Gibbs phase rule reduced

For three-component (C = 3) or ternary systems the Gibbs phase rule reads Ph + F = C + 2 = 5. In the simplest case the components of the system are three elements, but a ternary system may for example also have three oxides or fluorides as components. As a rule of thumb the number of independent components in a system can be determined by the number of elements in the system. If the oxidation state of all elements are equal in all phases, the number of components is reduced by 1. The Gibbs phase rule implies that five phases will coexist in invariant phase equilibria, four in univariant and three in divariant phase equilibria. With only a single phase present F = 4, and the equilibrium state of a ternary system can only be represented graphically by reducing the number of intensive variables. 

Multiphase phenomenon is more frequently encountered in multicomponent mixtures, such as reaction mixtures. From a thermodynamic perspective, multiphase phenomena exist because multiple phases reduce the Gibbs free energy of the system. More components mean more ways and phases in which to partition this energy. Due to the Gibbs phase rule, a third component extends multiphase equilibrium as seen in binary mixtures, such as LLV and SLV equihbrium, from a lirte to a region of pressure and concentration at a given temperature. 

Systems with reactions are discussed in 10.3.1. When no other internal constraints apply, then S = 0, and the general rule (9.1.13) reduces to the Gibbs phase rule,... 

Here S counts any additional internal constraints besides those for phase and reaction equilibria. When S = 0 (10.3.1) reduces to the traditional form of the Gibbs phase rule extended to reacting systems. 

Equation (1.81) is the generalized Gibbs phase rule. Note that Equation (1.81) reduces to Equation (1.72) for the special case of a unary system. 

The next step is to make clear the Gibbs adsorption amount, using the above relative adsorption. Recall (8.27), in which the interfacial tension is a function of i -H 2 independent variables. However, the Gibbs phase rule permits only i independent variables for two phases including i components. Therefore, the problem is how to reduce the number of intensive variables by two while keeping thermodynamical consistency. The Gibbs-Duhem equations for two homogeneous phases a and respectively, are... 

Turning now to adsorption equilibrium, let us apply algebraic methods to a two component 1,2 phase system. From the phase rule there will be two degrees of freedom, but we shall reduce this to one by maintaining the temperature constant. Then for the total system there exists a Gibbs-Duhem equation... 

When we have reduced the representing of a problem by an equation to be no more than an algebraic expression, the first point we have to examine is the following How many distinct quantities are there in the equations of the problem And the examination of this point is immediately followed by the study of this other point Among these distinct quantities, how many independent relations does algebra furnish In making this double enumeration for the problems of chemical mechanics, J. Willard Gibbs was led to the propositions whose ensemble constitutes the phase rule. 

Equations of a relation between the parameters of a system based on a phase Gibbs rule follows from the principle of detailed equilibrium in its different displays. Thus, for a multi-phase system the principle of a detailed equilibrium requires the equilibrium of any two phases with each other. This permits to separate them and to consider them separately from others. General conditions for an equilibrium in an isolated system are reduced to partial conditions of thermal (temperature of all phases is equal), mechanical (at plain... 

Due to this structure they tend to adsorb at the interfaces between a polar and a nonpolar fluid, for example water and oil. Emulsifiers reduce the surface tension and stabilize the surface by steric, electrostatic or hydrodynamic (Gibbs-Mar-angoni) effects [14], Droplet coalescence (flowing of one or more droplets together) can thus be reduced or prevented. Some emulsifiers can be characterized by their hydrophilic/lipophilic balance (HLB) value that provides information on the ratio of hydrophilic to lipophilic character of the surfactant molecule. The HLB value helps to determine the phase in which the emulsifier is soluble. Usually, the emulsifier used is soluble in the continuous phase (Bancroft rule). Furthermore, the HLB value gives a first hint whether the emulsifier is suitable for the production of an o/w (HLB value 8-18) or a w/o emulsion (HLB value 4—6) [15]. 

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