Equilibrium pure liquids

These expressions are identical to those for the equilibrium constant given in Section 8.1.2, except that they apply to any concentrations or partial pressures, not just those when the system is at equilibrium. Pure liquids or solids, or water in solutions, appearing in the reaction equation do not appear in the equations for Q. (The quantity of importance is the activity rather than the concentration. Activity and concentration are equal in dilute solutions see Section S3.2). 

Let us now consider the process of capillary condensation. For the pure liquid (a) in equilibrium with its vapour fi), the condition for mechanical equilibrium is given by Equation (3.6) and that for physicochemical equilibrium by... 

Lj and are the pure liquid and inert gas loading rates, respectively, in units of Ib-moles/hr-ft. The second expression is the operating line on an equilibrium diagram. In all scrubbing application, where the transfer of solute is from the gas to the liquid, the operating line will lie above the equilibrium curve. When the mass transfer is from the liquid to the gas phase, the operating line will lie below the equilibrium curve. The latter case is known as stripping . 

Despite these reaction products there is little evidence for an ionic self-dissociation equilibrium in liquid CIF3 such as may be formally represented by 2CIF3 V— CIF2 + C1F4, and the electrical conductivity of the pure liquid (p. 828) is only of the order of 10 ohm cm. The structures of these ions are discussed more fully in subsequent sections. 

In addition to its use as a straight fluorinating agent, BrF3 has been extensively investigated and exploited as a preparative nonaqueous ionizing solvent. The appreciable electrical conductivity of the pure liquid (p. 828) can be interpreted in terms of the dissociative equilibrium... 

The chemical reactions of IF5 have been more extensively and systematically studied because the compound can be handled in glass apparatus and is much less vigorous a reagent than the other pentafluorides. The (very low) electrical conductivity of the pure liquid has been ascribed to slight ionic dissociation according to the equilibrium... 

The vapor pressure (P ) of a pure liquid at a given temperature (T) is the pressure exerted by its vapor in equilibrium with the liquid phase in a closed system. All liquids and solids exhibit unique vapor pressure-temperature curves. For instance, in Figure 2-79, lines BA and AC represent the equilibrium vapor pressure curves of the solid and liquid phases, respectively. 

In the reactions described so far, all the reactants and products have been gaseous the equilibrium systems are homogeneous. In certain reactions, at least one of the substances involved is a pure liquid or solid the others are gases. Such a system is heterogeneous, because more than one phase is present. Examples include... 

Strategy First write the chemical equation for the equilibrium system. Then write the expression for K, leaving out pure liquids and solids. Remember that gases are represented by their partial pressures. 

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—... 

We should emphasize that adding a pure liquid or solid has no effect on a system at equilibrium. The rule is a simple one For a species to shift the position of an equilibrium, it must appear in the expression for K. 

Let a given liquid solution (e.g.f a solution of sugar in water) be separated from the pure liquid solvent by a fixed rigid diaphragm, permeable only to the latter. If -n, tt are the pressures which must be applied to solvent and solution, respectively, to maintain equilibrium, then ... 

Example 5.3 Predict the degrees of freedom for (a) pure liquid water and solid ice in equilibrium (b) pure liquid water, solid ice, and water vapor in equilibrium, and (c) solid ice in equilibrium with a liquid mixture of (ethanol + water). 

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. 

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... 

If two immiscible liquids A and B (i.e., possessing very different 8 values) form two layers when brought together, and an elastomer of similar 6 to A is completely immersed in the (denser) B layer (schematically in Eigure 23.5), nevertheless, the elastomer will evenmaUy swell as if immersed completely in A. This arises because each liquid of an immiscible mixture stiU dissolves a minute amount of the other. At equilibrium, the chemical potential p of A will be the same, whether as pure liquid, dissolved in B, or dissolved in the elastomer. At the same temperature, the same p would apply for the elastomer immersed directly in A. However, the kinetics of absorption will be different, being much slower than... 

Molecular views of the rates of solid-liquid phase transfer of a pure liquid and a solution at the normal freezing point. The addition of solute does not change the rate of escape from the solid, but it decreases the rate at which the solid captures solvent molecules from the solution. This disrupts the dynamic equilibrium between escape and capture. 

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 ... 

Vapor pressure provides a simple illustration of why adding a pure liquid or solid does not change equilibrium concentrations. Recall from Chapter H that any liquid establishes a dynamic equilibrium with its vapor, and the partial pressure of the vapor at equilibrium is the vapor pressure. The vapor pressure is independent of the amount of liquid present. Figure 16-8 illustrates that the vapor pressure of water above a small puddle is the same as the vapor pressure above a large pond at the same temperature. More molecules escape from the larger surface of the pond, but more molecules are captured, too. The balance between captures and escapes is the same for both puddle and pond. 

The temperature at which this condition is satisfied may be referred to as the melting point Tm, which will depend, of course, on the composition of the liquid phase. If a diluent is present in the liquid phase, Tm may be regarded alternatively as the temperature at which the specified composition is that of a saturated solution. If the liquid polymer is pure, /Xn —mS where mS represents the chemical potential in the standard state, which, in accordance with custom in the treatment of solutions, we take to be the pure liquid at the same temperature and pressure. At the melting point T of the pure polymer, therefore, /x2 = /xt- To the extent that the polymer contains impurities (e.g., solvents, or copolymerized units), ixu will be less than juJ. Hence fXu after the addition of a diluent to the polymer at the temperature T will be less than and in order to re-establish the condition of equilibrium = a lower temperature Tm is required. 

All in aqueous solution at 25°C standard states are 1 M ideal solution with an infinitely dilute reference state, and the pure liquid for water equilibrium constants from reference 100, except as noted. 

Similar relationships can be written for the dissolution of hydrogen and oxygen. These relationships are expressions of Sievert s law which can be stated thus the solubility of a diatomic gas in a liquid metal is proportional to the square root of its partial pressure in the gas in equilibrium with the metal. The Sievert s law behaviour of nitrogen in niobium is illustrated in Figure 3.8. The law predicts that the amount of a gas dissolved in a metal can be reduced merely by reducing the partial pressure of that gas, as for example, by evacuation. In practice, however, degassing is not as simple as this. Usually, Sievert s law is obeyed in pure liquid metals only when the solute gas is present in very low concentrations. At higher concentrations deviations from the law occur. 

Water is considered like any other pure liquid its concentration does not alter significantly in dilute solutions, so it does not figure in the equilibrium expression ... 

Henry s law constants for most of the compounds of interest can be found in the literature.54 Figure 18.11 shows Henry s law constants for TCE, EDC and several gasoline compounds.19 These data are derived from water solubility data and the equilibrium vapor pressure of pure liquids at certain temperatures, and may be extrapolated correctly to field design work. Temperature has a major effect on Henry s constant and on stripper performance. Each rise of 10°C in temperature... 

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. 

This illustrates the statement made earlier that the most convenient choice of standard state may depend on the problem. For gas-phase problems involving A, it is convenient to choose the standard state for A as an ideal gas at 1 atm pressure. But, where the vapor of A is in equilibrium with a solution, it is sometimes convenient to choose the standard state as the pure liquid. Since /a is the same for the pure liquid and the vapor in equilibrium... 

Since these two chemical potentials must be equal (given the equilibrium between the pure liquid and the saturated solution), it must be the case that... 

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. 

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. 

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