Solution-vapour equilibrium constant pressure curves

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... 

Corresponding to the point Q/the melting-point of pure iodine, there is the point C, which represents the vapour pressure of iodine at its melting-point. At this point three curves cut i, the sublimation curve of iodine 2, the vaporisation curve of fused iodine 3, CiB, the vapour-pressure curve of the saturated solutions in equilibrium with solid iodine. Starting, therefore, with the system solid iodine— liquid iodine, addition of chlorine will cause the temperature of equilibrium to fall continuously, while the vapour pressure will first increase, pass through a maximum and then fall continuously until the eutectic point, B (Bjl), is reached. At this point the system is invariant, and the pressure will therefore remain constant until all the iodine has disappeared. As the concentration of the chlorine increases in the manner represented by the curve B/H, the pressure of the vapour also increases as represented by the curve Bj/iHi. At the eutectic point for iodine monochloride and iodine trichloride, the pressure again remains constant until all the monochloridc has disappeared. As the concentration of the solution passes along the curve HF, the pressure... 

Van t Hoff then deals widi chemical equilibrium on the basis of the law of mass action, and the change of equilibrium constant with temperature, introducing the case of condensed s rstems in the absence of vapour and a transition mint (point de transition). Physical equilibria are special cases of chemical equilibria. Graphical methods with vapour pressure curves (e.g. for the allotropic forms of sulphur) are introduced. The principle of mobile equilibrium is explained for homogeneous and heterogeneous equilibria, and the Thomsen-Berthelot principle criticised (see pp. 614, 620). The last chapter, on affinity , gives the definition The work of affinity (A) is equal to the heat produced in the transformation (9), divided by the solute t -perature of the transition point (P) and multiplied by the diflierence between this and the given temperature (T) ... 

The equilibrium of solutions with a solubility gap is shown in Fig. 13 at constant pressure. Points A and B give the composition of the two liquid phases, point C the composition of the vapour in equilibrium with these. Point C corresponds to a certain degree to the azeotropic point in Fig. 7. For as long as both liquid phases exist and the pressure remains unchanged, the evaporation takes place at constant temperature and constant composition of the vapour. The boiling point and dew point curves which extend up to the boiling points D and E of the pure components, arc valid, if only one of the two liquid phases exists. This means for example, that to the left of C only the liquid phase poor in the second component will be in equilibrium with the vapour. 

At z in the curve, however (the minimum of vapour pressure), the solution and vapour are in equilibrium and the liquid at this point will distil without any change in composition. The mixture at z is said to be azeotropic or a constant boiling mixture. The composition of the azeotropic mixture does vary with pressure. 

The two liquid phases can be regarded, the one as a solution of the component I. in component II., the other as a solution of component II. in component I. If the vapour phase be removed and the pressure on the two liquid phases be maintained constant (say, at atmospheric pressure), the system will still be univariant, and to each temperature there will correspond a definite concentration of the components in the two liquid phases and addition of excess of one will merely alter the relative amounts of the two solutions. As the temperature changes, the composition of the two solutions will change, and there will therefore be obtained two solubility curves, one showing the solubility of component I. in component IL, the other showing the solubility of component II. in component I. Since heat may be either evolved or absorbed when one liquid dissolves in another, the solubility may diminish or increase with rise of temperature (theorem of Lc Chatelier, p. i8). The two solutions which at a given temperature coexist in equilibrium are known as conjugate solutions. 

Specifying p (or T) eq 9.38 permits the calculation of the equilibrium temperature (or p) as function of ij. The curve T 1 ) at constant p or p l ) at constant T is called Equilibrium-Flash-Vaporization (EFV) curve. Knowing T, p and with eqs 9.36 and 9.37 the distribution functions for the phases L and Vmay be calculated.An analytical solution of the integral of eq 9.38 is only possible for 1 = 0, that is when the feed and liquid phases are equal, when the following assumptions hold (1), the distribution function of the given liquid phase has to be Gaussian and (2), the vapour pressure function p x, T) has to be calculated with a combination of Clausius-Clapeyron s equation and Trouton s rule. 

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