Phase rule substances

Many issues raised in previous sections invite further investigation. The remarks that follow should be taken as highlighting some working hypotheses for further research in the ontology of chemistry. Components (in the sense of the phase rule), substances (identified in terms of separation methods), and chemical species... 

Because, in the end, substance is a proto-scientific concept (not defined in science) and identification (isolation, separation) depends on specific properties that are considered relevant and must be known, substance will remain a pragmatic notion and ambiguous situations may arise as to whether to count a sample as one, two, or three substances (cf. non-stoichiometric compounds, inclusion compounds, racemic species, tautomers, etc.). In ambiguous cases, substance identity is best correlated with its possible isolation, as distinct from phase rule substances (identification via a phase diagram) and individuation of chemical species. 

The phase rule is a mathematical expression that describes the behavior of chemical systems in equilibrium. A chemical system is any combination of chemical substances. The substances exist as gas, liquid, or solid phases. The phase rule applies only to systems, called heterogeneous systems, in which two or more distinct phases are in equilibrium. A system cannot contain more than one gas phase, but can contain any number of liquid and solid phases. An alloy of copper and nickel, for example, contains two solid phases. The rule makes possible the simple correlation of very large quantities of physical data and limited prediction of the behavior of chemical systems. It is used particularly in alloy preparation, in chemical engineering, and in geology. 

The material in this section is divided into three parts. The first subsection deals with the general characteristics of chemical substances. The second subsection is concerned with the chemistry of petroleum it contains a brief review of the nature, composition, and chemical constituents of crude oil and natural gases. The final subsection touches upon selected topics in physical chemistry, including ideal gas behavior, the phase rule and its applications, physical properties of pure substances, ideal solution behavior in binary and multicomponent systems, standard heats of reaction, and combustion of fuels. Examples are provided to illustrate fundamental ideas and principles. Nevertheless, the reader is urged to refer to the recommended bibliography [47-52] or other standard textbooks to obtain a clearer understanding of the subject material. Topics not covered here owing to limitations of space may be readily found in appropriate technical literature. 

Chapters 7 to 9 apply the thermodynamic relationships to mixtures, to phase equilibria, and to chemical equilibrium. In Chapter 7, both nonelectrolyte and electrolyte solutions are described, including the properties of ideal mixtures. The Debye-Hiickel theory is developed and applied to the electrolyte solutions. Thermal properties and osmotic pressure are also described. In Chapter 8, the principles of phase equilibria of pure substances and of mixtures are presented. The phase rule, Clapeyron equation, and phase diagrams are used extensively in the description of representative systems. Chapter 9 uses thermodynamics to describe chemical equilibrium. The equilibrium constant and its relationship to pressure, temperature, and activity is developed, as are the basic equations that apply to electrochemical cells. Examples are given that demonstrate the use of thermodynamics in predicting equilibrium conditions and cell voltages. 

The phase rule as has been pointed out in the preceding paragraph deals with the behavior of heterogeneous systems at equilibria. It essentially includes three special terms. These are (i) number of phases in the system (P) (ii) the number of components for the system (C) and (iii) the number of degrees of freedom available to the system (F). A system for the present purpose could be any substance or combination of substances, which is set apart from its surroundings or other substances, such that its equilibrium state may be studied. The simplest way to express the rule in the form of an equation combining the three terms is as follows ... 

It is sometimes convenient to fix the pressure and decrease the degrees of freedom by one in dealing with condensed phases such as substances with low vapour pressures. Gibbs phase rule then becomes... 

It is sometimes convenient to fix the pressure and decrease the degrees of freedom by one in dealing with condensed phases such as substances with low vapour pressure. The Gibbs phase rule for a ternary system at isobaric conditions is Ph + F = C + 1=4, and there are four phases present in an invariant equilibrium, three in univariant equilibria and two in divariant phase fields. Finally, three dimensions are needed to describe the stability field for the single phases e.g. temperature and two compositional terms. It is most convenient to measure composition in terms of mole fractions also for ternary systems. The sum of the mole fractions is unity thus, in a ternary system A-B-C ... 

The mathematical basis of classic thermodynamics was developed by J. Willard Gibbs in his essay [1], On the Equilibrium of Heterogeneous Substances, which builds on the earlier work of Kelvin, Clausius, and Helmholtz, among others. In particular, he derived the phase mle, which describes the conditions of equilibrium for multiphase, multicomponent systems, which are so important to the geologist and to the materials scientist. In this chapter, we will present a derivation of the phase rule and apply the result to several examples. 

A substance that can be added to a system independently (or removed from it, say by precipitation or vaporization) is called a component of such a system. The phase rule, summarizing a general behavior of nature, says ... 

The phase rule states that, when equilibrium conditions are sustained, a minimum number of intensive properties of the (subsurface) system can be used to calculate its remaining properties. An intensive property is a property that is independent of the amount of substance in the domain. Examples of intensive properties include temperature (7), pressure (P), density (p), and chemical potential (p), which is a relative measure of the potential energy of a chemical compound. The phase rule specifies the minimum number of intensive properties that must be determined to obtain a comprehensive thermodynamic depiction of a system. 

A phase is defined as a state of matter that is uniform throughout in terms of its chemical composition and physical state in other words, a phase may be considered a pure substance or a mixture of pure substances wherein intensive properties do not vary with position. Accordingly, a gaseous mixture is a single phase, and a mixture of completely miscible liquids yields a single hquid phase in contrast, a mixture of several solids remains as a system with multiple solid phases. A phase rule therefore states that, if a limited number of macroscopic properties is known, it is possible to predict additional properties. 

The normal freezing point of the liquid under pressure is given by Tp, and OS is the melting curve of the substance, i.e. the locus of the points defining the co-existence of solid and liquid. If we measure the freezing point of a liquid in a closed system, the Phase Rule tells us that since at that temperature all three phases will be in equilibrium, F=0, and we obtain the... 

Applying the phase rule, it is found that, in the two component system NaP03 + H20, a maximum of four phases is possible at the quadruple points 199,302). In addition to, at the most, two crystalline substances and water vapor, an amorphous glass-like phase is always present. This phase consists of mixtures of polyphosphates, the chain length of which rises with increasing temperature. Only Na2H2P207, Maddrell s salt (h) and trimetaphosphate occur as stable solid phases in addition to NaH2P04. 

To explore the ramifications of the phase rule (7.6), we shall first consider the phase equilibria of pure chemical substances (c = 1). Subsequent sections will examine the more complex behavior of binary (c = 2) and ternary (c = 3) multiphase systems. 

Some phenomenological features of a representative phase diagram (for C02) were previously described in Section 2.5. In the present section, we shall first review key topological features of the phase diagram for H20 from the perspective of the phase rule (Section 7.2.1). The general theory of phase boundaries will then be developed (Section 7.2.2) and illustrated (Section 7.2.3) for some simple elemental and molecular substances. These representative examples will serve to illustrate the bewildering multiplicity of phase forms and properties that are possible even in the simple c = 1 limit. 

Once a quantity of a third substance (solute) is added to a system of two immiscible liquids, it will distribute or divide between the layers in definite proportions. Applying the phase rule to such a system reveals that we have a system of three components (C) and two phases (P). Thus, the system has three degrees of freedom (F), that is, pressure, temperature, and concentration. 

This typical application of the second kind is the Gibbs Phase Rule (for inert systems). This rule is often stated merely for systems with only two external coordinates (n = 2, e.g., xt = P,x2 = T). There must then be no internal partitions within the system, nor may it, for instance, contain magnetic substances in the presence of external magnetic fields. 

Let the number of basic overall equations be Q it is evident that Q< P. Let us denote the number of substances participating in the reaction as M and the number of independent components, in the sense this notion is used in the Gibbs phase rule, as C then... 

By Gibbs Phase Rule illustrated in this chapter s introduction, a second intensive variable is needed (in addition to either temperature or pressure) to specify the three-phase binary system with an inhibitor (F = 3 — 3 + 2). Typically, the concentration of the inhibitor in the free water phase is specified as the second intensive variable. Substances that have considerable solubility in the aqueous phase, such as alcohols, glycols, and salts, normally act as inhibitors to hydrate formation. The colligative mechanism of formation inhibition is aided by increased competition for water molecules by the dissolved inhibitor molecule or ion through hydrogen bonding for alcohols or glycols, or via Coulombic forces (for salt ions). 

Phase rule studies and describes the occurence of modifications and states of aggregation of pure substances or in mixtures in closed systems as well as the changes which occur in those systems when the pressure, temperature and composition of these substances in the system change. The behaviour of many pure substances and mixtures has thus been studied and recorded in diagrams. These diagrams constitute a vital aid for any scientist studying the development of materials, e.g. ceramics. 

Another important concept in phase rule is component . A component is a separate substance, i.e. a substance which cannot be formed out of one or more other substances in the system. For example the system C0-C02-C consists of the solid phase carbon and the gaseous phases... 

Many choices of independent variables such as the energy, volume, temperature, or pressure (and others still to be defined) may be used. However, only a certain number may be independent. For example, the pressure, volume, temperature, and amount of substance are all variables of a single-phase system. However, there is one equation expressing the value of one of these variables in terms of the other three, and consequently only three of the four variables are independent. Such an equation is called a condition equation. The general case involves the Gibbs phase rule, which is discussed in Chapter 5. 

Now, a question arises, Is there a way to quantitatively describe the phase boundaries in terms of P and T The phase rule predicts the existence of the phase boundaries, but does not give any clue on the shape (slope) of the boundaries. To answer the above question, we make use of the fact that at equilibrium the chemical potential of a substance is the same in all phases present. 

The system of equations (2.27) is seen to be rather complicated. Its solution, if obtainable at all in quadratures, must probably be even more complicated. However, in experiments certain conditions which enable the initial equations to be simplified are usually fulfilled. Consider limiting cases of particular interest from both theoretical and practical viewpoints.134,136,139,140 The process of growth of the ApBq and ArBs layers will be analysed in its development with time from the start of the interaction of initial substances A and B up to the establishment of equilibrium at which, according to the Gibbs phase rule (see Refs 126-128), no more than two phases should remain in any two-component system at constant temperature and pressure. 

The lacking special description of the Gibbs phase rule in MEIS that should be met automatically in case of its validity is very important for solution of many problems on the analysis of multiphase, multicomponent systems. Indeed, without information (at least complete enough) on the process mechanism (for coal combustion, for example, it may consist of thousands of stages), it is impossible to specify the number of independent reactions and the number of phases. Prior to calculations it is difficult to evaluate, concentrations of what substances will turn out to be negligibly low, i.e., the dimensionality of the studied system. Besides, note that the MEIS application leads to departure from the Gibbs classical definition of the notion of a system component and its interpretation not as an individual substance, but only as part of this substance that is contained in any one phase. For example, if water in the reactive mixture is in gas and liquid phases, its corresponding phase contents represent different parameters of the considered system. Such an expansion of the space of variables in the problem solved facilitates its reduction to the CP problems. 

Displacement of equilibria in adsorbed layers. If an equilibrium exists in solution between two or more constituent substances, and one of these is adsorbed more strongly than another, that one will be more concentrated in the surface and the equilibrium in the surface layer will be shifted in the direction of that constituent. It often happens, owing to electrolytic dissociation or to hydrolysis, that a single pure substance when dissolved in water consists of such an equilibrium mixture, and if the bulk solution alone were under consideration, an aqueous solution of such a substance would naturally be treated, according to the phase rule, as a two-component system. But when surfaces enter into consideration, unless the ease of adsorption of both the constituents of the equilibrium mixture in solution is identical, the adsorption of each has to be considered separately and consequently the system must be regarded as consisting of three components at least, not two.5... 

When the system is a homogeneous substance of constant composition, the phase rule indicates that fixing the values of two intensive properties establishes its state. The molar or specific enthalpy of a substance may therefore be expressed as a function of two other state variables. Arbitrarily selecting these asrtemperature and pressure, we write... 

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