Pressure chemical equilibrium relationship

Chapters 7 to 9 apply the thermodynamic relationships to mixtures, to phase equilibria, and to chemical equilibrium. In Chapter 7, both nonelectrolyte and electrolyte solutions are described, including the properties of ideal mixtures. The Debye-Hiickel theory is developed and applied to the electrolyte solutions. Thermal properties and osmotic pressure are also described. In Chapter 8, the principles of phase equilibria of pure substances and of mixtures are presented. The phase rule, Clapeyron equation, and phase diagrams are used extensively in the description of representative systems. Chapter 9 uses thermodynamics to describe chemical equilibrium. The equilibrium constant and its relationship to pressure, temperature, and activity is developed, as are the basic equations that apply to electrochemical cells. Examples are given that demonstrate the use of thermodynamics in predicting equilibrium conditions and cell voltages. 

The most fundamental manner of demonstrating the relationship between sorbed water vapor and a solid is the water sorption-desorption isotherm. The water sorption-desorption isotherm describes the relationship between the equilibrium amount of water vapor sorbed to a solid (usually expressed as amount per unit mass or per unit surface area of solid) and the thermodynamic quantity, water activity (aw), at constant temperature and pressure. At equilibrium the chemical potential of water sorbed to the solid must equal the chemical potential of water in the vapor phase. Water activity in the vapor phase is related to chemical potential by... 

The mixture we have just described, even with a chemical reaction, must obey thermodynamic relationships (except perhaps requirements of chemical equilibrium). Thermodynamic properties such as temperature (T), pressure (p) and density apply at each point in the system, even with gradients. Also, even at a point in the mixture we do not lose the macroscopic identity of a continuum so that the point retains the character of the mixture. However, at a point or infinitesimal mixture volume, each species has the same temperature according to thermal equilibrium. 

We define the number of components in a system as N R, which is also the minimum number of chemical species from which all phases in the system can be prepared. Each equilibrium relationship decreases by one the number of species required to prepare a phase. Thus, the quantity (N — R) in Equation (13.12) is equivalent to C in Equation (13.9). For example, water in equilibrium with its vapor at room temperature and atmospheric pressure is a one-component system. Water in equilibrium with H2 and O2 at a temperamre and pressure at which dissociation... 

The Gibbs phase rule is the basis for organizing the models. In general, the number of independent variables (degrees of freedom) is equal to the number of variables minus the number of independent relationships. For each unique phase equilibria, we may write one independent relationship. In addition to this (with no other special stipulations), we may write one additional independent relationship to maintain electroneutrality. Table I summarizes the chemical constituents considered as variables in this study and by means of chemical reactions depicts independent relationships. (Throughout the paper, activity coefficients are calculated by the Debye-Hiickel relationship). Since there are no data available on pressure dependence, pressure is considered a constant at 1 atm. Sulfate and chloride are not considered variables because little specific data concerning their equilibria are available. Sulfate may be involved in a redox reaction with iron sulfides (e.g., hydrotroilite), and/or it may be in equilibrium with barite (BaS04) or some solid solution combinations. Chloride may reach no simple chemical equilibrium with respect to a phase. Therefore, these two ions are considered only to the... 

The number of unknown variables for a single unit is the sum of the unknown component amounts or flow rates for ail inlet and outlet streams, plus all unknown stream temperatures and pressures, plus the rates of energy transfer as heat and work. The equations available to determine these unknowns include material balances for each independent species, an energy balance, phase and chemical equilibrium relations, and additional specified relationships among the process variables. 

Table 2.3 summarizes the essential relationships for pressure effects on chemical equilibrium for the variable-pressure standard-state convention. Note, that these relationships can apply to any consistent choice of standard part ial molar volumes, for example, one for which an ionic medium such as seawater is adopted as the solute reference state. For detailed discussion of applications to seawater see, for example, Millero (1969) and Whitfield (1975). A compie-... 

The results of the experiments shown in color plates 1 and 2 illustrate that the concentration relationship at chemical equilibrium (that is, the position of equilibrium) is independent of the route by which the equilibrium state is achieved. This relationship is altered by the application of stress to the system, however. Such stresses include changes in temperature, in pressure (if one of the reactants or... 

If a gas phase is present, chemical species may volatilize from the liquid or solid phase, which is an important partitioning process in a variety of circumstances (e.g., transport in the unsaturated zone, or for treatment processes). The equilibrium vapor pressure can be used with the ideal gas law to estimate the mass in a given volume and temperature under equilibrium conditions. For solutions with more than one component, Raoult s law can be used to quantify the vapor pressure of each component. For dilute aqueous solutions, Henry s law describes the equilibrium relationship between dissolved chemicals and their vapor pressure ... 

Chemical Equilibrium When a reaction occurs at equilibrium, the temperature and pressure in the system remain constant and the change in free energy is zero. These restraints can be used to develop the following relationship between the standard free energy change AF" and the equilibrium constant K ... 

This is the Gibbs-Duhem equation, which relates the variation in temperature, pressure, and chemical potentials of the C components in the solution. Of these C + 2 variables, only C + 1 can vary independently. The Gibbs-Duhem equation has many applications, one of which is providing the basis for developing phase equilibrium relationships. 

Only a brief outline of the effects of pressure on rates and equilibria is given here since the subject is amply documented elsewhere. " It has long been appreciated that the position of a chemical equilibrium may be shifted by the application of external pressure in reactions in both the liquid and the gaseous phase. This shift in equilibrium favours the direction of the reaction which results in the smaller volume this is an application of the Le Chatelier s principle. In gas-phase reactions the term volume denotes the total volume of the system in dilute solutions the term volume denotes the algebraic sum of the partial molar volumes of the individual reagents and products. The thermodynamic relationship which summarizes this effect is... 

The relationship between the electrolyte concentration in the solution and that in the membrane can be obtained by assuming chemical equilibrium between the two phases and electro neutrality in both the solution and the membrane. For negligible small pressure... 

Gibbs called the differential quotients of equation (3.2) the chemical potential fi. In the following, let us only consider the Gibbs function G, which is best suited for expressing equilibrium relationships with respect to pressure and temperature as independent variables. The differential of the Gibbs function may be written in the form of jv... 

A simple equation of state should be chosen. The deterioration of accuracy of fugacity coefficients obtained will be negligible. Moreover, in the effort at elucidating the chemical equilibrium in a broad temperature and pressure range, extrapolation outside the limits of validity may be subject to greater risk in the case of multi-constant equations as opposed to simple relationships. 

Although the existence of inert gas has without poison on the iron catalyst, from the perspective of chemical equilibrium, increasing the content of inert gas tp ) is equivalent to the reducing the effective pressure The relationship for operating pressure (po), effective pressure (pe) and content of inert gas (pi) is as follows ... 

A method of estimating carbon monoxide vapor pressures over aqueous copper-ammonium salt solutions, under conditions outside the range of experimental data, was proposed by van Krevelen and Baans (1950). These authors concluded that the basic chemical reaction involved in the absorption of carbon monoxide by aminoniacal solutions is expressed in equation 16-26. By considering equilibrium relationships in this reaction, they derived an equation relating the carbon monoxide partial pressure to the solution composition as follows ... 

The residence time of the ZrHi 7 layer would be the same as that of the blanket fuel, that is, three fuel cycles in the inner blanket or six fuel cycles in the radial blanket. During that time, hydrogen from ZrHi 7 will permeate through the stainless steel layers, which wrap the ZrHi 7. The permeation rate is estimated assuming that the chemical equilibrium of zirconium and hydrogen in ZrH is achieved. The hydrogen pressure P is determined from the following relationship [13] ... 

Relationships from thennodynamics provide other views of pressure as a macroscopic state variable. Pressure, temperature, volume and/or composition often are the controllable independent variables used to constrain equilibrium states of chemical or physical systems. For fluids that do not support shears, the pressure, P, at any point in the system is the same in all directions and, when gravity or other accelerations can be neglected, is constant tliroughout the system. That is, the equilibrium state of the system is subject to a hydrostatic pressure. The fiindamental differential equations of thennodynamics ... 

Multicomponent distillations are more complicated than binary systems due primarily to the actual or potential involvement or interaction of one or more components of the multicomponent system on other components of the mixture. These interactions may be in the form of vapor-liquid equilibriums such as azeotrope formation, or chemical reaction, etc., any of which may affect the activity relations, and hence deviations from ideal relationships. For example, some systems are known to have two azeotrope combinations in the distillation column. Sometimes these, one or all, can be broken or changed in the vapor pressure relationships by addition of a third chemical or hydrocarbon. 

Thus, for each component, its chemical potential is the same in all phases that are in equilibrium. We will see below that the relationships involving the pressure and temperature variations of the chemical potential that we have developed earlier will be helpful in explaining the effect of these variables on phase equilibria. 

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