Solids equilibrium constant

Kn = vapor-solid equilibrium constant for hydrocarbon component n... 

The vapor-solid equilibrium constant is determined experimentally and is defined as the ratio of the mol fraction of the hydrocarbon component in gas on a water-free basis to the mol fraction of the hydrocarbon component in the solid on a water-free basis. That is ... 

Graphs giving the vapor-solid equilibrium constants at various temperatures and pressures are given in Figures 4-1 through 4-4. For nitrogen and components heavier than butane, the equilibrium constant is taken as infinity. 

Figure 4-1. Vapor-solid equilibrium constant for (a) methane, (b) ethane, and n-butane. (From Gas Processors Suppliers Association, Engineering Data Book.)...

The usual situation, true for the first three cases, is that in which the reactant and product solids are mutually insoluble. Langmuir [146] pointed out that such reactions undoubtedly occur at the linear interface between the two solid phases. The rate of reaction will thus be small when either solid phase is practically absent. Moreover, since both forward and reverse rates will depend on the amount of this common solid-solid interface, its extent cancels out at equilibrium, in harmony with the thermodynamic conclusion that for the reactions such as Eqs. VII-24 to VII-27 the equilibrium constant is given simply by the gas pressure and does not involve the amounts of the two solid phases. 

Figure 2.6. Hammett plots for the equilibrium constant of binding of 2.4 to Co, NL, Cu and (open symbols), and for the rate constants of reaction of the metal-ion - 2.4 complex with 2.5 (solid symbols).

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... 

The equilibrium constant for a reaction in which a solid dissociates into its ions... 

Equilibrium constants for complexation reactions involving solids are defined by combining appropriate Ksp and K expressions. Eor example, the solubility of AgCl increases in the presence of excess chloride as the result of the following complexation reaction... 

From a general point of view, the tautomeric studies can be divided into 12 areas (Figure 20) depending on the migrating entity (proton or other groups, alkyl, acyl, metals. ..), the physical state of the study (solid, solution or gas phase) and the thermodynamic (equilibrium constants) or the kinetic (isomerization rates) approach. 

Together with pyridones, the tautomerism of pyrazolones has been studied most intensely and serves as a model for other work on tautomerism (76AHC(Sl)l). 1-Substituted pyrazolin-5-ones (78) can exist in three tautomeric forms, classically known as CH (78a), (DH (78b) and NH (78c). In the vapour phase the CH tautomer predominates and in the solid state there is a strongly H-bonded mixture of OH and HN tautomers (Section 4.04.1.3.1). However, most studies of the tautomerism of pyrazolones correspond to the determination of equilibrium constants in solution (see Figure 20). 

When one of the elements is solid, as in tire case of carbon in the calculation of the partial pressures of tire gaseous species in the reaction between methane and air, CO(g) can be used as a basic element together widr hydrogen and oxygen molecules, and thus the calculation of the final partial pressure of methane must be evaluated using the equilibrium constant for CH4 formation... 

The simplest mode of IGC is the infinite dilution mode , effected when the adsorbing species is present at very low concentration in a non-adsorbing carrier gas. Under such conditions, the adsorption may be assumed to be sub-monolayer, and if one assumes in addition that the surface is energetically homogeneous with respect to the adsorption (often an acceptable assumption for dispersion-force-only adsorbates), the isotherm will be linear (Henry s Law), i.e. the amount adsorbed will be linearly dependent on the partial saturation of the gas. The proportionality factor is the adsorption equilibrium constant, which is the ratio of the volume of gas adsorbed per unit area of solid to its relative saturation in the carrier. The quantity measured experimentally is the relative retention volume, Vn, for a gas sample injected into the column. It is the volume of carrier gas required to completely elute the sample, relative to the amount required to elute a non-adsorbing probe, i.e. 

If the composition of the stream is known, the hydrate temperature can be predicted using vapor-solid (hydrate) equilibrium constants. The basic equation for this prediction is ... 

At a given temperature, the pressure of iodine vapor is constant, independent of the amount of solid iodine or any other factor. The equilibrium constant expression is... 

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 equilibrium constant expression for the dissolving of SrCr04 can be written following the rules in Chapters 12 and 13. In particular, the solid does not appear in the expression the concentration of each ion is raised to a power equal to its coefficient in the chemical equation. 

This is because the concentrations of solid copper and solid silver are incorporated into the equilibrium constant. The concentration of solid copper is fixed by the density of the metal—it cannot be altered either by the chemist or by the progress of the reaction. The same is true of the concentration of solid silver. Since neither of these concentrations varies, no matter how much solid is added, there is no need to write them each time an equilibrium calculation is made. Equation (21) will suffice. 

In summary, the concentrations of solids and the concentrations of solvent (usually water) can be and usually are incorporated in the equilibrium constant, so they do not appear in the equilibrium law relation. 

It can be shown from a consideration of the overall stability constants of the ions [Ni( CN)4] 2 " (1027) and [ Ag( CN)2 ] (1021) that the equilibrium constant for the above ionic reaction is 1015, i.e. the reaction proceeds practically completely to the right. An interesting exercise is the analysis of a solid silver halide, e.g. silver chloride. 

We see that in determining the equilibrium the concentrations of the solids do not appear at all. This important result was first stated by Guldberg and Waage in 1867 in the form that the active mass of a solid is constant. It is true only when the solids are of unvarying composition. 

Salts of diazonium ions with certain arenesulfonate ions also have a relatively high stability in the solid state. They are also used for inhibiting the decomposition of diazonium ions in solution. The most recent experimental data (Roller and Zollinger, 1970 Kampar et al., 1977) point to the formation of molecular complexes of the diazonium ions with the arenesulfonates rather than to diazosulfonates (ArN2 —0S02Ar ) as previously thought. For a diazonium ion in acetic acid/water (4 1) solutions of naphthalene derivatives, the complex equilibrium constants are found to increase in the order naphthalene < 1-methylnaphthalene < naphthalene-1-sulfonic acid < 1-naphthylmethanesulfonic acid. The sequence reflects the combined effects of the electron donor properties of these compounds and the Coulomb attraction between the diazonium cation and the sulfonate anions (where present). Arenediazonium salt solutions are also stabilized by crown ethers (see Sec. 11.2). 

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),... 

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

Up to this point, we have focused on aqueous equilibria involving proton transfer. Now we apply the same principles to the equilibrium that exists between a solid salt and its dissolved ions in a saturated solution. We can use the equilibrium constant for the dissolution of a substance to predict the solubility of a salt and to control precipitate formation. These methods are used in the laboratory to separate and analyze mixtures of salts. They also have important practical applications in municipal wastewater treatment, the extraction of minerals from seawater, the formation and loss of bones and teeth, and the global carbon cycle. 

The equilibrium constant for the solubility equilibrium between an ionic solid and its dissolved ions is called the solubility product, Ksp, of the solute. For example, the solubility product for bismuth sulfide, Bi2S3, is defined as... 

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... 

STRATEGY First, we write the chemical equation for the equilibrium between the solid solute and the complex in solution as the sum of the equations for the solubility and complex formation equilibria. The equilibrium constant for the overall equilibrium is therefore the product of the equilibrium constants for the two processes. Then, we set up an equilibrium table and solve for the equilibrium concentrations of ions in solution. 

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