Thermodynamics functions of state

The activation parameters from transition state theory are thermodynamic functions of state. To emphasize that, they are sometimes designated A H (or AH%) and A. 3 4 These values are the standard changes in enthalpy or entropy accompanying the transformation of one mole of the reactants, each at a concentration of 1 M, to one mole of the transition state, also at 1 M. A reference state of 1 mole per liter pertains because the rate constants are expressed with concentrations on the molar scale. Were some other unit of concentration used, say the millimolar scale, values of AS would be different for other than a first-order rate constant. 

Electrode potentials are determined by the affinities of the electrode reactions. As the affinities are changes in thermodynamic functions of state, they are additive. The affinity of a given reaction can be obtained by linear combination of the affinities for a sequence of reactions proceeding from the same initial to the same final state as the direct reaction. Thus, the principle of linear combination must also be valid for electrode potentials. The electrode oxidation of metal Me to a higher oxidation state z+>2 can be separated into oxidation to a lower oxidation state z+>1 and subsequent oxidation to the oxidation state z+>2. The affinities of the particular oxidation processes are equivalent to the electrode potentials 2 0, i-o> and E2-. ... 

Remember that G, H and S are all thermodynamic functions of state, i.e. they depend only on the initial and final states of the system, not on the ways the last is reached. As we have seen, for AG = 0 the reaction has reached equilibrium (and in isolated systems AS has reached a maximum). If AG < 0 the reaction was spontaneous, but if AG > 0 the reaction could not have taken place unless energy was provided from other coupled source. If the source is external then the system is not isolated it is closed if there is no exchange of material or open if there is such exchange. In both cases the environmental changes must be taken into account. 

Whether obtained from an actual experimentally feasible process or from a thought process, As i Gg, which is obtained from Eq. (2.9) by re-arrangement, pertains to the solvation of the solute and expresses the totality of the solute-solvent interactions. It is a thermodynamic function of state, and so are its derivatives with respect to the temperature (the standard molar entropy of solvation) or pressure. This means that it is immaterial how the process is carried out, and only the initial state (the ideal gaseous solute B and the pure liquid solvent) and the final state (the dilute solution of B in the liquid) must be specified. 

The fundamental question in transport theory is Can one describe processes in nonequilibrium systems with the help of (local) thermodynamic functions of state (thermodynamic variables) This question can only be checked experimentally. On an atomic level, statistical mechanics is the appropriate theory. Since the entropy, 5, is the characteristic function for the formulation of equilibria (in a closed system), the deviation, SS, from the equilibrium value, S0, is the function which we need to use for the description of non-equilibria. Since we are interested in processes (i.e., changes in a system over time), the entropy production rate a = SS is the relevant function in irreversible thermodynamics. Irreversible processes involve linear reactions (rates 55) as well as nonlinear ones. We will be mainly concerned with processes that occur near equilibrium and so we can linearize the kinetic equations. The early development of this theory was mainly due to the Norwegian Lars Onsager. Let us regard the entropy S(a,/3,. ..) as a function of the (extensive) state variables a,/ ,. .. .which are either constant (fi,.. .) or can be controlled and measured (a). In terms of the entropy production rate, we have (9a/0f=a)... 

Let us return to Figure 8-1 and ask about the nature of the steady state in a multi-component, multiphase system when we establish different (constant) intensive thermodynamic functions of state at the end reservoirs (R, and R2). Hereby, we generalize the situations which have been discussed so far. Without working out the solutions in any detail, let us nevertheless consider the necessary conditions and equations for a quantitative treatment and visualize the multiphase demixing with the help of reaction paths in the pertinent phase diagrams. The nomenclature is given in Figure 8-1. 

There are two interpretations of the statistical quantity A, both being closely related to the geometrical interpretation of the term phase boundary . From a purely macroscopic point of view, the gel of course represents a phase to which thermodynamical functions of state are related. Nevertheless, such a macroscopic image with a sharp boundary can hardly be correct in a PDC-column considering the range of end-to-end distances of the transported coils in the concentration profile, because the transported P-mer and the stationary gel are chemically equal in PDC. The two possible definitions of the quantity A(P) are ... 

A new interesting fact is that the application of thermodynamic functions of states together with material balances suggests a non-trivial consideration concerning the system behaviour not only under equilibrium but also in the course of approaching this equilibrium. 

By convention, thermodynamic functions of state refer to the system and not the environment, so - AG (exergonic) represents the Gibbs energy potentially available for expenditure and potentially dissipated to the environment. Under suitable conditions, this energy could be made to perform work. An endergonic reaction (+ AG) cannot proceed spontaneously and requires an input of Gibbs energy to proceed from its initial to its final state. 

The affinity of irreversible processes is a thermodynamic function of state related to the creation of entropy and uncompensated heat during the processes. The second law of thermodynamics indicates that all irreversible processes advance in the direction of creating entropy and decreasing affinity. This chapter examines the property affinity in chemical reactions and the relation between the affinity and various other thermodynamic quantities. 

The enthalpy change AH, being an important thermodynamic function of state, is identical with the negative value of the heat of reaction (Qp), when the reaction proceeds under constant pressure in a purely chemical way (e. g. in a calorimeter), the A// = — Qp. The quantity AH expresses, therefore, the value of the total energy set free or absorbed during a reaction proceeding under constant pressure. 

Next, in the CE, the "natural" thermodynamic variable is A = kBT lneQ, and expressions for S, P, fi, and LI were found explicitly in Section 5.3. Can we find new expressions for the "other" thermodynamic functions of state, such as H and VI... 

The above concepts may be summarized in four equivalent statements. Let F be a thermodynamic function of state then the following holds ... 

Notice that in Eq. (1.16.4) there is now no explicit reference to any heat flow from or to the surroundings. Rather, emphasis is placed on the work term 3W, which can always be either measured or calculated by the methodology of Section 1.7. In fact, we will presently show how the calculation of 3W under a variety of constraints permits one to evaluate certain thermodynamic functions of state that are of general interest. Also, we show how one can ascertain whether physical system are at equilibrium or not. Namely,... 

The present section is fundamental in the sense that both the methodology for interrelating various thermodynamic functions of state introduced in Section 1.16 and the final results will be utilized over and over in subsequent portions of this book. It should be noted in passing that whenever thermodynamic relations involve the entropy, standard operating procedure calls for the immediate substitution for S in terms of measurable quantities. These matters are illustrated below. 

In this Section the internal energy function has been introduced in the form E - E(T,V), whereas in Section 1.18 it has been formulated as E - E(S,V). Considering that thermodynamic functions of state should be useful in deriving various intensive and extensive variables, are the two formulations equivalent If not, which one is more fundamental In a similar vein discuss the relation between H... 

In Sec. 1.23 we introduced thermodynamic functions of state for systems of variable composition. For example, the energy function was written as c... 

Show how the affinity A may be specified in terms of the four thermodynamic functions of state. 

We have thus introduced a new set of conjugate variables (ip,n) which play a central role in the present case. As a consequence the number of possible thermodynamic functions of state has been doubled relative to those displayed in Section 1.18. It turns out, however, that Eqs. (5.1.25) are not useful because they involve a change in gravitational potential ip at the location of the small volume element situated at height z. Since such an alteration is experimentally impossible we ignore this latter set of relations. 

It should be evident that aside from Eqs. (5.8.1) and (5.8.4), eight additional equations may be set up to specify differentials for the four thermodynamic functions of state in terms of the pairs (P,Ha) or (P,M) of field variables. Their construction is called for in Exercise 5.8.1. 

Systematics of Thermodynamic Functions of State 1.13.1 Thermodynamic Functions of State... 

At this point we extend the earlier discussions to open systems, in which the mole numbers n, of the different components of a systems are allowed to change through the exchange of material with the surroundings. Thus, the various thermodynamic functions of state, V, E, H, S, A,G are now functions of these mole numbers in the manner already displayed for V and G in the preceding section. 

Similar arguments may be advanced for virtual changes involving the other thermodynamic functions of state. However, one must be careful for example, virtual changes in the Helmholtz function assume the form... 

We next take up the topic of adsorption of gases on surfaces. This problem is not only of intrinsic interest but also provides valuable pedagogical insight on the systematics that obtain for the many choices for thermodynamic functions of state. These involve new degrees of freedom that are needed to characterize the adsorption process. Accordingly, we consider a system consisting of a very thin layer of atoms held on the surface of a material exposed to a gas phase. The bulk solid or liquid is termed the adsorbent, while the material held on its surface is termed the adsorbate. The process by which material is transferred from the gas to the surface phase is called adsorption. 

The above presentation shows that we must introduce (p and As as conjugate variables in setting up the thermodynamic functions of state of the surface phase. Accordingly, we write the First Law of Thermodynamics in the form... 

There is an important difference among the thermodynamic functions of state as far as phase equilibria are concerned. Some thermodynamic functions of state, such as temperature and pressure, have the same value in all the phases of a system under equilibrium conditions. They are actually the forces driving a system to its equilibrium. Such functions are referred to as fields [1],... 

The other thermodynamic functions of state generally have different values in the different phases of a system at equilibrium. Typical examples are the phase volumes, composition, enthalpy, etc. Such functions are known as densities. 

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