Equilibria heterogeneous

In this section, we present a discussion of the equilibrium criteria of an isolated heterogeneous system in which no chemical reactions occur. 

A heterogeneous system is one consisting of two or more phases. By definition, these are separated from each other by surfaces of discontinuity in one or more of the intensive properties. We will assume that the phases are originally isolated, with each of them in internal equilibrium, and thus that each phase is homogeneous. The problem is thereby reduced to finding conditions on the intensive properties which are necessary and sufficient to ensure equilibrium after the restraint of isolation is removed. The heterogeneous system considered here is an solated system in which no chemical reactions occur. 

We note that the arguments presented here can be applied to a one-phase system. In this case the conditions on the intensive properties within the phase necessary to ensure internal equilibrium can be derived. 

In this approximation, we have for a system of v bulk phases 

Equation (6-65) implies that we consider those variations in which the system may be assumed to be enclosed in a rigid container. Equation (6-66) is the condition for conservation of the /th material component. Operationally, then, Eqs. (6-64) to (6-66) imply that we consider an isolated system in which no chemical reactions may occur. 

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Although Gibbs published his monumental treatise on heterogeneous equilibrium in 187S, his work was not generally appreciated until the turn of the century, and it was not until many years later that the field of surface chemistry developed to the point that experimental applications of the Gibbs equation became important. 

The immobilization of reagents onto sorbents often results in increase of their sensitivity and, in some cases, selectivity, allows to simplify the analysis and to avoid necessity of use of toxic organic solvents. At the same time silicas are characterized by absence of swelling, thenual and chemical stability, rapid achievement of heterogeneous equilibrium. 

Among many other valuable results in his memoir on heterogeneous equilibrium is a formulation of the Gibbs free energy, also called the Gibbs function, which is defined by the equation... 

If a heterogeneous equilibrium is such that the pressure of the system depends on the temperature alone, and is unchanged when the phases alter in relative amount, it is called a completely heterogeneous equilibrium (Roozeboom), or an indifferent equilibrium (Duhem). 

The theorems of Moutier and Robin apply to evaporation, fusion, polymorphic change, or dissociation of systems in com pletely heterogeneous equilibrium. 

Hess s law A reaction enthalpy is the sum of the enthalpies of any sequence of reactions (at the same temperature and pressure) into which the overall reaction can be divided, heterogenous alloy See alloy. heterogeneous catalyst See catalyst. heterogeneous equilibrium An equilibrium in which at least one substance is in a different phase from the others. Example AgCI(s) Ag+(aq) + Cl "(aq). heterogeneous mixture A mixture in which the... 

Since initially [C02] = 0, the reverse reaction will predominate. Note that this is a heterogeneous equilibrium, so we can ignore the solid graphite. 

The purpose of this chapter is to outline the simplest methods of arriving at a description of the distribution of species in mixtures of liquids, gases and solids. Homogeneous equilibrium deals with single phase systems, such as electrolyte solutions (e.g., seawater) or gas mixtures (e.g., a volcanic gas). Heterogeneous equilibrium involves coexisting gaseous, liquid and solid phases. 

Ricci, J. E. The Phase Rule and Heterogeneous Equilibrium (van Nostrand, New York, 1951). 

The Sample Problems that follow all involve homogeneous equilibrium systems. Each problem illustrates a particular type of system and includes brief tips. Each problem also includes a table like the one on page 339 to organize the data. Because this table is used to record the initial, change, and equilibrium values of the reacting species, it is often called an ICE table. In Chapters 8 and 9, you will use ICE tables again to help you solve problems that involve heterogeneous equilibrium systems. 

As more ions enter the solution, the rate of the reverse change, recrystallisation, increases. Eventually, the rate of recrystallisation becomes equal to the rate of dissolving. As you know, when the forward rate and the backward rate of a process are equal, the system is at equilibrium. Because the reactants and the products are in different phases, the reaction is said to have reached heterogeneous equilibrium. For solubility systems of sparingly soluble ionic compounds, equilibrium exists between the solid ionic compound and its dissociated ions in solution. 

In heterogeneous equilibria, not all the species present are in the same state. An example of a heterogeneous equilibrium reaction is heating calcium carbonate in a closed system so that the carbon dioxide gas produced cannot escape and equilibrium is established. The equation for the reaction is ... 

Before examining in detail the present-day knowledge of the solubihties of various gaseous species in magmas, it is necessary to describe solubility in terms of reactivity of gaseous species with melt components. A simple heterogeneous equilibrium between gas and melt involves the inert gas Ar ... 

However, not all the CO2 is present in the melt in the form of carbonate ion molecular CO2 is also present, based on the heterogeneous equilibrium... 

CVT makes use of the temperature dependence of the above heterogeneous equilibrium to transport solid A through the vapour phase by means of gaseous intermedi-ate(s) C. That the process involves true transport and not just evaporation and condensation is evident from the fact that solid A does not possess an appreciable vapour pressure at the experimental temperature moreover, transport of A is not observed without the transporting agent B. 

In an equilibrium reaction, the states of reactants and products may be the same or different. If the states of reactants and products are the same, the equilibrium is called a homogeneous equilibrium. If they are different, then it is called a heterogeneous equilibrium. 

For a heterogeneous equilibrium, the effect of volume is predicted by counting the number of moles of gas indicated on each side of an equation. 

Heterogeneous equilibrium A type of equilibrium involving reactants and/or products in more than one phase. 

Equations (12.68) establish how any /+ 1 intensive vectors must be related to one another in the heterogeneous equilibrium of p phases. Let us now assume for definiteness that these are labeled... 

Heterogeneous equilibrium. C02 dissolves in water to give carbonic acid (which is mostly dissolved C02, as described in Box 6-4). 

The mass-action equations have been written in the same form as those given by Marynowski et al. (6) so that the equilibrium constants can be used directly. (Should more accurate data become available, the equilibrium yields calculated here will require revision.) The fourth equation, which applies to the heterogeneous equilibrium between carbon and nitrogen, is included for completeness but is unnecessary for the general solution. It can be shown that when the total pressure of the system is F, the partial pressure of cyanogen radicals is given by the equation ... 

The equilibrium interfaces of fluid systems possess one variant chemical potential less than isolated bulk phases with the same number of components. This is due to the additional condition of heterogeneous equilibrium and follows from Gibbs phase rule. As a result, the equilibrium interface of a binary system is invariant at any given P and T, whereas the interface between the phases a and /3 of a ternary system is (mono-) variant. However, we will see later that for multiphase crystals with coherent boundaries, the situation is more complicated. 

To distinguish from solubility equilibria, this heterogeneous equilibrium is listed with the homogeneous equilibria. 

Heterogeneous equilibrium involves reactants and products in dilTcrent phases. For example, when calcium carbonate is heated in a closed vessel, the following equilibrium reaction occurs ... 

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