Equilibrium constant solid-liquid

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... 

In this and succeeding chapters, a wide variety of different types of equilibria will be covered. They may involve gases, pure liquids or solids, and species in aqueous solution. It will always be true that in the expression for the equilibrium constant—... 

The system H2S-CH4-H20 is an example of a ternary system forming a continuous range of mixed hydrates of Structure I. For this system Noaker and Katz22 studied the H2S/CH4 ratio of the gas in equilibrium with aqueous liquid and hydrate. From the variation of this ratio with total pressure at constant temperature it follows that complete miscibility must occur in the solid phase. 

At fairly high nitrous acid concentrations (0.1 m) and at moderate acidities (4 m) the blue color of N203 (Amax = 625 nm) is easily detected by eye. The overall equilibrium of Scheme 3-10 has been determined. A relatively recent determination of the equilibrium constant gave the value K = 3.0 x 10"3 m (Markovits et al., 1981). Accurate determinations of this constant are difficult, as N203 decomposes easily into NO and N02. Pure N203 is stable only as a pale blue solid or as an intensely blue liquid just above its freezing point (-100°C). The liquid starts to boil with decomposition above -40°C. 

We use a different measure of concentration when writing expressions for the equilibrium constants of reactions that involve species other than gases. Thus, for a species J that forms an ideal solution in a liquid solvent, the partial pressure in the expression for K is replaced by the molarity fjl relative to the standard molarity c° = 1 mol-L 1. Although K should be written in terms of the dimensionless ratio UJ/c°, it is common practice to write K in terms of [J] alone and to interpret each [JJ as the molarity with the units struck out. It has been found empirically, and is justified by thermodynamics, that pure liquids or solids should not appear in K. So, even though CaC03(s) and CaO(s) occur in the equilibrium... 

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),... 

In general, liquids have lower entropies than gases, since the molecules of gas have much more freedom and randomness. Solids, of course, have still lower entropies. Any reaction in which the reactants are all liquids and one or more of the products is a gas is therefore thermodynamically favored by the increased entropy the equilibrium constant for that reaction will be higher than it would otherwise be. Similarly, the entropy of a gaseous substance is higher than that of the same substance dissolved in a solvent. 

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. 

For a heterogeneous reaction, the state of all components is not uniform, for example, a reaction between a gas and a liquid. This requires standard states to be defined for each component. The activity of a solid in the equilibrium constant can be taken to be unity. 

The melting point of carbon dioxide increases with increasing pressure, since the solid-liquid equilibrium line on its phase diagram slopes up and to the right. If the pressure on a sample of liquid carbon dioxide is increased at constant temperature, causing the molecules to get closer together, the liquid will solidify. This indicates that solid carbon dioxide has a higher density than the liquid phase. This is true for most substances. The notable exception is water. 

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. 

We remember that neither solids, such as Ca5(P04)30H(s), nor liquids, such as H20(1), appear in the equilibrium constant expression. Concentrations of products appear in the... 

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. 

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. 

There are two themes in this work (1) that all soil is complex and (2) that all soil contains water. The complexity of soil cannot be overemphasized. It contains inorganic and organic atoms, ions, and molecules in the solid, liquid, and gaseous phases. All these phases are both in quasi equilibrium with each other and are constantly changing. This means that the analysis of soil is subject to complex interferences that are not commonly encountered in standard analytical problems. The overlap of emission or absorption bands in spectroscopic analysis is but one example of the types of interferences likely to be encountered. 

The initial concentration distribution is therefore simply translated at the velocity of the liquid steady flow and full equilibrium between the liquid and its matrix require that the amount of element transported by the concentration wave is constant. In more realistic cases, either the flow is non-steady due to abrupt changes in fluid advection rate or porosity, or solid-liquid equilibrium is not achieved. These cases may lead to non-linear terms in the chromatographic equation (9.4.35) and unstable behavior. The rather complicated theory of these processes is beyond the scope of the present book. 

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

The reactant quotient can be written at any point during the reaction, but the most useful point is when the reaction has reached equilibrium. At equilibrium, the reaction quotient becomes the equilibrium constant, IQ (or Kp if gas pressures are being used). Usually this equilibrium constant is expressed simply as a number without units, since it is a ratio of concentrations or pressures. In addition, the concentrations of solids or pure liquids (not in solution) that appear in the equilibrium expression are assumed to be 1, since their concentrations do not change. 

Transesterification is the main reaction of PET polycondensation in both the melt phase and the solid state. It is the dominant reaction in the second and subsequent stages of PET production, but also occurs to a significant extent during esterification. As mentioned above, polycondensation is an equilibrium reaction and the reverse reaction is glycolysis. The temperature-dependent equilibrium constant of transesterification has already been discussed in Section 2.1. The polycondensation process in the melt phase involves a gas phase and a homogeneous liquid phase, while the SSP process involves a gas phase and two solid phases. The respective phase equilibria, which have to be considered for process modelling, will be discussed below in Section 3.1. 

Very few generalized computer-based techniques for calculating chemical equilibria in electrolyte systems have been reported. Crerar (47) describes a method for calculating multicomponent equilibria based on equilibrium constants and activity coefficients estimated from the Debye Huckel equation. It is not clear, however, if this technique has beep applied in general to the solubility of minerals and solids. A second generalized approach has been developed by OIL Systems, Inc. (48). It also operates on specified equilibrium constants and incorporates activity coefficient corrections for ions, non-electrolytes and water. This technique has been applied to a variety of electrolyte equilibrium problems including vapor-liquid equilibria and solubility of solids. 

As a technique for selective surface illumination at liquid/solid interfaces, TIRF was first introduced by Hirschfeld(1) in 1965. Other important early applications were pioneered by Harrick and Loeb(2) in 1973 for detecting fluorescence from a surface coated with dansyl-labeled bovine serum allbumin, by Kronick and Little(3) in 1975 for measuring the equilibrium constant between soluble fluorescent-labeled antibodies and surface-immobilized antigens, and by Watkins and Robertson(4) in 1977 for measuring kinetics of protein adsorption following a concentration jump. Previous rcvicws(5 7) contain additional references to some important early work. Section 7.5 presents a literature review of recent work. 

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