Pressure equilibrium expressions

Some chemical reactions are reversible and, no matter how fast a reaction takes place, it cannot proceed beyond the point of chemical equilibrium in the reaction mixture at the specified temperature and pressure. Thus, for any given conditions, the principle of chemical equilibrium expressed as the equilibrium constant, K, determines how far the reaction can proceed if adequate time is allowed for equilibrium to be attained. Alternatively, the principle of chemical kinetics determines at what rate the reaction will proceed towards attaining the maximum. If the equilibrium constant K is very large, for all practical purposes the reaction is irreversible. In the case where a reaction is irreversible, it is unnecessary to calculate the equilibrium constant and check the position of equilibrium when high conversions are needed. 

This equilibrium constant is often given the symbol Kp to emphasize that it involves partial pressures. Other equilibrium expressions for gases are sometimes used, including Kc ... 

The liquid line and vapor line together constitute a binary (vapor + liquid) phase diagram, in which the equilibrium (vapor) pressure is expressed as a function of mole fraction at constant temperature. At pressures less than the vapor (lower) curve, the mixture is all vapor. Two degrees of freedom are present in that region so that p and y2 can be varied independently. At pressures above the liquid (upper) curve, the mixture is all liquid. Again, two degrees of freedom are present so that p and. v can be varied independently/... 

After the solid sample has been weighed and degassed, a known amount of the adsorbate is admitted to the vessel containing the evacuated sample. When equilibrium has been reached, the amount of gas adsorbed can be calculated from the pressure change. Thus, a correlation between the equilibrium pressure, p, and the amount of gas adsorbed, Wad, can be established. Usually, the pressure is expressed as the relative pressure, where p represents the saturation pressure of the adsorbate at the temperature of measurement. 

Substituting for number density in terms of pressure and expressing mean speed in terms of absolute temperature and molecular mass m then gives the desired final result for total intensity, or number of molecules in an equilibrium gas striking a surface of unit surface area per unit time,... 

To construct such a diagram, a set of defect reaction equations is formulated and expressions for the equilibrium constants of each are obtained. The assumption that the defects are noninteracting allows the law of mass action in its simplest form, with concentrations instead of activities, to be used for this purpose. To simplify matters, only one defect reaction is considered to be dominant in any particular composition region, this being chosen from knowledge of the chemical attributes of the system under consideration. The simplified equilibrium expressions are then used to construct plots of the logarithm of defect concentration against an experimental variable such as the log (partial pressure) of the components. The procedure is best illustrated by an example. 

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. 

Although one can probably find exceptions, most equilibrium calculations involving flue gas slurries are performed with temperature as a known variable. With temperature known, the numerical values of the appropriate equilibrium constants can be immediately calculated. The remaining unknown variables to be determined are the activities, activity coefficients, molalities, and the gas phase partial pressures. The equations used to determine these variables are formulated from among the equilibrium expressions presented in Table 1, the expressions for the activity coefficients, ionic strength, material balance expressions, and the electroneutrality balance. Although there are occasionally exceptions, the solution sequence generally is an iterative or cyclic sequence. 

The Kp/s for substances containing carbon tabulated by JANAF are in reality Kp, and the condensed phase is simply ignored in evaluating the equilibrium expression. The number of moles of carbon (or any other condensed phase) is not included in the n, since this summation is for the gas phase components contributing to the total pressure. 

The equilibrium constant, Kc, is calculated by substituting equilibrium concentrations into the equilibrium expression. Experimentally, this means that a reaction mixture must come to equilibrium. Then one or more properties are measured. The properties that are measured depend on the reaction. Common examples for gaseous reactions include colour, pH, and pressure. From these measurements, the concentrations of the reacting substances can be determined. Thus, you do not need to measure all the concentrations in the mixture at equilibrium. You can determine some equilibrium concentrations if you know the initial concentrations of the reactants and the concentration of one product at equilibrium. 

This assumes H2O = 1, which is nearly true, even in seawater. For example, H2O = 0.98 at 35%o, 25°C, and 1 atm. As with other equilibrium expressions, and can be rewritten as stoichiometric constants that are specific for a particular temperature, pressure, and ionic strength. 

Pressure of each column (set through constants in equilibrium expression for each component). 

Kp = (pressure NOj) x (pressure Oj) 1 point for correct equilibrium expression. 

The conditions of equilibrium expressed by Equations (5.25)—(5.29) and (5.46) involve the temperature, pressure, and chemical potentials of the components or species. The chemical potentials are functions of the temperature, pressure or volume, and composition, according to Equations (5.54) and (5.56). In order to study the equilibrium properties of systems in terms of these experimentally observable variables, expressions for the chemical potentials in terms of these variables must be obtained. This problem is considered in this chapter and in Chapter 8. 

Solution Because vCaCC,3 = -1, vCaQ = 1, and vCq2 = 1, Ka = flco2flCao/flCaCo3> CaO and CaC03 are condensed phases their activities are unity and they do not enter into the equilibrium expression (as long as some of these materials are present). The activity of C02 is acc>2 = f o.JP, which, at pressures where C02 behaves ideally, is just the partial pressure of C02 in units of bar. Equation (36) then becomes... 

Total adsorption The amount of gas adsorbed on the substrate, at equilibrium pressure. This value is frequently used in adsorption isotherms the equilibrium pressure is expressed as (p/p0) cfr. chapter 8. 

Relationships (40.6) and (40.7) recognise the proportionality between concentration, c and partial pressure, pi (atm) at constant temperature, T (having the proportionality constant = 1 /RT). The former measure (concentration, c/) can be used when dealing with solutions which are present in reactions (see notes about solids in equilibrium expressions later - Frame 43). 

There are two main ways to describe the equilibrium of a reaction. The first is in terms of the concentrations of reactions and products. The expression that describes the equilibrium of a reaction where the concentrations of the materials are known is Kc. When the reactants and products are in the gaseous state, we can also use the equilibrium constant expression, Kp, where partial pressures are used instead of concentration units. Solids and pure liquids (like water) are omitted from equilibrium expressions because their concentrations do not change during chemical reactions. 

S is the amount of substance (gas) per unit volume of solvent (polymer) in equilibrium with a unit partial pressure, as expressed in the equation ... 

An intrinsic property of a polyhedral foam is the reduced pressure in its Plateau borders. At the moment of foam formation the pressure in the borders depends mainly on the foam expansion ratio, dispersity and surface tension (see Eqs. (4.9) and (4.10)). At hydrostatic equilibrium the border pressure is expressed by Eqs. (1.37) and (1.38). 

You have been assigned to simulate a flash evaporator that separates a liquid feed stream containing benzene and toluene at temperature Tf ( C) into liquid and vapor product streams m equilibrium at temperature T( C) and pressure P mm Hg). The compositions of the product streams are related by Raoulfs law (Equation 6.4-1), and the component vapor pressures are expressed by the Antoine equation (Table B.4). 

Substitution of this equation into Eq. (13.25) provides an equilibrium expression displaying the pressure and the composition ... 

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