Isolated 3, 102 Thermodynamic functions

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. 

Although the statistical approach to the derivation of thermodynamic functions is fairly general, we shall restrict ourselves to a) crystals with isolated defects that do not interact (which normally means that defect concentrations are sufficiently small) and b) crystals with more complex but still isolated defects (i.e., defect pairs, associates, clusters). We shall also restrict ourselves to systems at some given (P T), so that the appropriate thermodynamic energy function is the Gibbs energy, G, which is then constructed as... 

An alternative reference state from which to tabulate thermodynamic functions is that of isolated atoms. The use of this reference state is shown in Fig. 4, where Abd//, is a bond dissociation enthalpy in a reactant or product molecule. (Remember that the v, s are negative for reactants.) The heat of reaction is then... 

Up to now our attention was mainly devoted to calculations of the energy and other quantities referring to free, isolated molecules. The computational techniques and their applications were demonstrated to be profitable in the exploration of physico-chemical properties of free molecules and their reactivity in the gas phase (thermodynamic functions, equilibrium and rate constants). However, the gas-phase processes represent only a special minor part of chemistry. Not only processes in biological systems, but also processes in laboratory conditions proceed typically in the liquid phase - or expressed more specifically - in the solution. It is therefore not surprising that the effort for applications of ab initio calculations is also still increasing in this very important field . ... 

However, using good quality ab initio calculations (extended basis set, electron correlation included, some relativistic effects accounted for) appropriate partition functions can be generated consequently, all the thermodynamic functions are evaluable (for an isolated pair of LS and HS molecules). Unfortunately, cooperativity effects in the solid (condensed) phase contribute to the thermodynamic functions and a proper estimation of such contributions is of extreme difficulty. 

Unless the progress variable A can be controlled, the thermodynamic functions cannot be determined at all possible compositions. This is necessary in order for the general discussion of equilibrium criteria to be operationally meaningful. The rigorous thermodynamic theory of chemical equilibrium does not apply to reactions of the type N2O4 2NO2 since neither component can be isolated. 

In order to illustrate the use of thermodynamic functions, we start with the isolated system and then cross to the closed and open system. 

Next, to determine the parameter f in Eq. (1.134), one appeals to the physical situation which is characteristic for constancy of the total energy which modulates in the thermodynamic function of the macrostate (formulated as a Lagrange expansion) in this respect we consider that the system exchanges the thermal energy with the environment after which is again isolated, so that the total number of particles of the system do not ever change. Thus we have... 

Let it be supposed that the body is isolated so that all of these states are of equal energy. Then, according to the basic postulate, all of the P s become equal when the body reaches equilibrium. It follows from the above that the function S simultaneously reaches a mazimumf value and, of course, this is also a property of the thermodynamic function called entropy, under the same physical conditions. The same postulate gives also... 

We have already seen that all isolated systems evolve to the state of equilibrium in which the entropy reaches its maximum value. This is the basic extremum principle of thermodynamics. But we don t always deal with isolated systems. In many practical situations, the physical or chemical system under consideration is subject to constant pressure or temperature or both. In these situations the positivity of entropy change due to irreversible processes, diS > 0, can also be expressed as the evolution of certain thermodynamic functions to their... 

Note - The isolated ensemble, in which the number of molecules, volume and energy ate chosen as variables and kept constant, is the micro-canonical that we came across in Chapter 4. Its potential function is entropy. The corresponding partition function is simply the molecular partition functioa However, calculating thermodynamic functions is tricky, hence, the preference to use the canonical ensemble when attempting to describe phases. 

Marcus Y, Loewenschuss A (1996) Standard thermodynamic functions of some additional isolated ions at 100-1000 K. J Phys Chem Ref Data 25 1495-1507... 

The primary function of a coating is to act as a barrier which isolates the underlying metal from the environment, and in certain circumstances such as an impervious continuous vitreous enamel on steel, this could be regarded as thermodynamic control. However, whereas a thick bituminous coating will act in the same way as n vitreous enamel, paint coatings are normally permeable to oxygen and water and in the case of an inhibitive primer (red lead, zinc chromate) anodic control will be significant, whilst the converse applies to a zinc-rich primer that will provide cathodic control to the substrate. 

The first law of thermodynamics states that the internal energy of an isolated system is constant. A state function depends only on the current state of a system. The change in a state function between two states is independent of the path between them. Internal energy is a state function work and heat are not. 

Entropy is a measure of disorder according to the second law of thermodynamics, the entropy of an isolated system increases in any spontaneous process. Entropy is a state function. 

Scaling by use of dimensionless numbers only is limited in two-phase flow to simple and isolated problems, where the physical phenomenon is a unique function of a few parameters. If there is a reaction between two or more physical occurrences, dimensionless scaling numbers can mainly serve for selecting the hydrodynamic and thermodynamic conditions of the modelling tests. In... 

Although there have been few reports on the chemistry of transient silanethiones,113 some stable examples have been successfully isolated by thermodynamic stabilization. In 1989, Corriu et al. reported the first synthesis of an isolable silanethione 31a (mp 170-171°C) by the reactions of the pentacoordinated functionalized silane 30a with elemental sulfur or carbon disulfide (Scheme 8).17... 

The first term on the right is the formula for the chemical potential of component a at density pa = na/V in an ideal gas, as would be the case if interactions between molecules were negligible, fee is Boltzmann s constant, and V is the volume of the solution. The other parameters in that ideal contribution are properties of the isolated molecule of type a, and depend on the thermodynamic state only through T. Specifically, V/A is the translational contribution to the partition function of single a molecule at temperature T in a volume V... 

The thermodynamic chemical potential is then obtained by averaging the Boltzmann factor of this conditional result using the isolated solute distribution function Sa Sn). Notice that the fluctuation contribution necessarily lowers the calculated free energy. 

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