Solid-vapour equilibria

The phase diagram also illustrates why some substances which melt at normal pressure, will sublime at a lower pressure the line p = Pa intersects at Tg the locus OR of the points defining the solid-vapour equilibrium, i.e. at the pressure pj, the substance will sublime at the temperature T. Sometimes the opposite behaviour is observed, namely that a substance which sublimes at normal pressure will melt in a vacuum system under its own vapour pressure This is a non-equilibrium phenomenon and occurs if the substance is heated so rapidly that its vapour pressure rises above that of the triple point this happens quite frequently with aluminium bromide and with iodine. 

The Clapeyron-Clausius equation for solid/ vapour equilibrium may be put as... 

Concomitant crystallization is by no means limited to crystallization from solution, nor to preservation of constant molecular conformation. As noted in Section 2.2.5 the classic pressure vs temperature phase diagram for two solid phases (Fig. 2.6) of one material exhibits two lines corresponding to the solid/vapour equilibrium for each of two polymorphs. At any one temperature one would expect the two polymorphs to have different vapour pressures. This, in fact, is the basis for purification of solids by sublimation. Nevertheless there are examples where the two have nearly equal vapour pressures at a particular temperature and thus cosublime. This could be near the transition temperature or simply because the two curves are similar over a large range of temperatures or in close proximity at the temperature at which the sublimation is carried out. For instance, the compounds 3-VI and 3-Vn both yield two phases upon... 

Schwarz and Knoetze [24] found that for their VLE data an approximately linear relationship exists between temperature and the phase transition pressure at constant composition. This relationship has a positive gradient and indicates a higher solubility at lower temperatures, converse to that of the solid-vapour equilibrium (SVE) phase behaviour. This positive gradient was also found through the entire mass fraction range studied and the authors did not find any indications of temperature inversions in this system. 

When investigating solid/vapour equilibrium by this technique, only the vapour phase is recirculated [64]. 

An alternative explanation concerns the existence of two equilibria. As the vapour/liquid equilibrium is disturbed by the passage of air, the concentration of dissolved compounds in the liquid phase falls, disturbing the solid /liquid equilibrium. The kinetics of transfer across this latter phase boundary are much slower than for the liquid/vapour transfer, so that the extraction of odour becomes limited by the rate of diffusion into the liquid phase. 

In this expression (known as Young s equation), ySG is the surface tension of the solid in equilibrium with the vapour of the wetting liquid. If ys is the surface tension of the solid against its own vapour, then... 

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. 

The Clapeyron-Clausius equation (1.52) for solid = liquid equilibrium cannot be integrated easily since Vs cannot be ignored in comparison with Vt. Also the laws of liquid state are not so simple as those for gaseous state. However, this equation can be used for calculating the effect of pressure on the melting point of a solid. Eq. 1.52 can also be used for calculating heats of fusion from vapour pressure data obtained at different temperatures. 

Spreading wetting is a process in which a drop of liquid spreads over a solid substrate (the liquid and solid being previously in equilibrium with the vapour). Here, the solid-vapour interface is replaced by two new interfaces (solid-liquid and liquid-vapour) of same area. 

Assessment of wettability from the contact angle. A favourable case is when a contact angle 6 can be measured between the liquid and solid in equilibrium with the vapour, so that the Young-Duprd equation can be applied. As early as 1805, Young considered the possibility of such an equilibrium between surface tensions, but it was only in 1869 that Duprd put it in the well-known form of equation ... 

With a drop of liquid in contact with a solid (Figure C2-7), there are three interfaces the solid/liquid the solid/vapour and the liquid/vapour interfaces. Each of these has its own interface tension. For a drop that partially wets a solid, the horizontal components of the interface tensions must be in equilibrium. This determines the value of the contact angle 0... 

Recalling the classic definition of the triple point, say, for water as the intersection of the solid-vapour and the liquid-vapour curves, the analogy in Fig. 2.7 is the intersection of the II<->v. and I<->v. curves. Below the triple point only one of the solid phases (I) can exist in stable equilibrium with the vapour above the triple point only II... 

The tensUeudiometer, for determining the composition of solid phases in equilibrium with vapour of given pressure, consists of a modified tensimeter connected with bulbs of known volume, previously exhausted. By putting a bulb in connection with the tensimeter, a known amount of vapour is extracted from the solid-vapour system, and from the known composition of the solid at the start, the amount of volatile component left in it can be calculated. 

In the following equilibrium systems for a pure substance (not a solution) solid liquid (s l) fusion liquid vapour (/ g) evaporation solid vapour (s g) sublimation... 

As for the meaning of in [5.2.2b and c], we proceed as in connection with the spreading tension, see [5.2.1]. When, before adhering to the liquid, the solid particle is completely dry, is. In that case, is Identified as the initial work of adhesion, a> (ln). However, in practice this situation is not easily realized mostly the solid will have been exposed to the vapour of the liquid and hence has to be replaced by y - n[t). For solids at equilibrium with the vapour before adhesion, y is Just the equilibrium solid-gas interfacial tension. Only under that condition is = 0 and does Young s equation apply. 

The process of wetting involves replacing the solid/vapour interface (with interfacial tension ygy) with a solid/liquid interface (with interfacial tension yg ). Wetting can be described in equilibrium thermodynamics in terms of the contact angle 0 by Young s equation at the wetting line [5]. 

Equilibrium between Solid and Vapour. Sublimation Curve. — Just as in the case of the system liquid— vapour, so also in the case of the system solid—vapour tbjgre jsdll bo, -for each temperature, a certain definite pressure of the vapour and this pressure.wijl be independent of the relative or absolute amounts of the solid or vapour present, and will depend solely on the temperature. The curve representing the conditions of equilibrium between a solid and its vapour is called a its general form is the same... 

In order to derive a vapour-pressure formula kinetically, a model of molecular mechanism must be constructed which illustrates the solid in equilibrium with its vapour. Any such model must, if it is to conform with the equations of mechanics, show the same thermodynamically calculable dependence of vapour pressure on temperature for the same vt A0, and molecular weight. The representation here used is as follows Let there be, in a given space, points P which attract the atoms with a force directly proportional to the distance r. Since the heat of evaporation has a... 

Figure 5.1 presents the behaviour of a pure species that can exist as solid, liquid or vapour in a pressure-temperature diagram. We may have three types of two-phase equilibrium solid/liquid, vapour/liquid and solid/vapour. There is a point where all three phases coexist, designated by the triple point. Here the phase rule gives F=C+2-P= +2-3=Q degrees of freedom. Neither pressure nor temperature can be used to modify the equilibrium. If only two phases can be found at equilibrium F=l+2-2=l, and either pressure or temperature can vary. The most important equilibrium in process engineering is vapour-liquid equilibrium, abbreviate as VLE. It may be observed that the two phases will coexist up to a point where it is difficult to make a distinction between vapour and liquid. This is the critical point, a fundamental physical property characterised by critical parameters and. Above the critical point the state... 

A multipurpose cell which can be used in a recirculating or one-shot apparatus for either solid-vapour or liquid-vapour equilibrium has been described by Duncan and Hiza. ... 

Muir, R.F. and Howatt, C.S. (1982) Predicting solid-liquid equilibrium data from vapour-liquid data. Chemical Engineering, 22 Feb, 89-92. 

Let us assume that in the absence of surfactant the drop forms an equilibrium contact angle above If the water contains surfactants then three transfer processes take place from the liquid onto all three interfaces surfactant adsorption at both (i) the inner liquid-solid interface and (ii) the liquid-vapor interface, and (iii) transfer from the drop onto the solid-vapor interface just in front of the drop. Adsorption processes (i) and (ii) result in a decrease of corresponding interfacial tensions, and y. The transfer of surfactant molecules onto the solid-vapour interface in front of the drop results in an increase of a local free energy, however, the total free energy of the system decreases. That is, surfactant molecule transfer ii) goes via a relatively high potential barrier and, hence, goes considerably slower than adsorption processes (i) and (ii). Hence, they are "fast" processes as compared with the third process (iii). 

Domanska, U. Lachwa, J. Thermodynamics of binary mixtures of N-methyl-2-pyrrolidinone and ketone. Experimental results and modelling of the (solid + liquid) equilibrium and the (vapour + liquid) equilibrium. The modified UNIFAC (Do) model characterization J. Chem. Thermodyn. 2005,37, 692-704... 

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