Pressure on equilibria

In the previous sections we have been concerned with high-pressure equilibria in systems containing one liquid phase and one vapor phase. We now briefly consider the effect of pressure on equilibria between two liquid phases. In particular, we are concerned with the question of how pressure may be used to induce miscibility or immiscibility in a binary liquid system. 

The effects of pressure on equilibria in the oceans within depth profiles have been studied mostly in relation to the problem of calcium carbonate saturation in this environment (Millero, 1969 Bemer, 1965 Millero and Bemer, 1972 Edmond and Gieskes, 1970). The early calculations by Owen and Brinkley (1941) concerning the effect of pressure upon ionic equilibria in salt solutions have been extended to studies of BaS04 solubility at different depths (Chow and Goldberg, 1960) and to the pressure dependence of sulfate associations (Fisher, 1972). 

Section 8.2.1 was concerned with equilibrium between a condensed phase and the vapour. It is often necessary, however, to estimate the effect of pressure on equilibria between two condensed phases. For example, the melting point of sodium at one atmosphere pressure is 97.6°C. Can it be used as a liquid heat transfer medium at 100°C, at a pressure of 100 atm, or will it solidify It is known that the liquid is less dense than the solid, and this argues that high pressures will encourage solidification. This is another aspect of Le Chatelier s work, which we can now quantify. This and similar problems may be solved by the Clapeyron equation, which we shall now derive. 

For typical conditions in the chemical industry, the effect of pressure on liquid-liquid equilibria is negligible and therefore in this monograph pressure is not considered as a variable in Equation (2). 

Predict the direction in which each of the following equilibria will shift if the pressure on the system is increased by compression. 

With a suitable equation of state, all the fugacities in each phase can be found from Eq. (6), and the equation of state itself is substituted into the equilibrium relations Eq. (67) and (68). For an A-component system, it is then necessary to solve simultaneously N + 2 equations of equilibrium. While this is a formidable calculation even for small values of N, modern computers have made such calculations a realistic possibility. The major difficulty of this procedure lies not in computational problems, but in our inability to write for mixtures a single equation of state which remains accurate over a density range that includes the liquid phase. As a result, phase-equilibrium calculations based exclusively on equations of state do not appear promising for high-pressure phase equilibria, except perhaps for certain restricted mixtures consisting of chemically similar components. 

Schneider (SI) has presented a thorough review of the effect of pressure on liquid-liquid equilibria. Certain phenomena discussed in his review are of particular interest to chemical engineers, and are indicated here. 

Effect of Pressure on Solid + Liquid Equilibrium Equation (6.84) is the starting point for deriving an equation that gives the effect of pressure on (solid + liquid) phase equilibria for an ideal mixture in equilibrium with a pure... 

State what happens to the concentration of the indicated substance when the total pressure on each of the following equilibria is increased (by compression) ... 

If AV is negative, the rate constant will increase with increasing pressure. Similarly, the effect of pressure on the reaction equilibria is given by the following equation ... 

Chemical equilibria being of a dynamic type, equilibrium states are altered by changes in the variables controlling them. The effect of such changes can be interpreted qualitatively on the basis of a principle which was enunciated independently by Le Chatelier in 1885 and by Braun one year later. It states that when a system in a state of dynamic equilibrium is subjected to a stress imposed by variation in anyone of the variables controlling the equilibrium state, the system will tend to adjust itself in such a way as to minimize the effect of the stress. The variables of interest in this connection are temperature of the system, pressure on the system, and concentrations for the reactants and products taken individually. 

It may be added here that Le Chatelier s principle is quite general in nature, and that its applicability is not restricted only to chemical equilibria. It can also be applied to physical equilibria, as for example, to explain qualitatively the effects of temperature and pressure on solubility or the effect of pressure on the melting of a solid. 

Himeno S., Komatsu T., et al. High-pressure adsorption equilibria of methane and carbon dioxide on several activated carbones. 2005 Journal of Chemical Enginnering Data 50(2) 369-376. 

The effect of pressure on AG° and AH0 depends on the choice of standard states employed. When the standard state of each component of the reaction system is taken at 1 atm pressure, whether the species in question is a gas, liquid, or solid, the values of AG° and AH0 refer to a process that starts and ends at 1 atm. For this choice of standard states, the values of AG° and AH0 are independent of the system pressure at which the reaction is actually carried out. It is important to note in this connection that we are calculating the enthalpy change for a hypothetical process, not for the actual process as it occurs in nature. This choice of standard states at 1 atm pressure is the convention that is customarily adopted in the analysis of chemical reaction equilibria. 

The effect of pressure on chemical equilibria and rates of reactions can be described by the well-known equations resulting from the pressure dependence of the Gibbs enthalpy of reaction and activation, respectively, shown in Scheme 1. The volume of reaction (AV) corresponds to the difference between the partial molar volumes of reactants and products. Within the scope of transition state theory the volume of activation can be, accordingly, considered to be a measure of the partial molar volume of the transition state (TS) with respect to the partial molar volumes of the reactants. Volumes of reaction can be determined in three ways (a) from the pressure dependence of the equilibrium constant (from the plot of In K vs p) (b) from the measurement of partial molar volumes of all reactants and products derived from the densities, d, of the solution of each individual component measured at various concentrations, c, and extrapolation of the apparent molar volume 4>... 

The names of van t Hoff, Arrhenius, Ostwald, and Nernst dot the pages of Van Hise s work and with good reason. His understanding of the effects of temperature and pressure on chemical reactions and of the roles of water and ionic equilibria in metamorphic processes was derived largely from his reading of the work of these physical chemists. "The handling of the problems of rock alteration with fairly satisfactory results," he later wrote, "was possible because of the rise of physical chemistry. 

The pressure-volume-temperature (PVT) properties of aqueous electrolyte and mixed electrolyte solutions are frequently needed to make practical engineering calculations. For example precise PVT properties of natural waters like seawater are required to determine the vertical stability, the circulation, and the mixing of waters in the oceans. Besides the practical interest, the PVT properties of aqueous electrolyte solutions can also yield information on the structure of solutions and the ionic interactions that occur in solution. The derived partial molal volumes of electrolytes yield information on ion-water and ion-ion interactions (1,2 ). The effect of pressure on chemical equilibria can also be derived from partial molal volume data (3). 

Temperature and pressure are the two variables that affect phase equilibria in a one-component system. The phase diagram in Figure 15.1 shows the equilibria between the solid, liquid, and vapour states of water where all three phases are in equilibrium at the triple point, 0.06 N/m2 and 273.3 K. The sublimation curve indicates the vapour pressure of ice, the vaporisation curve the vapour pressure of liquid water, and the fusion curve the effect of pressure on the melting point of ice. The fusion curve for ice is unusual in that, in most one component systems, increased pressure increases the melting point, whilst the opposite occurs here. 

A sublimation process is controlled primarily by the conditions under which phase equilibria occur in a single-component system, and the phase diagram of a simple one-component system is shown in Figure 15.30 where the sublimation curve is dependent on the vapour pressure of the solid, the vaporisation curve on the vapour pressure of the liquid, and the fusion curve on the effect of pressure on the melting point. The slopes of these three curves can be expressed quantitatively by the Clapeyron equation ... 

The plan of this chapter is as follows. In Section 11 the basics of high-pressure technology and equipment are covered with particular reference to (a) the types of equipment that have actually been used to smdy chemical reactions and (b) the techniques in use for in situ and on-the-fly monitoring of chemical equilibria, products structure, reaction kinetics, and mechanism. Section III deals with fundamental concepts to treat the effect of high pressure on chemical reactions with several examples of applications, but with no claim of extensive covering of the available hterature. In Section IV the results obtained in the study of molecular systems at very high pressures will be discussed, and some conclusive remarks will be presented in Section V. 

The effect of pressure on chemical equilibria and reaction rates is described by the following standard equations which define the reaction volume A V and activation volume of a reaction ... 

Figure 5.46 shows the stability field of the annite end-member at 1 kbar total pressure, based on equilibria 5.131, 5.133, and 5.135, as a function of temperature and hydrogen fugacity in the system. The figure also shows the positions of the iron-wuestite (IW) and wuestite-magnetite buffer (WM). 

Pressure effects on equilibria in liquids or solids are generally less spectacular than temperature effects, at least at the pressures normally encountered in chemical engineering (a few tens of megapascals) or in the environment (hydrostatic pressures in the ocean trenches exceed 100 MPa, but about 40 MPa would be more typical of the ocean floors). Higher lithostatic pressures are, of course, found beneath the Earth s surface, reaching 370 GPa (0.37... 

General Method. The effects of composition of mixtures and of pressure on key properties such as enthalpy and entropy are deduced from PVT equations of state. This process is described in books on thermodynamics, for example, Reid, Prausnitz, and Sherwood (Properties of Liquids and Gases, McGraw-Hill, New York, 1977) and Walas (Phase Equilibria in Chemical Engineering, Butterworths, Stoneham, MA, 1985). Only the simplest correlations of these effects will be utilized here for illustration. 

In order to relate yx and xu the bubblepoint temperatures are found over a series of values of xv Since the activity coefficients depend on the composition of the liquid and both activity coefficients and vapor pressures depend on the temperature, the calculation requires a respectable effort. Moreover, some vapor-liquid measurements must have been made for evaluation of a correlation of activity coefficients. The method does permit calculation of equilibria at several pressures since activity coefficients are substantially independent of pressure. A useful application is to determine the effect of pressure on azeotropic composition (Walas, 1985, p. 227). 

Figure 13.28. Vapor-liquid equilibria of some azeotropic and partially miscible liquids, (a) Effect of pressure on vapor-liquid equilibria of a typical homogeneous azeotropic mixture, acetone and water, (b) Uncommon behavior of the partially miscible system of methylethylketone and water whose two-phase boundary does not extend byond the y = x line, (c) x-y diagram of a partially miscible system represented by the Margules equation with the given parameters and vapor pressures Pj = 3, = 1 atm the broken line is not physically significant but is...

Further carbonylation can occur, adversely affecting the selectivities obtained. Where it is used, the effect of hydrogen pressure on selectivity is also significant, as not all of the reactions require hydrogen. The production of water and the presence of alcohols lead to esterification-hydrolysis equilibria and water can affect the hydrogen pressure via the reversible water-gas shift reaction (equation 70). 

We are now ready to expand our discussion of phase equilibria to consider composition as a variable. In doing so, we will usually hold temperature constant and see the effect of composition (usually mole fraction) on the equilibrium pressure (or pressure on the equilibrium mole fraction) or we will hold pressure constant and describe the relationship between temperature and mole fraction. 

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