Gibbs stoichiometric rule

This relationship is called the Gibbs stoichiometric rule. 

The steps for constructing and interpreting an isothermal, isobaric thermodynamic model for a natural water system are quite simple in principle. The components to be incorporated are identified, and the phases to be included are specified. The components and phases selected "model the real system and must be consistent with pertinent thermodynamic restraints—e.g., the Gibbs phase rule and identification of the maximum number of unknown activities with the number of independent relationships which describe the system (equilibrium constant for each reaction, stoichiometric conditions, electroneutrality condition in the solution phase). With the phase-composition requirements identified, and with adequate thermodynamic data (free energies, equilibrium con-... 

A simple classification scheme of solids is given in Fig. 7.1. In order to differentiate between the types of solids, we have to consider the Gibbs phase rule, which is discussed in any physical chemistry textbook. The basic question is whether the solid substance consists of only one chemical entity (component) or more than one. Usually the component is one molecular unit, with only covalent bonded atoms. However, a component can also consist of more constituents if their concentration cannot be varied independently. An example of this is a salt. The hydrochloride salt of a base must be regarded as a one-component system as long as the acid and the base are present in a stoichiometric ratio. A deficiency of hydrochloric acid results in a mixture of the salt and the free base, which behave as two completely different substances (i.e. two different systems). Polymorphic forms, the glassy state, or the melt of the base (or the salt) are considered as different phases within such a system (a phase is defined as the portion of a system that itself is homogeneous in composition but physically distinguishable from other phases). When the base (or salt) is dissolved in a solvent, a new system is obtained this is also tme when a solvent is part of the crystal lattice, as in the case of a solvate. Thus, each solvate represents a different multicomponent system of a compound, whereas, polymorphic forms are different phases. The variables in the solvate are the kind of solvate (hydrate. 

There are two main methods for assigning in advance the dynamics of the chemical system composition, via the determination of a concentration of reacting substances in time and via the rates of the elementary and the final reaction. The first method leads to the number of independent composites and intermediate substances as a number of independent elements of the vectors trf and The second method leads to the number of independent elementary and final reactions as a number of the independent composites vectors v and R. Both methods allow the assignment in advance of the dynamics of the chemical system composition, only at known starting composition. The characteristic numbers determined in this way can be called the dynamic ones. As shown, they do not coincide with the numbers of the stoichiometric independent composites and intermediate substances, and elementary and final reactions. In the equilibrium system (at t (4) the dynamic characteristic numbers are equal to zero its decomposition at the well-known start is determined by the external parameters. So, the dynamic characteristic numbers of the equilibrium system do not coincide with the characteristic numbers determined in accordance with the Gibbs phase rule. This is connected with the fact that the Gibbs characteristic numbers of the equilibrium system determine its state (composition) in an unknown starting state (composition). 

In this chapter, we discuss classical non-stoichiometry derived from various kinds of point defects. To derive the phase rule, which is indispensable for the understanding of non-stoichiometry, the key points of thermodynamics are reviewed, and then the relationship between the phase rule, Gibbs free energy, and non-stoichiometry is discussed. The concentrations of point defects in thermal equilibrium for many types of defect structure are calculated by simple statistical thermodynamics. In Section 1.4 examples of non-stoichiometric compounds are shown referred to published papers. 

Both stoichiometric and correlative bonds decrease the number of parameters of a chemical system needed and sufficient for the description of dynamics of a system s composition during its transition from the initial indignant state to the final equilibrium state. However, in order to understand their physical sense, let us consider briefly the characteristic numbers of the equilibrium chemical system. A minimal number of parameters, the assigning of which completely and synonymously determines the state of thermodynamical system, represents its fundamental characteristic, that is the number of degrees of freedom. In accordance with the phase Gibbs rule c = k + 2-f (here k is the number of independent substances or system components, / is the number of phases, n is the number ol external parameters influencing the equilibrium state of system). Usually, these are pressure and the temperature and that is why most often the phase Gibbs rule is denoted in the form c = k + 2-/[9, 101. 

The first important contribution to atomic stoichiometry in this century seems to be provided by Brinkley (1946). He has shown the importance of the rank of the atomic matrix and presented a proof of the phase rule of Gibbs (1876). A systematic outline of stoichiometry was presented by Petho (sometimes Petheo) and Schay (Petheo Schay, 1954 Schay, Petho, 1962). They gave a necessary and sufficient condition for the possibility of calculating an unknown reaction heat from known ones based upon the rank of the stoichiometric matrix. They introduced the notion of independence of components and of elementary reactions, the completeness of a complex chemical reaction (see the Exercises and Problems) and gave a method to generate a complete set of independent elementary reactions with as many zeros in the stoichiometric matrix as possible (see Petho, 1964). 

In the general case of size-composition-dependent surface energy contribution for equilibrium two-phase state, one must solve the above given system of equations with complementary parameters and terms da/dr and da/dC. Furthermore, the rule may be applied to a multicomponent system as well when a new phase is not determined by strong stoichiometric composition that is, there exists the solubility interval on the diagram Gibbs free energy density-concentration (Ag(Q — C). As was mentioned before in the presented case. Equation 13.A.4 is applied to nucleation and separation of nanoparticles in which the composition of the new phase is a function of size. 

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