Vapour pressure curve

Figure A2.5.1. Schematic phase diagram (pressure p versus temperature 7) for a typical one-component substance. The full lines mark the transitions from one phase to another (g, gas liquid s, solid). The liquid-gas line (the vapour pressure curve) ends at a critical point (c). The dotted line is a constant pressure line. The dashed lines represent metastable extensions of the stable phases.

The vapour pressure of a liquid increases with rising temperature. A few typical vapour pressure curves are collected in Fig. 7,1, 1. When the vapour pressure becomes equal to the total pressure exerted on the surface of a liquid, the liquid boils, i.e., the liquid is vaporised by bubbles formed within the liquid. When the vapour pressure of the liquid is the same as the external pressure to which the liquid is subjected, the temperature does not, as a rale, rise further. If the supply of heat is increased, the rate at which bubbles are formed is increased and the heat of vaporisation is absorbed. The boiling point of a liquid may be defined as the temperature at which the vapour pressure of the liquid is equal to the external pressure dxerted at any point upon the liquid surface. This external pressure may be exerted by atmospheric air, by other gases, by vapour and air, etc. The boiling point at a pressure of 760 mm. of mercury, or one standard atmosphere, may be termed the normal boiling point. 

The reason for the constancy and sharpness of the melting j)oint of a pure crystalline solid can be appreciated upon reference to Fig. 7,10, 1, in which (a) is the vapour pressure curve of the solid and (6) that of the liquid form of the substance. Let us imagine a vessel, maintained at constant temperature, completely filled with a mixture of the above liquid and solid. The molecules of the solid can only pass into the liquid and the molecules of the liquid only into the solid. We may visualise two competitive processes taking place (i) the solid attempting to evaporate but it can only pass into the liquid, and (ii) the liquid attempting to distil but it can only pass into the solid. If process (i) is faster, the solid will melt, whereas if process (ii) proceeds with greater speed the... 

It is a well-known fact that substances like water and acetic acid can be cooled below the freezing point in this condition they are said to be supercooled (compare supersaturated solution). Such supercooled substances have vapour pressures which change in a normal manner with temperature the vapour pressure curve is represented by the dotted line ML —a continuation of ML. The curve ML lies above the vapour pressure curve of the solid and it is apparent that the vapour pressure of the supersaturated liquid is greater than that of the solid. The supercooled liquid is in a condition of metastabUity. As soon as crystallisation sets in, the temperature rises to the true freezing or melting point. It will be observed that no dotted continuation of the vapour pressure curve of the solid is shown this would mean a suspended transformation in the change from the solid to the liquid state. Such a change has not been observed nor is it theoretically possible. 

To understand the conditions which control sublimation, it is necessary to study the solid - liquid - vapour equilibria. In Fig. 1,19, 1 (compare Fig. 1,10, 1) the curve T IF is the vapour pressure curve of the liquid (i.e., it represents the conditions of equilibrium, temperature and pressure, for a system of liquid and vapour), and TS is the vapour pressure curve of the solid (i.e., the conditions under which the vapour and solid are in equili-hrium). The two curves intersect at T at this point, known as the triple point, solid, liquid and vapour coexist. The curve TV represents the... 

The horizontal isopiestic cuts the vapour-pressure curve of the solid in the first case, that of the liquid in the second. Melting can be brought about in case (1) by an increased pressure. 

The melting-point (T,p) curve (unlike a vapour-pressure curve of a liquid) does not end abruptly at a critical point (Ar = 0, L = 0) it is an endless curve, probably forming a closed loop ABCD, unless it intersects some other curve or the axes of co-ordinates. At high pressures it bends round towards the p axis, and according to Tammann, takes the shape indicated by the following considerations. It is known from experiment that (for substances of the wax-type) the melting-point increases with rise of pressure,... 

The incorrectness of Kegnault s conclusion was demonstrated by Kirchhoff in 1858 he proved that the vapour-pressure curves of solid and liquid are not continuous through the freezing-point, but are inclined at an angle. 

Kirchhoffs investigation does not show that the sublimation and evaporation curves meet each other at the temperature at which solid and liquid are in equilibrium with vapour it proves that they are inclined at an angle, but the further fact that they intersect requires separate proof, which was inferred by James Thomson, and experimentally demonstrated by Ferche (1891) in the case of benzene the point of intersection, calculated from the vapour-pressure curves, was 5 405° C, whereas the melting-point was 5 42° C. 

Nevertheless, we may still conclude that the vapour-pressure curves are similar, and do not intersect. 

That this value of T is greater for the solution than for the solvent, follows from the fact that the curve of the latter is intersected first, for the vapour-pressure curve of the solution (s s ) must lie beneath that of the pure solvent (ss) in the vicinity of the boiling-point. The corollary (1) to equation (7) below extends this conclusion over the whole length of t. u... 

Thus the vapour-pressure curves of the solution and solvent are similar and similarly situated, i.c., if we know the form of the vapour-pressure curve of the pure solvent, those of all the solutions are also known. 

Let AA BB represent portions of the vapour-pressure curves p of pure solvent and solution, respec-... 

Let OA, AS represent the vapour-pressure curves of the ice and liquid solvent respectively, BS that of the dilute solution. AC is the vapour-pressure curve of supercooled liquid. T0 is the freezing-point of pure solvent, T that of the solution. Along CS, OA we have /... 

If the total pressure of the vapour at constant temperature is represented as a function of the compositions of the two phases, the p-liquid and p-vapour curves are obtained. The p-liquid curves—that is, the curves representing the total vapour pressures of liquid binary mixtures as functions of the composition of the liquid phase—are most important they are usually referred to simply as the vapour-pressure curves of the mixture. Each curve is an isotherm. 

It therefore follows that a transition from a rising to a falling part of a vapour pressure curve can occur only when the concentration of a specified component in the vapour is neither greater... 

The vapour-pressure curves of binary liquid mixtures have been considered from another point of view by Dolezalek (Zeitscher. physik. Chem. 64, 727, (1908)), who starts out with the very simple assumption that the partial pressure of each component is proportional to its concentration in the liquid phase, provided no chemical change occurs when the liquids are mixed, and that neither component is polymerised in the liquid state. Thus ... 

Vapour-Pressure Curves of Partially Miscible Liquids. 

The vapour-pressure curves for such mixtures as ether and water consist of three parts ... 

According to Nernst, the vapour-pressure curves of different substances can be represented over a considerable range by means of the empirical equation ... 

Kinetic, energy, 24 theory of dissipation, 87 theory of gases, 515 theory of solids, 517 theories in thermodynamics, 513 Kirchoff s equation for effect of temperature, 112, 259 equations for vapour-pressure, 179, 190, 192, 390, 412 Konowalow s theorem, 385, 407 vapour-pressure curves, 382... 

For a system that obeys Raoult s law, show that the relative volatility aAB is PA/PB, where PA and P% are the vapour pressures of the components A and B at the given temperature. From vapour pressure curves of benzene, toluene, ethyl benzene and of o, m- and / -xylenes, obtain a plot of the volatilities of each of the materials relative to m-xylene in the range 340-430 K. 

On the Theory of Steam Distillation.—The ideal case occurs when the substance to be distilled is insoluble, or, more accurately, sparingly soluble in water (examples toluene, bromobenzene, nitrobenzene) so that the vapour pressures of water and the substance do not affect each other, or hardly so. The case of substances which are miscible with water (alcohol, acetic acid) is quite different and involves the more complicated theory of fractional distillation. Let us consider the first case only and take as our example bromobenzene, which boils at 155°. If we warm this liquid with water, its vapour pressure will rise in the manner shown by its own vapour pressure curve and independently of that of water. Ebullition will begin when the sum of the vapour pressures of the two substances has become equal to the prevailing atmospheric pressure. This is the case, as we can find from the vapour pressure curves, at 95-25° under a pressure of 760 mm. 

Accordingly, if the vapour pressure curve of a substance not miscible with water is known, it is easy to calculate approximately its degree of volatility with steam. The calculation is approximate only because the condition of mutual insolubility is hardly ever fulfilled. 

The equation-of-state method, on the other hand, uses typically three parameters p, T andft/for each pure component and one binary interactioncparameter k,, which can often be taken as constant over a relatively wide temperature range. It represents the pure-component vapour pressure curve over a wider temperature range, includes the critical data p and T, and besides predicting the phase equilibrium also describes volume, enthalpy and entropy, thus enabling the heat of mixing, Joule-Thompson effect, adiabatic compressibility in the two-phase region etc. to be calculated. 

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