Monovariant system

THE.5. R. Defay et I. Prigogine, Systemes monovariants et systemes indifferents (Monovariant systems and indifferent systems). Bull. Cl. Set Acad. Roy. Belg. 29, 525—535 (1943). 

Here the state with [ZA] = [Z] is taken as a standard state of the adsorbed layer thus, in the case when only one gas is adsorbed, the layer is in the standard state at the coverage 1 /2. It can be easily seen that 1 /a is the equilibrium pressure at [ZA] = [Z], i.e., at the standard state of the adsorbed substance. This value may be called desorption pressure we shall denote it as b. It is analogous to vapor pressure or dissociation pressure in monovariant systems (24). Indeed, in the case of equilibrium of liquid with its vapor, the surface from which evaporation occurs is equal to the surface for condensation the same equality is realized at the adsorption equilibrium if the fraction of the occupied surface is equal to that of the free surface. This analogy explains the applicability of the Nernst approximate formula to desorption pressure (24) ... 

Monovariant systems. Transformation tension at a given temperature. Transformation point imder a given pressure.— A system whose variance is equal to unity is called a monovariant... 

Examples of monovariant systems.—The most simple type of monovariant system is furnished by a liquid in the presence of its vapor a single component (c=l) is divided into two phases ( =2). 

A system which includes a single substance at once in the solid and liquid states is also a monovariant system under a given... 

A system which contains a gas such as cyanogen and a poly-merous solid from this gas such as paracyanogen, is also a monovariant system similarly, at a given temperature, it is necessary for equilibrium that the gas reach a definite tension this tension, which depends upon the temperature alone, is the tranaformor turn tension for this temperature this is, in fact, the law found to be true by Troost and Hautefeuille in their clasdc investigations. 

These examples, that might be multiplied, suggest the infinite variety of t3rpes of monovariant systems and nevertheless, in spite of the diversity of these t3q>es, the value of the variance common to them all imposes upon them all the same form of the law of equilibrium in all we find a iranaformation tension depending solely upon the temperature. 

R6le of monovariant systems in the history of chemical mechanics.— The rdle that the monovariant systems have played in the history of chemical mechanics is well known it is because they appealed to monovariant systems that Debray, Isambert, Troost, and Hautefeuille found, in the study of chemical decompositions, in the study of allotropic modifications, a dissociation tension, a transformation tension, analogous to the tension of saturated vapors it is in showing the analogy between the dissociation tension, the transformation tension, and the tension of saturated vapor that th have made ev the most skeptic accept the far-reaching thought of Henri Sainte-Claire Deville Ihere is no chemical mechanics distinct from physical mechanics aU... 

Biyariant systems.—The importance of monovariant systems should not make us forget the not less important Bivariant systems. 

One component existing in two phases.— Among the monovariant systems we find in the first place all those where a single component is divided between two phases among the most remarkable examples are ... 

Two components divided among three phases.— We find next, among the monovariant systems, those formed of two inde pendent components divided into three phases among them let us mention ... 

Three components with four phases.—system for which three independent components are divided among four phases is also a monovariant system. As, for example ... 

Law of equilibrium for monovariant systems. Transformation tension and transformation point.— e equilibrium states of a monovariant system obey a law which, for all these systems, has the same form, as follows ... 

Robin s law.—In order that a monovariant system taken at a certain temperature and under a certain pressure may be in equilibrium, it is necessary that this pressure be equal to the transformation tension relative to this temperature in other words, it is necessary that the representative point which haa for abscissa this temperature and for ordinate this pressure bo located on the curve of transformation tensions ... 

Let us take as a second example a monovariant system formed of calcium carbonate, carbonic acid gas, and lime denote by P the dissociation tension of calcium carbonate for the temperature T if, at the same temperature, the pressure is greater than P, the system will be the seat of a reaction accompanied by a decrease in volume, that is, of a combination of carbonic acid gas with lime if, on the contrary, the pressure is less than P, the system will be the seat of a reaction accompanied by an increase in volume, or of dissociation of calcium carbonate. 

Motttier s Law.—Some years before Robin stated the rule which permits predicting the nature of the modification which is produced in a monovariant system when the representative point is above or below the curve of transformation tensions, J. Moutier had stated an analogous rule the latter predicts the nature of the modification of which the system is the seat according as the representative point is to the left or to the right of the curve of transformation tensions. 

Under a pressure r let be the value of the transformation point of a monovariant system let us consider a reaction taking pLoe in this system under the same pressure n and at the temperature T, different from 0 this reaction calls into play a certain quantity of heat, which depends upon the temperature T, as we have seen (Chap. Ill, Art. 41) if, therefore, without changing the pressure, we ause the temperature T to vaiy, making it approach 0, the value of the quantity of heat set free by the reaction will vaiy, and even its sign may change this last circumstance will certainly not be produced if the temperatures T are not too far distant from the transformation point 0 let us suppose that this is not produced for the monovariant S3 tems which we shall study and in the conditions under which we study them Moutier s rule may then be stated ... 

At a given pressure, every change produced in a monovariant system at a temperature less than the transformation point is accompanied by a liberation of heat every modification produced at a temperature higher than the transformation point is accompanied by an absorption of heat. 

Imagine that in the same monovariant system, under (he same pressure, but at two different temperatures, two reactions, the inverse of each other, are observed the reaction taking place at the lower temperature is exothermic, Oie one produced at the higher tempera lure is endothermic. 

Let 6 and P be the coordinates of a point M on the curve of trans forrnation tensions of a monovariant system choose a modifica tion of this system which liberates heat when it is supposed to take place at the temperature 0 and the pressure P if this modification... 

We shall go farther and find the value of the tangent to the curve of transformation tensions but in order to be able to state the important equation which determines the value of this quantity, we must first speak of the modifications that a monovariant system may be supposed to assume. 

Z44 In every monovariant system there may be two modir-fications, the inverse of each other, which change the masses of the phases without changing their composition.— In certain monovariant systems only two modifications can be observed, the inverse of each other thus, in a system which encloses a liquid and its vapor, only the vaporization of the liquid or the condensation of the vapor in a system containing a solid and the liquid resulting from its fusion, only the fusion of the solid or the freezing of the liquid can be observed in a system containing carbonate of calcium, lime, and carbonic acid gas, one may observe only the combination of carbonic acid with lime or the dissociation of the carbonate of calcium. 

In any monovariant system two kinds of modification the opjxh site of each other may he imagined which change gradually the mass of each of the phases without altering the composition of any of them,... 

The equilibrium of a monovariant system is indifferent. —This proposition gives rise to a cons uence which should be noted. 

Let T be any temperature whatever in order that a monovariant system be in equilibrium at this temperature T, it is necessary and sufficient that the pressure have a definite value P, which is the transformation tension for this temperature, and that each of the phases into which the system is divided have a definite composition then it is easy to see that if the temperalure T and the pressure P are kept constant, the monovariant system is in indifferent equilibrium. 

At temperatures less than the temperature 6 of the triple point there may be observed in equilibrium only a single kind of monovariant system, that formed of solid and vapor in order for this equilibrium to take place it is necessary and sufficient that the representative point be on the branch F 3 of the curve of tensions of saturated vapor from the solid. 

At temperatures higher than the temperatmre 0 of the triple point two kinds of monovariant systems in equilibrium may be observed ... 

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