Phase equilibria vapour pressure

The general field of measuring thermodynamic quantities using gas-phase methods is based simply on Eq. (3.55) where the activity of component i (Oj) is equal to the vapour pressure of i in the alloy divided by the equilibrium vapour pressure of pure i. 

Using this equation AHV can be estimated with a knowledge of the equilibrium vapour pressure of a liquid at two different temperatures. For the solid-vapour phase boundary (sublimation), an analogous equation is obtained by replacing AHv with the heat of sublimation AHs. 

If pure chlorine is to be liquefied at a constant temperature, it must be compressed to a pressure equalling the equilibrium vapour pressure of the liquid chlorine at the same temperature. The evolved condensation heat must be then lead away. If the chlorine is not entirely pure, compression must be increased by partial pressure of all inert gases. If chlorine containing other gases which cannot be liquefied readily is compressed it will be liquefied alone and its concentration in the gas phase will be decreased. Should further portions of chlorine be liquefied it would be necessary to increase the pressure in proportion to the increasing concentration of the inert gases in the gas phase. 

Several authors [3-9] studied the solubility of polymers in supercritical fluids due to research on fractionation of polymers. For solubility of SCF in polymers only limited number of experimental data are available till now [e.g. 4,5,10-12], Few data (for PEG S with molar mass up to 1000 g/mol) are available on the vapour-liquid phase equilibrium PEG -CO2 [13]. No data can be found on phase equilibrium solid-liquid for the binary PEG S -CO2. Experimental equipment and procedure for determination of phase equilibrium (vapour -liquid and solid -liquid) in the binary system PEG s -C02 are presented in [14]. It was found that the solubility of C02 in PEG is practically independent from the molecular mass of PEG and is influenced only by pressure and temperature of the system. 

For a pure substance in condensed phase (solid or liquid) their vapour pressure is taken to be related to their activities. When we measure equilibrium vapour pressure, the vapour and the solid (or liquid) are at equilibrium and hence the activities of the constituent in both phases are the same. Hence, the activity of the vapour phase would represent the activity of the solid or liquid. 

Let us consider a pure substance say, water, at ambient conditions. Water naturally evaporates, and its equilibrium vapour pressure is equal to the pressure of vapour when water is kept in an evacuated chamber. Since equilibrium condition exists, free energy of transformation is zero or, stated differently, the free energies of the two phases are same. Since it is the case of a single pure substance, we say that the activities of the two phases are same. 

Particularly in dilute solutions in water, solvents tend to behave in a very non-ideal way and their equilibrium vapour pressure has to be calculated either using an activity coefficient or Henry s law constant (H). The literature contains compilations of the latter for aqueous solutions but they are reported in several different units, all of which are a pressure divided by a concentration, i.e. H = P/x, where P is the vapour pressure of the pure solvent at the solution temperature and x its concentration in the liquid phase. 

A similar example of a promising application of solar heat for intensified process systems is pervaporation. In pervaporation, a selective membrane is used as barrier between two phases, the liquid feed and the vapour permeate. The process depends on the sorption equilibrium and the mobility of the components through the membrane and is rather independent of the vapour liquid equilibrium. The desired component, which is in liquid form in the feed, permeates through the membrane and evaporates while passing the membrane, because the partial pressure of the permeating component is kept lower than the equilibrium vapour pressure [21]. Permeabilities depend on the solubility and diffusion rates through the membrane. 

SO that Equation (9.2) effectively defines the equilibrium vapour pressure, p at a particular temperature. It follows from Equations (9.1) and (9.2) that spontaneous growth of the solid phase can only occur if the vapour pressure... 

The preceding treatment implies that the equilibrium vapour pressure depends only on the temperature of the system concerned. This will be true when the solid phase is present as a macroscopic solid with large surface area, but if the solid phase (or liquid phase) is present as small crystallites or droplets, the contribution of surface free energy must be taken into account. 

If the values of U and T8 of the total crystal-vapour system are calculated by statistical methods and plotted against the firaction of the substance which is present as a vapour, curves are obtained as shown in Pig. 14.f The minimum value of A, for a particular temperature and volume of the system, occurs when there is a certain fraction of the substance present in the vapour phase. This is the equilibrium state, at prescribed temperature and volume, and the corresponding pressure in the vapour phase isthesaturation vapour pressure. 

The generation of vapour from a condensed phase is also a temperature-dependent effect, the simple case of the equilibrium vapour pressure (P) above a liquid being determined by the Clausius-Clapeyron equation (eqn (13)). 

M and B are function of the gas concentration C and of the gas diffusivity D, respectively ka is the Boltzmann constant Py e Pt are the equilibrium vapour pressure and the pressure in the liquid phase, whose difference describes the supersaturation of the expanding gas in the solution. 

The Clausius-CIapeyron equation shows the following characteristic property at the vapour pressure of the substances. Depicting the logarithm of the equilibrium vapour pressure (p) as ordinate and (1/T) as abscissa results in curves with the slope —AH/R. The curves will be almost rectilinear since AH is only slightly dependent on temperature. Such form of depicting is, for example, useful for experimental determination of AH for phase transformations in systems of matter. 

When oil and gas are produced simultaneously into a separator a certain amount (mass fraction) of each component (e.g. butane) will be in the vapour phase and the rest in the liquid phase. This can be described using phase diagrams (such as those described in section 4.2) which describe the behaviour of multi-component mixtures at various temperatures and pressures. However to determine how much of each component goes into the gas or liquid phase the equilibrium constants (or equilibrium vapour liquid ratios) K must be known. 

In the phase equilibrium between a pure solid (or a liquid) and its vapour, the addition of other gases, as long as they are insoluble in the solid or liquid, has negligible effect on the partial pressure of the vapour. 

Thus a solution containing mol fractions of 0-25 and 0-75 of A and B respectively is in equilibrium with a vapour containing 16-7 and 83 -3 mol per cent, of A and B respectively. The component B with the higher vapour pressure is relatively more concentrated in the vapour phase than in the liquid phase. 

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