Pressure, effecting equilibrium

In catalysis applications, the tunable solvent properties result in a variety of effects, such as controllable component and catalyst solubilities. Moreover, it is possible that kinetic rates are affected by both temperature and pressure effects, equilibrium constants are shifted in favor of the desired products, and selectivity and yields are increased by manipulating the solvent s dielectric constant or by controlling the temperature in highly exothermic reactions through an adjustment of the solvent s heat capacity [18-23]. 

At equilibrium, these concentration and pressure effects must be equal and opposite for Eq. (8.75) to apply. Equation (8.13) describes the concentration dependence of jui, and Eq. (8.12) describes the pressure effect. Assembling these results, we write... 

For the liquid-phase mass-transfer coefficient /cl, the effects of total system pressure can be ignored for all practical purposes. Thus, when using Kq and /cl for the design of gas absorbers or strippers, the primary pressure effects to consider will be those which affect the equilibrium curves and the values of m. If the pressure changes affect the hydrodynamics, then Icq, and a can all change significantly. 

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

Gas production and subsequent pressure-time histories can be investigated successfully only in pressure vessels such as the VSP. If the gaseous product dissolves partly in the reaction mixture (i.e., the vapor-liquid equilibrium is changed), careful investigations of the pressure effect within the possible variations of the operating conditions are necessary. Pressurized vessels are also useful to investigate any mass transfer improvement for gas-liquid or gas-dissolved (suspended) solid reactions. 

Application of ion exchange refining to the process for the manufacture of dextrose may be understood from the following description of such a process. Triple-washed starch is diluted with ion-free water to the desired concentration and is acidified with a definite quantity of mineral acid such as hydrochloric or sulfuric. It is desirable that the acidified starch slurry be held for at least thirty minutes in order to permit an effective equilibrium acidity to be reached. The starch slurry may contain a quantity of soft water salts which consume acid, and since this consumption is variable, the acidity is checked and adjusted to the desired level following the holding period. The conversion is then carried out at elevated temperature and under pressure for a period sufficient to yield maximum dextrose. The conversion may be carried out batchwise in an autoclave, or continuously. 

Remember, in working Le Chatelier problems, pressure effects are important only for gases that are involved in the equilibrium. 

As the pressure is increased in the system, the equilibrium designated as reaction (9.2) shifts to Ti305(l) because the pressure effect overrides the increase in temperature with pressure that would make the shift to the gaseous products. Indeed, at a given assigned enthalpy, the Ti305(l) mole fraction increases as the total pressure increases. For the equilibrium designated as... 

Equilibrium constants are also dependent on temperature and pressure. The temperature functionality can be predicted from a reaction s enthalpy and entropy changes. The effect of pressure can be significant when comparing speciation at the sea surface to that in the deep sea. Empirical equations are used to adapt equilibrium constants measured at 1 atm for high-pressure conditions. Equilibrium constants can be formulated from solute concentrations in units of molarity, molality, or even moles per kilogram of seawater. 

Vertical concentration profiles of (a) temperature, (b) potential density, (c) salinity, (d) O2, (e) % saturation of O2, (f) bicarbonate and TDIC, (g) carbonate alkalinity and total alkalinity, (h) pH, (i) carbonate, ( ) carbon dioxide and carbonic acid concentrations, and (k) carbonate-to-bicarbonate ion concentration ratio. Curves labeled f,p have been corrected for the effects of in-situ temperature and pressure on equilibrium speciation. Curves labeled t, 1 atm have been corrected for the in-situ temperature effect, but not for that caused by pressure. Data from 50°27.5 N, 176°13.8 W in the North Pacific Ocean on June 1966. Source From Culberson, C., and R. M. Pytkowicz (1968). Limnology and Oceanography, 13, 403-417. 

Let us now consider the effect of pressure on equilibrium. We assume for the sake of simplicity that fluid pressure is equal to total pressure and that gaseous components mix ideally. From... 

Pokrovsky OS, Viers J, Emnova EE, Kompantseva El, Freydier R (2008) Copper isotope fractionation during its interaction with soil and aquatic microorganisms and metal oxy(hydr)oxides possible structural control. Geochim Cosmochim Acta 72 1742-1757 Polyakov VB (1997) Equilibrium fractionation of the iron isotopes estimation from Mossbauer spectroscopy data. Geochim Cosmochim Acta 61 4213 217 Polyakov VB, Kharlashina NN (1994) Effect of pressure on equilibrium isotope fractionation. Geochim Cosmochim Acta 58 4739 750... 

Supercritical solvents can be used to adjust reaction rate constants (k) by as much as two orders of magnitude by small changes in the system pressure. Activation volumes (slopes of In k vs P) as low as —6000 cm3/mol were observed for a homogeneous reaction (97). Pressure effects can also be pronounced on reversible reactions (17). In one example the equilibrium constant was increased from two- to sixfold by increasing the solvent pressure. The choice of supercritical solvent can also dramatically affect an equilibrium constant. An obvious advantage of using supercritical fluid solvents as a media for chemical reactions is the adjustability of the reaction kinetics and equilibria owing to solvent effects. 

Elementary and advanced treatments of such cellular functions are available in specialized monographs and textbooks (Bergethon and Simons 1990 Levitan and Kaczmarek 1991 Nossal and Lecar 1991). One of our objectives in this chapter is to develop the concepts necessary for understanding the Donnan equilibrium and osmotic pressure effects. We define osmotic pressures of charged and uncharged solutes, develop the classical and statistical thermodynamic principles needed to quantify them, discuss some quantitative details of the Donnan equilibrium, and outline some applications. 

Figure 5. Effect of pressure on equilibrium composition of the carbon-nitrogen system at 4000° K.

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