System of two components

The simplest application of the Gibbs adsorption isotherm is a system of two components, e.g., a solvent 1 and a solute 2. In this case we have 

The ideal interface is conveniently defined such that Ti = 0. Then we get 

The superscript (1) should remind us of the special choice of the interface. The chemical potential of the solute is described by the equation 

a is the activity and a0 is a standard activity (1 mol/L). Differentiating with respect to a/a0 at constant temperature leads to 

This is a very important equation. It directly tells us that when a solute is enriched at the interface (T 0), the surface tension decreases when the solution concentration is increased. Such solutes are said to be surface active and they are called surfactants or surface active agents. Often the term amphiphilic molecule or simply amphiphile is used. An amphiphilic molecule consist of two well-defined regions One which is oil-soluble (lyophilic or hydrophobic) and one which is water-soluble (hydrophilic). 

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Two other types of equilibrium curves are occasionally encountered with the system of two components forming a continuous series of solid solutions. These are shown in Figs. 1,16, 3 and 1,16, 4. In the former the freezing or melting curve passes through a minimum (examples p-chloroiodobenzene, m.p. 57° - p-dichlorobenzene, m.p. 53° naphtha-... 

In 163—167 we have deduced some properties of systems of two components in two phases ( binary systems V) directly from the fundamental principles, and in 169—173 we have obtained quantitative relations in certain special cases. Here we shall j obtain some general equations relating to such systems with the i help of the thermodynamic potential (cf. 155)., ... 

We consider for simplicity systems of two components, and take as unit quantity of a phase that containing x mols of the first... 

The phase diagram for aluminum/silicon (Fig. 4.5) is a typical example of a system of two components that form neither solid solutions (except for very low concentrations) nor a compound with one another, but are miscible in the liquid state. As a special feature an acute minimum is observed in the diagram, the eutectic point. It marks the melting point of the eutectic mixture, which is the mixture which has a lower melting point than either of the pure components or any other mixture. The eutectic line is the horizontal line that passes through the eutectic point. The area underneath is a region in which both components coexist as solids, i.e. in two phases. 

SOLIDUS CURVE. A curve representing the equilibrium between the solid phase and the liquid phase m a condensed system of two components. The relationship is reduced to a two-dimensional curve by disregarding the influence, of the vapor phase. The points on the solidus curve are obtained by plotting the temperature at which the last of the liquid phase solidifies, against the composition, usually in terms of the percentage composition of one of the two components. 

In this work a system of two-component polymer blends with a com-J)osition range much wider than those of practical importance was studied... 

Multivariant systems may also become indifferent under special conditions. In all considerations the systems are to be thought of as closed systems with known mole numbers of each component. We consider here only divariant systems of two components. The system is thus a two-phase system. The two Gibbs-Duhem equations applicable to such a system are... 

Consider a system of two components, A and B, which are completely soluble in one another in the liquid state, but completely insoluble in one another in die solid state. 

In the preceding chapter we have been considering the equilibrium of two phases of the same substance. Some of the most important cases of equilibrium come, however, in binary systems, systems of two components, and we shall take them up in this chapter. Wo can best understand what is meant by this by some examples. The two components mean simply two substances, which may be atomic or molecular and which may mix with each other. For instance, they may be substances like sugar and wrater, one of which is soluble in the other. Then the study of phase equilibrium becomes the study of solubility, the limits of solubility, the effect of the solute on the vapor pressure, boiling point, melting point, etc., of the solvent. Or the components may be metals, like copper and zinc, for instance. Then we meet the study of alloys and the whole field of metallurgy. Of course, in metallurgy one often has to deal with alloys with more than two components—ternary alloys, for instance, with three components—but they arc considerably more complicated, and we shall not deal with them. 

To discuss the addition of adsorbate to a monodisperse adsorbent we shall use a similar device, a function G for the system of two components that strictly is equal to the free energy only when the number of moles of adsorbent, nl9 is a multiple of the number of moles of adsorbent in a single standard droplet. For each value of nl9 however, G = G varies continuously as a function of n2. G2 may be defined in the usual manner ... 

This experiment is concerned with the heterogeneous equilibrium between two phases in a system of two components. The particular system to be studied is cyclohexanone-tetrachloroethane at 1 atm pressure. This system exhibits a strong negative deviation from Raoult s law, resulting in the existence of a maximum boiling point. 

Two compment systems. Let us now consider systems of two component substances which can react with one another. The reaction may consist of the formation of solutions, or of one or more chemical compounds. By solutions we mean phases which contain both components, and which remain homogeneous when their percentage composition is varied continuously within certain limits. As each component of the system and each compound of the components can exist in at least three modifications, it would at first sight appear possible for a great number of such phases to exist in equilibrium with one another. We shall see, however, that the number of phases which can exist in contact with one another is limited in various ways. 

For the moment we shall consider a system of two components A and B which do not form a solid solution. The pressure applied to the system is always assumed to be greater than the vapour pressure of the liquid mixture. The only phases which can be present are therefore the liquid solution A + B, the sofid A and the solid B. We also assume that A and B do not react with one another chemically. 

Equation (5.3) is the general form for the Gibbs adsorption isotherm. The simplest case of this isotherm is a system of two components in which the solute [Eq. (5.2)1 is the surface-active component - that is, it is adsorbed at the surface of the solvent [Eq. (5.1)]. For such a case. Equation (5.3) may be written as ... 

For notational convenience, we shall discuss a two-component mixture of A and B. The generalization for multicomponent system is quite straightforward. We consider a system of two components in the T, P, NA, NB ensemble. We have chosen the T, P, NA, NB ensemble because the isothermal-isobaric systems are the most common ones in actual experiments. By very similar components, we mean, in the present context, that the potential energy of interaction among a group of n molecules in a configuration X is independent of the species we... 

The mass flux j of component 1 and heat flux q in a system of two components at uniform pressure are related to the gradient of the mole fraction of component 1 and the gradient of temperature by the phenomenological relations... 

Different Systems of Two Components.— Applying the Phase Rule... 

In addition to the pressure and temperature, therefore, a third variable factor must be chosen, and as such there is taken the concentration of the components. In systems of two components, therefore, not only may there be change of pressure and temperature, as in the case of one-component systems, but the concentration of the components in the different phases, or the composition of the phases, may also alter a variation which did not require to be considered in the case of one-component systems. 

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