt to cast them into a unique set of thermodynamic parameters. The following summarizes the conflicting data and our pragmatic solutions. 

The advantage of the chemical potential over the other thermodynamic quantities, U, H, and G, is that it is an intensive quantity—that is, is independent of the number of moles or quantity of species present. Internal energy, enthalpy, free energy, and entropy are all extensive variables. Their values depend on the extent of the system—that is, how much there is. We will see in the next section that intensive variables such as p., T, and P are useful in defining equilibrium. 

Since the state of a crystal in equilibrium is uniquely defined, the kind and number of its SE s are fully determined. It is therefore the aim of crystal thermodynamics, and particularly of point defect thermodynamics, to calculate the kind and number of all SE s as a function of the chosen independent thermodynamic variables. Several questions arise. Since SE s are not equivalent to the chemical components of a crystalline system, is it expedient to introduce virtual chemical potentials, and how are they related to the component potentials If immobile SE s exist (e.g., the oxygen ions in dense packed oxides), can their virtual chemical potentials be defined only on the basis of local equilibration of the other mobile SE s Since mobile SE s can move in a crystal, what are the internal forces that act upon them to make them drift if thermodynamic potential differences are applied externally Can one use the gradients of the virtual chemical potentials of the SE s for this purpose ... 

A defining characteristic of a solid is the ability to resist shear. Therefore, stress is an additional feature which has to be taken into account when the physical chemistry of solids is at issue. Gibbs treated the thermodynamics of stressed solids a century ago in his classic work Equilibrium of Heterogeneous Substances under the title The Conditions of Internal and External Equilibrium for Solids in Contact with Fluids with Regard to all Possible States of Strain of the Solid . We have already mentioned in the introduction that stress is an unavoidable result of chemical processes in solids. Let us therefore briefly discuss the basic concepts of the thermodynamics of stressed solids. 

Thermodynamic systems are parts of the real world isolated for thermodynamic study. The parts of the real world which are to be isolated here are either natural water systems or certain regions within these systems, depending upon the physical and chemical complexity of the actual situation. The primary objects of classical thermodynamics are two particular kinds of isolated systems adiabatic systems, which cannot exchange either matter or thermal energy with their environment, and closed systems, which cannot exchange matter with their environment. (The closed system may, of course, consist of internal phases which are each open with respect to the transport of matter inside the closed system.) Of these, the closed system, under isothermal and iso-baric conditions, is the one particularly applicable for constructing equilibrium models of actual natural water systems. 

For any chemical system the second law of thermodynamics furnishes useful equalities and inequalities which characterize the state of that system. At a state of equilibrium in a closed system, the total internal... 

Homogeneous systems, such as cooking oil, exist in thermodynamic equilibrium and the properties of these systems are determined by their chemical composition.1 Heterogeneous systems are not in thermodynamic equilibrium. The properties of these systems are governed by both the chemical composition and the internal framework formed by the spatial arrangement of the individual chemical components present. The formation of steric, electrostatic and covalent forces between these individual components can have a dramatic effect on the properties of the product. Ice cream is a classic example, which is primarily composed of ice cream mix and air. The pure components of ice cream have different structural properties in the mixture than they do in their isolated form. Frozen ice cream has a certain consistency and texture, which is quite different from any of the individual frozen ingredients. 

Equilibrium is a very important concept in discussions of thermodynamics. An isolated system is at equilibrium when it has no tendency to change—a condition that is called internal equilibrium. This implies that the system is at mechanical equilibrium (i.e., it has no tendency for bulk movement of material), thermal equilibrium [i.e., it has no tendency for transport of energy (without bulk movement of material)], and material equilibrium [i.e., it has no tendency for material to change form (such as by a phase transformation or a chemical reaction)]. 

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