Equilibrium pure solids

In the phase equilibrium between a pure solid (or a liquid) and its vapour, the addition of other gases, as long as they are insoluble in the solid or liquid, has negligible effect on the partial pressure of the vapour. 

Effect of impurities upon the melting point. Let us take a specific example and examine the effect of the addition of a small quantity of naphthalene to an equilibrium mixture of pure solid and liquid a-naphthol at the temperature of the true melting point (95 5°) at atmospheric pressure. 

Even though water is a reactant (a Brpnsted base) its concentration does not appear m the expression for because it is the solvent The convention for equilibrium constant expressions is to omit concentration terms for pure solids liquids and solvents... 

Fig. 1. The pressure-temperature-composition surfaces for the equilibrium between two pure solid phases, a liquid phase, and a vapor phase.

The equilibrium between a pure solid and a gaseous mixture is one of very few classes of solution for which an exact treatment can be made by the methods of statistical mechanics. The earliest work on the theory of such solutions was based on empirical equations, such as those of van der Waals,45 of Keyes,44 and of Beattie and Bridgemann.3 However, the only equation of state of a gas mixture that can be derived rigorously is the virial expansion,46 66... 

According as we put dT, dp, or ds equal to zero, we have the equations representing the alteration of pressure required to keep a solution of altered concentration in equilibrium with ice at the same temperature, or the alteration of freezing-point with concentration, or the alteration of freezing-point of a given solution with pressure, respectively. Similar equations apply when the solid is the pure solid solute, e.g., a salt along with its saturated solution. 

E4.2 Solid phases a and j3 are in equilibrium for a pure solid substance at 12 K. Below 12 K, the heat capacities of a and 3 vary with temperature according to the equations... 

For a pure substance, having three phases in equilibrium results in a triple point that is invariant. When pure solid, liquid, and gaseous water are in equilibrium, the temperature is fixed at a value of 273.16 K, and the pressure of the gas is fixed at the vapor pressure value (0.6105 kPa). 

We now have the foundation for applying thermodynamics to chemical processes. We have defined the potential that moves mass in a chemical process and have developed the criteria for spontaneity and for equilibrium in terms of this chemical potential. We have defined fugacity and activity in terms of the chemical potential and have derived the equations for determining the effect of pressure and temperature on the fugacity and activity. Finally, we have introduced the concept of a standard state, have described the usual choices of standard states for pure substances (solids, liquids, or gases) and for components in solution, and have seen how these choices of standard states reduce the activity to pressure in gaseous systems in the limits of low pressure, to concentration (mole fraction or molality) in solutions in the limit of low concentration of solute, and to a value near unity for pure solids or pure liquids at pressures near ambient. 

In a two-phase region, the composition oC the two phases in equilibrium are given by the end points of tie-lines. Thus, under curve ac. the phases are pure solid benzene ( v — 0) and a liquid with composition given by line ac. 

The equilibrium constants for heterogeneous reactions are also given by the general expression in Eq. 2 all we have to remember is that the activity of a pure solid or liquid is 1. For instance, for the calcium hydroxide equilibrium (reaction H),... 

The pure solid nickel must be present for the equilibrium to exist, but it does not appear in the expression for the equilibrium constant. 

Solid Bi2S3 does not appear in the expression for K,p, because it is a pure solid and its activity is 1 (Section 9.2). A solubility product is used in the same way as any other equilibrium constant. However, because ion-ion interactions in even dilute electrolyte solutions can complicate its interpretation, a solubility product is generally meaningful only for sparingly soluble salts. Another complication that arises when dealing with nearly insoluble compounds is that dissociation of the ions is rarely complete, and a saturated solution of Pbl2, for instance, contains substantial... 

Solubility equilibria are described quantitatively by the equilibrium constant for solid dissolution, Ksp (the solubility product). Formally, this equilibrium constant should be written as the activity of the products divided by that of the reactants, including the solid. However, since the activity of any pure solid is defined as 1.0, the solid is commonly left out of the equilibrium constant expression. The activity of the solid is important in natural systems where the solids are frequently not pure, but are mixtures. In such a case, the activity of a solid component that forms part of an "ideal" solid solution is defined as its mole fraction in the solid phase. Empirically, it appears that most solid solutions are far from ideal, with the dilute component having an activity considerably greater than its mole fraction. Nevertheless, the point remains that not all solid components found in an aquatic system have unit activity, and thus their solubility will be less than that defined by the solubility constant in its conventional form. 

Chemical equilibria often involve pure liquids and solids in addition to gases and solutes. The concentration of a pure liquid or solid does not vary significantly. Figure 16-4 shows that although the amount of a solid or liquid can vary, the number of moles per unit volume remains fixed. In other words, the concentrations of pure liquids or solids are always equal to their standard concentrations. Thus, division by standard concentration results in a value of 1 for any pure liquid or solid. This allows us to omit pure liquids and solids from equilibrium constant expressions. For a general reaction (2A + iBt= C D-l-. S where S is a pure solid or liquid ... 

The stoichiometry of the reaction determines the form of the equilibrium constant expression. Pure solids, liquids, or solvents do not appear in the expression, since their concentrations are constant. 

In this reaction, Fe is a pure solid and H2 O is the solvent, so they do not appear in the equilibrium expression. The other reagents have exponents equal to their stoichiometric coefficients ... 

Pure Solid in Contact with a Single- or Multi-Component Environment Considering the example of a Pt surface in contact and in thermodynamic equilibrium with an oxygen atmosphere, the surface free energy (5.5) becomes... 

BaS04 and BaC03 are pure solids and their active masses may be taken as constant and included in the equilibrium constant, K, which now simplifies to ... 

It thus follows that in the general equation, A + B C + D, if, for example, B and D are pure solids, the equilibrium constant can be expressed as ... 

The equilibrium constants are based on a standard state of unit fugacity for the gaseous species and on a standard state corresponding to the pure solid for carbon. 

We omit concentrations of pure solids and pure liquids from equilibrium constant expressions because their activity is taken to be 1 and the thermodynamic equilibrium constant involves activities, rather than concentrations. 

In the strict thermodynamic definition of the equilibrium constant, the activity of a component is used, not its concentration. The activity of a species in an ideal mixture is the ratio of its concentration or partial pressure to a standard concentration (1 M) or pressure (1 atm). The concentrations of pure solids and pure liquids are omitted from the equilibrium constant expression because their activity is taken to be 1. 

First we write the balanced chemical equation for the reaction. Then we write the equilibrium constant expressions, remembering that gases and solutes in aqueous solution appear in the Kc expression, but pure liquids and pure solids do not. 

CaO(s) is a pure solid, its concentration does not appear in the equilibrium constant expression and thus its addition will have no direct effect on the position of equilibrium. 

Pressures of gases and molarities of solutes in aqueous solution appear in thermodynamic equilibrium constant expressions. Pure solids and liquids (including solvents) do not appear. 

In writing the thermodynamic equilibrium constant, recall that neither pure solids (PbS(s) and S(s)) nor pure liquids (H20(1)) appear in the thermodynamic equilibrium constant expression. Note also that we have written H+(aq) here for brevity even though we understand that H30+(aq) is the acidic species in aqueous solution. 

The concentrations of pure solids and liquids do not appear in the equilibrium constant expression. 

Sol id Sol utions. The aqueous concentrations of trace elements in natural waters are frequently much lower than would be expected on the basis of equilibrium solubility calculations or of supply to the water from various sources. It is often assumed that adsorption of the element on mineral surfaces is the cause for the depleted aqueous concentration of the trace element (97). However, Sposito (Chapter 11) shows that the methods commonly used to distinguish between solubility or adsorption controls are conceptually flawed. One of the important problems illustrated in Chapter 11 is the evaluation of the state of saturation of natural waters with respect to solid phases. Generally, the conclusion that a trace element is undersaturated is based on a comparison of ion activity products with known pure solid phases that contain the trace element. If a solid phase is pure, then its activity is equal to one by thermodynamic convention. However, when a trace cation is coprecipitated with another cation, the activity of the solid phase end member containing the trace cation in the coprecipitate wil 1 be less than one. If the aqueous phase is at equil ibrium with the coprecipitate, then the ion activity product wi 1 1 be 1 ess than the sol ubi 1 ity constant of the pure sol id phase containing the trace element. This condition could then lead to the conclusion that a natural water was undersaturated with respect to the pure solid phase and that the aqueous concentration of the trace cation was controlled by adsorption on mineral surfaces. While this might be true, Sposito points out that the ion activity product comparison with the solubility product does not provide any conclusive evidence as to whether an adsorption or coprecipitation process controls the aqueous concentration. 

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