Heterogeneous equilibria involving

In Part III heterogeneous equilibria involving clathrates are discussed from the experimental point of view. In particular a method is presented for the reversible investigation of the equilibrium between clathrate and gas, circumventing the hysteresis effects. The phase diagrams of a number of binary and ternary systems are considered in some detail, since controversial statements have appeared in the literature on this subject. 

When studying heterogeneous equilibria involving clathrates, one is faced with peculiar difficulties owing to the hysteresis effects mentioned in the introduction the solute in a clathrate crystal of hydroquinone, for instance, will not come to thermodynamic equilibrium with the vapor in which it is placed. Consequently it is impossible, or at least very difficult, to measure the equilibrium vapor pressure of the solute in a clathrate by placing some crystals in a tensometer (cf. the experiments of Wynne-Jones and Anderson,58 and those of Leech and Richards reported by Powell33). 

Usually, in plots such as those in figure 8.20, for the sake of simplicity, the boundaries between solutes and condensed phases are not drawn for the various molal concentrations in solution, as seen for cerium, but for a selected bulk molal amount, which in geochemistry is normally 10 . This choice is dictated by the fact that, at this bulk molal concentration, the solid phase can be considered effectively inert from the point of view of reactivity (cf Garrels and Christ, 1965). In the various heterogeneous equilibria involving aqueous solutions and condensed or gaseous phases, it is nevertheless opportune always to specify the molal concentrations to which the various boundaries refer. 

Heterogeneous Equilibria Involving Oxides, Hydroxides, Carbonates, and Hydroxide Carbonates... 

Schindler, P. W. (1967) Heterogeneous Equilibria Involving Oxides, Hydroxides, Carbonates and Hydroxide Carbonates. In Equilibrium Concepts in Natural Water Systems, Adv. Chem. Ser., No. 67, American Chemical Society, Washington DC, p. 196. 

Thus far, we have considered only equilibria involving species in a single phase, that is, homogeneous equilibria. Heterogeneous equilibria involve species in more than one phase. Consider the following reversible reaction at 2 5°C. 

ScHiNDi.KR, P. W. 1967, Heterogeneous equilibria involving oxides, hydroxides, carbonates, and hydroxide carbonates, In Equilibrium concepts in natural water sy.stems. Am. Chem. Soc. Adv. Chem. Ser. 67, pp. 196 221. Washington, DC Am. Chem. Soc. 

SCH] Schindler, P. W., Heterogeneous equilibria involving oxides, hydrox-... 

In the next section, we shall discuss the use of thermod)mamic functions in calculations of heterogeneous equilibria involving lanthanide trichlorides. The results obtained will be analyzed to draw conclusions on the possibility of using the data described in this work for thermodynamic modeling purposes. 

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. 

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 ... 

You are given a heterogeneous equilibrium involving gases and solids. The general form of the equilibrium constant expression for this reaction is... 

An important type of heterogeneous equilibrium involves partitioning a solute species between two immiscible solvent phases. Such equilibria are used in many separation processes in chemical research and in industry. 

A heterogeneous phase equilibrium involving a gas phase represents a convenient way of determining the Gibbs energy of a substance. A substance may evaporate congruently ... 

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. 

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 ... 

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. 

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

J.W. Gibbs developed the thermodynamic methods for the characterisation of equilibrium states of heterogeneous systems involving any number of substances. Before deriving a thermodynamic method for the characterisation of equilibrium states of heterogeneous systems, we define two important terms i.e., phase and component. 

The mass action law assumes that the reaction medium is homogeneous. In heterogeneous reactions (involving different substances in multiple phases), the densities and effective concentrations of pure condensed phases (liquids or solids) are constant. The concentrations of such species are set to unity in the equilibrium constant expression for such reactions. For example, given the following decomposition,... 

Hess s law in going from a particular set of reactants to a particular set of products, the enthalpy change is the same whether the reaction takes place in one step or in a series of steps in summary, enthalpy is a state function. (9.5) Heterogeneous equilibrium an equilibrium involving reactants and/or products in more than one phase. (6.5) Hexagonal closest packed (hep) structure a structure composed of closest packed spheres with an ababab arrangement of layers the unit cell is hexagonal. (16.4)... 

Studies of reaction rates become more complicated when it is realized that most reactions are reversible, so that while the rate of the forward reaction decreases that of the reverse reaction increases with time, and at equilibrium the overall net rate is zero. Other common complications involve consecutive reactions such as R P Q, competing reactions Ri -I- R2 products and Rj - - R3 other products, and chain reactions such as described in Section 15-8. Heterogeneous reactions involve two or more phases and are difficult to formulate. 

A homogeneous reaction is one that involves only one phase. A heterogeneous reaction involves more than one phase, and reaction usually occurs at, or very near the interface between the phases. An irreversible reaction is one that proceeds in only one direction and continues in that direction until the reactants Types of reactions are exhausted. A reversible reaction, on the other hand, can proceed in either direction, depending on the concentrations of reactants and products relative to the corresponding equilibrium concentrations. An irreversible reaction behaves as if no equilibrium condition exists. StrictW speaking, no chemical reaction is completely irreversible, but in very many reactions the equilibrium point lies so far to the right that they are treated as irreversible reactions. 

Form of Q for a Reaction Involving Pure Liquids and Solids Until now, we ve looked at homogeneous equilibria, systems in which all the components of the reaction are in the same phase, such as a system of reacting gases. When the components are in different phases, the system reaches heterogeneous equilibrium. 

This system consists of a solid in equilibrium with two aqueous species. If we want to write the equilibrium-constant expression for this process, we encounter a problem we have not encountered previously How do we express the concentration of a solid Although we can express that concentration in moles per unit volume, it is unnecessary to do so in writing equilibrium-constant expressions. Whenever a pure solid or a pure liquid is involved in a heterogeneous equilibrium, its concentration is not included in the equilibrium-constant expression. Thus, the equilibrium-constant expression for the reaction of Equation 15.18 is... 

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