Pressure Effects on Equilibria

Temperature and Pressure Effects on Equilibrium 55 Table 2.3. Continued)... 

Fig. 8.2 H2S partial pressure effect on equilibrium, calculated using Gaseq (Chemical equilibria in perfect gases)...

Predict the effect on equilibrium concentrations of an increase in (a) Temperature, (b) Pressure... 

Some Pressure Effects on Liquid Diffusion Coefficients and Equilibrium... 

For isotope effects on equilibrium constants in both gas and condensed phase the take-home lesson is there is no direct proportionality between measured isotope effects on logarithmic concentration or pressure ratios and isotopic differences in... 

Over the years, various other theories and models have been proposed for predicting salt effect in vapor-liquid equilibrium, including ones based on hydration, internal pressure, electrostatic interaction, and van der Waals forces. These have been reviewed in detail by Long and McDevit (25), Prausnitz and Targovnik (31), Furter (7), Johnson and Furter (8), and Furter and Cook (I). Although the electrostatic theory as modified for mixed solvents has had limited success, no single theory has yet been able to account for or to predict salt effect on equilibrium vapor composition from pure-component properties alone. 

We should note that in most cases in environmental organic chemistry, we can neglect the effect of pressure changes on equilibrium partitioning. Exceptions might... 

The thermodynamic pressure effect on the reaction rate constant can be explained in terms of transition state theory (Evans and Polanyi, 1935), when the reactants are in thermodynamic equilibrium with a transition state. Once the transition state complex is formed it proceeds directly to products. With this analysis the pressure effect on the reaction rate constant can be given as follows ... 

These pressure differences have no effect on heatup paths, Fig. 12.4 - and little effect on equilibrium curves and intercepts. Intercept temperature and % S02 oxidized both increase slightly with increasing pressure. 

Related Calculations. While nothing is said above about kinetics, increasing the temperature very frequently changes the reaction rate favorably. Accordingly, in some exothermic-reaction situations, it may be worthwhile to sacrifice some degree of equilibrium conversion in favor of shorter reactor residence time by raising reaction temperature. Similarly, a pressure change may have an effect on kinetics that is contrary to its effect on equilibrium. 

Equations (6.1) and (6.2) pertain to ideal systems, that is, systems where there are no interactions between the molecules. In a real system the pressure effect on p. in the vapor phase has to be modified by a fugacity coefficient < >, and the effect of mixing on the chemical potential in the liquid phase has to be modified by an activity coefficient 7,. The more general expression for equilibrium (called the 4>-y representation) then becomes... 

In all cases in the thermodynamic analysis we considered partial pressures of H2O, CO2, and other volatiles to be independent variables, if they were not related to one another by reactions. In addition the general conclusion was drawn that in thermodynamic calculations of metamorphic reactions it is impossible to assume different isotropic pressures on the solid phases and fluid. Lithostatic (nonhydrostatic) pressure or loading pressure has practically no effect on equilibrium in elastic deformation of rocks. Isotropic pressure equal to fluid pressure in the case of an excess of volatiles should be considered an equilibrium factor in actual natural processes. 

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-... 

Pressure Transition-state theory accounts for pressure effects on solution reaction rates through the effect of pressure on the equilibrium constant K. At constant temperature and electrolyte concentration (constant ionic strength),... 

Volumes of activation and reaction are themselves also pressure-dependent as shown for the volume of activation in Figure l. There is no theory explaining this pressure dependence which would allow the volume of activation or reaction to be determined over a larger range of pressure. Therefore, several empirical relations are employed to fit the pressure dependencies of rate and equilibrium constants " from which the least-squares fit [hiA (p) = a + b- p, hi= 0) = a, A= -b-R-T orhi f(p) = a - -b p, hiA (p = 0) = a, AV = y RT] is the simplest and in many cases also the most reliable method of computing A and A V, It is only applicable in the low-pressure range (<2000 bar) where the dependencies of hi (p) or In if (p) on pressure p are usually linear. Thus, this method requires a very precise measurement of the rate constants at relatively low-pressures (1-2000 bar) where the pressure effect on the rate constants is relatively... 

Pressure has almost no effect on equilibrium reactions that are in solution. Gases in equilibrium, however, may be affected by changes in pressure. 

For a purely gaseous equilibrium, does doubling the pressure have the same effect on equilibrium as doubling the concentration ... 

Solute-solvent clustering, as determined both from V2, and solvatochromic shifts for UV-visible and fluorescent probes, has been described by a unified theoretical result, eq 2. The degree of clustering is related quantitatively to the solute-solvent interaction strength multiplied by the isothermal compressibility. Large pressure effects on chemical potentials, solubilities, rate constants, and equilibrium constants are all a manifestation of and can be related to the isothermal ccHnpressibility. 

It should be pointed out however that Kramer and Leder (15) used CO2 as the SCF solvent because it also acts as a catalyst activator. Thus, factors other than temperature and pressure effects on reaction equilibrium can also dictate the choice of the SCF solvent. 

The WGS reaction (Eq. 6.1) is slightly exothermic (AH = -41.16kJ/mol, gas phase) and is a typical example of reaction controlled by equilibrium, especially at higher temperatures. The equilibrium constant is a function of temperature. The reaction proceeds without change in the number of moles and in consequence pressure does not have any significant effect on equilibrium. For pressures between 10 and 50 bar, the following expressions are recommended for the equilibrium constant as a function of temperature 5... 

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