Reference state, Idealized, definition

This is strictly true only for the ideal gas thermochemical reference state for which, by definition, there are no intermolecular interactions. In the absence of hydrogen bonding, complications and therefore corrections for nonideality are expected to be small. 

In order to get some information on the possible structure of the given molten system from the conductivity measurement, a suitable reference state should be defined. Since conductivity is a scalar quantity, no ideal behavior is given by definition. However, there were several attempts in the literature to present a model of electrical conductivity of molten salts, which would describe satisfactorily the course of the conductivity dependence on composition. 

So why are we devoting so much discussion to such a small point The reason will gradually become apparent. This topic is simply the first one in which the distinction between the thermodynamic model and the real world arises. The fact that real systems do achieve equilibrium tends to lead to the conclusion that thermodynamics refers to, or even is part of, real systems, and this inevitably leads to confusion with respect to reversible processes, infinitesimals, choice of components, and many other parts of the model. Our point of view is that real systems achieve the kind of practical equilibrium we defined in 3.3, including local and partial equilibria, but that the thermodynamic model uses idealized equilibrium states. If there is not too much difference between them, then the model results are useful in the real world. The definition of too much difference depends on the application. 

Standard states are simply a special sort of reference state for physical properties, made necessary, as we have mentioned several times, by our lack of knowledge of absolute values for the properties U, G, H, and A. Standard states are therefore systems or states of matter under specified conditions. The definition must be sufficiently complete as to determine the thermodynamic parameters of the substance, and therefore must have at least four attributes 1. temperature 2. pressure 3. composition 4. state of aggregation (solid polymorph, liquid, gas, ideal gas, ideal solution, etc.). Thus 25°C, 1 bar is not a standard state. The question is, what system at 25°C, 1 bar . 

The definition of the activity coefficient depends on the choice of the reference state in which y = 1. If we wish to compare the rate of reaction with the rate in the gas phase, then we will choose the reference state of unit activity coefficient as the ideal gas. This reduces Eq. (33.50) to... 

We cite two reasons for introducing fugacity as an alternative to the chemical potential. One is to obtain the algebraic form (4.3.12), which replaces a difference measure with a ratio measure. In many applications, functional forms for ratios are less complicated than the corresponding forms for differences. Such simplifications facilitate numerical calculations. Further, the expressions (4.3.7) and (4.3.8) for the chemical potential become troublesome as x, —> 0 in comparison, the fugacity remains well behaved (/ —> 0 as x, —> 0). A second reason is that the second part of the definition (4.3.9) identifies the ideal gas as the reference state for fugacity, and numerical values for ideal-gas fugacities are readily obtainable. 

In this subsection we introduce a ratio measure that indicates how the fugacity of a real substance deviates from that of an ideal gas. As the reference state, we choose the ideal-gas mixture at the same temperature, pressure, and composition as our real mixture. Then, on integrating the definition of fugacity (4.3.8) from the ideal-gas state to the real state, we obtain an algebraic form analogous to (4.3.12) that is, we find... 

In contrast to other textbooks on thermodynamics, we assume that the readers are familiar with the fundamentals of classical thermodynamics, that means the definitions of quantities like pressure, temperature, internal energy, enthalpy, entropy, and the three laws of thermodynamics, which are very well explained in other textbooks. We therefore restricted ourselves to only a brief introduction and devoted more space to the description of the real behavior of the pure compounds and their mixtures. The ideal gas law is mainly used as a reference state for application examples, the real behavior of gases and liquids is calculated with modern g models, equations of state, and group contribution methods. 

For a reaction system like the one shown above in Table 1.2 it is convenient to define the thermod5mamic reference state as the enthalpy and free energy of formations as an ideal gas at 25 C (298.15 K). This definition allows direct calculation of heat duty in the enthalpy calculation without having to distinguish between the parts for heating and reaction. 

Parametrization of the thermodynamic properties of pure electrolytes has been obtained [18] with use of density-dependent average diameter and dielectric parameter. Both are ways of including effects originating from the solvent, which do not exist in the primitive model. Obviously, they are not equivalent and they can be extracted from basic statistical mechanics arguments it has been shown [19] that, for a given repulsive potential, the equivalent hard core diameters are functions of the density and temperature Adelman has formally shown [20] (Friedman extended his work subsequently [21]) that deviations from pairwise additivity in the potential of average force between ions result in a dielectric parameter that is ion concentration dependent. Lastly, there is experimental evidence [22] for being a function of concentration. There are two important thermodynamic quantities that are commonly used to assess departures from ideality of solutions the osmotic coefficient and activity coefficients. The first coefficient refers to the thermodynamic properties of the solvent while the second one refers to the solute, provided that the reference state is the infinitely dilute solution. These quantities are classic and the reader is referred to other books for their definition [1, 4],... 

By definition, component i experiences in an ideal mixture the same inter-molecular forces as in the reference state and therefore all differences between pjd mix. pj fare caused by differences in the concentration (i.e., dilution) only ... 

We can rewrite this expression in a slightly different but more general way by defining a = P/P° as the activity of an ideal gas. Thus, for an ideal gas, the activity is simply the partial pressure of the gas divided by P° = 1 bar, the standard state pressure. Although we will have more to say about activity in Section 13-8, for now we need only say that ultimately, the activity of a substance depends not only on the amount of substance but also on the form in which it appears in the system. The following rules summarize how the activity of various substances is defined (see also Table 13.5). It is beyond the scope of this discussion to explain the reasons for defining activities in these ways, so we will simply accept these definitions and use them. However, it is important to note that the activity of a substance is defined with respect to a specific reference state. 

The definition above is not complete. The reference state is arbitrary we are free to choose the most convenient reference state imaginable however, both /a and f° depend on the single choice of reference state and may not be chosen independently. Lets consider a limiting condition to complete the definition. As the pressure goes to zero, all gases behave ideally consequently, we define ... 

To use fugacity in practice, the first step is to identify an appropriate reference state. There is an obvious choice of reference state for gases a low enough pressure that the gas behaves as an ideal gas. With this choice, f° P and 9" —> 1. Remember, as a result of our definition for fugacity, the reference state must be at the same temperature as the system of interest T° = T,y,. 

Using the ideal gas reference state, the definition for fugacity of a pure species is ... 

In the liquid phase, just as in the vapor phase, we need to choose a suitable reference state with a corresponding reference chemical potential and reference fugacity to complete the definition provided by Equation (7.3). We then adjust for the difference between the reference phase and the real system. However, while there is an obvious reference case for gases—the ideal gas—there is no single suitable choice for the liquid phase. There are two common choices for the reference state (1) the Lewis/Randall rule and (2) Henry s law. The choice of reference state often depends on the system. Both these reference states are limiting cases that result from a natural idealization for condensed phases the ideal solution. 

The fugacity in the vapor phase is commonly calculated using an ideal gas reference state. Thus, the reference state for pure species i is at a pressure low enough that it behaves as an ideal gas and at the temperature of the system, as restricted by the definition in Equation (7.3). For species i in a mixture, we also specify that the reference state is at the composition of the mixture. We can formulate the fugacity in terms of the fugacity coefficient—a dimensionless quantity that compares the fugacity of species i to the partial pressure species i would have in the system as an ideal gas ... 

The definition of crystal is itself a developing concept, as demonstrated by the ongoing discussions [5, 6]. Most ot the theoretical background proposed in this chapter is valid for a perfect crystal, i.e., an infinite mathematical object with an idealized crystal structure ideal crystal) in thermodynamic equilibrium at a given presstrre P and temperature T. In textbooks, only the gas phase thermodynamics is usually discussed in detail, whereas little attention is paid to the solid state. A full thermodynamic treatment of solids is beyond the scope of this chapter and the reader is referred to specific books on the subject, for example [7]. 

The just-suspended state is defined as the condition where no particle remains on the bottom of the vessel (or upper surface of the liquid) for longer than 1 to 2 s. At just-suspended conditions, all solids are in motion, but their concentration in the vessel is not uniform. There is no solid buildup in comers or behind baffles. This condition is ideal for many mass- and heat-transfer operations, including chemical reactions and dissolution of solids. At jnst-snspended conditions, the slip velocity is high, and this leads to good mass/heat-transfer rates. The precise definition of the just-suspended condition coupled with the ability to observe movement using glass or transparent tank bottoms has enabled consistent data to be collected. These data have helped with the development of reliable, semi-empirical models for predicting the just-suspended speed. Complete suspension refers to nearly complete nniformity. Power requirement for the just-suspended condition is mnch lower than for complete snspension. 

It is immediately apparent that the complete automation of this sub-stage is a difficult task. Only in a few instances (e.g. the automatic in vivo determinations described In Chapter 14 and performed with the on-line process analysers dealt with in Chapter 17) is this ideal objective affordable. Much more often, some of the above-mentioned operations involve human participation, although It is still termed automated [1]. Therefore, although many clinical analysers are classed as automatic, the blood and urine samples that they handle are collected and even treated manually before they are placed on the sampler. Such is also the case with automatic off-line water pollutant analysers, also calling for manual collection and preservation of samples. Consequently, the automated sampling concept as used here refers to the Introduction Into the analyser or instrument concerned of a definite portion of sample collected from its source and even treated manually, with the few exceptions stated above. 

---