The vapour pressure of liquids

Let us now consider the vaporization of a liquid from the standpoint of the free-energy change on vaporization. The free energy of one mole of perfect vapour is given by 

As the liquid and its vapour are in equilibrium there is no change in free energy when a quantity of the liquid is vaporized. Thus G(g) = G(l) and 

This equation tells us that the vapour pressure of a liquid is determined by the free energy change when one mole ofliquid is vaporized to produce one mole of vapour at one atmosphere pressure. At the normal boiling point where the liquid is in equilibrium with its vapour at one atmosphere pressure. P = 1 and AGvap 0. (At other temperatures AG ap represents a hypothetical process but is, none the less, a very useful function.) 

To find the temperature variation of vapour pressure we use the Gibbs-Helmholtz equations derived earlier (Section 4.4). 

This is the Clausius-Clapeyron equation we derived in another way in the previous section. 

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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. 

The vapour pressure of liquid Hg at 433 K is 4.19 mm Hg. The free energy change accompanying the expansion of one... 

The existence of two polymorphs Was questioned by Weber,3 who maintained that the j8-form was a hydrate of sulphur trioxide, and this also was the conclusion arrived at by Berthoud,4 after determinations of the melting-points of the two forms, and of the vapour pressures of liquid sulphur trioxide. The latter investigator, however, described it as a hydrate unique in its remarkably small water content—estimated at less than 1 molecule per million molecules of trioxide. 

Few liquid mixtures are actually ideal over their entire composition range. Figure 33.2 illustrates two cases where the vapour pressure of liquid mixtures (solutions) deviate from Raoult s Law (Frame 32 and this frame, equations (33.3) and (33.4)) (positively A/B or negatively C/D) over the composition range but shows (see caption to figure) the end composition members (both representing cases of dilute solutions) do follow Raoult s Law for a limited, small, composition range. 

As the area is diminished below some thousands of sq. A., where the molecules cover only a small fraction of the surface, the surface pressure rapidly becomes much smaller than that of a perfect gas, and in the four acids with the longest chains becomes constant over a considerable region. The curves are indeed a very faithful reproduction of Andrews s curves for the relation between pressure and volume, for carbon dioxide, at temperatures near the critical. The horizontal regions in the curves correspond to the vapour pressure of liquids, and indicate the presence of an equilibrium between two surface phases, the vapour film, and islands of liquid, coherent film. 

Vapour Pressures.—The vapour pressures of liquid phosphorus are tabulated overpage in three sections, namely—... 

THE VAPOUR PRESSURES OF LIQUID PHOSPHORUS. (a) Liquid White Phosphorus. 

Thus at 279° C. the vapour pressure of liquid phosphorus is 753 mm., while at 289° C. that of red phosphorus is 23 mm.s The pressures of red phosphorus are not in equilibrium, but fall slowly as the solid changes into the more stable pyromorphic (violet) form. 

Tellurium—Kelley 59 quotes some data on the vapour pressure of liquid tellurium, but states that the composition of the vapour is uncertain. It has since been shown by Niwa i that tellurium vapour at a few hundred degrees is composed of diatomic molecules. The N.B.S. 529 derive from this Ai (Tc2 g) =41 kcal,... 

A differential manometer of the Rayleigh type ( 14.VII A) was used in accurate measurements of the vapour pressure of water, and a simple apparatus for measuring the difference in vapour pressures of two liquids was described by Lord Kelvin. Stock s vapour pressure thermometer ( 19.V1 Q can be used to measure the vapour pressures of liquids, including those at low temperatures. Special techniques are necessary for very small vapour pressures,... 

The expression shows that the vapour pressures of liquid phases act independently of each other within the miscibility gap. This relationship is the basis for steam distillation. Here components with high boiling points can be distilled close to the boiling point of water with a vapour composition according to their vapour pressure ... 

The vapour pressure of liquid COF j from the triple point to the normal boiling temperature is given by Equation (13.12) [1580] the experimental data from which this... 

Fig. 13.3 The vapour pressure of liquid COFj as a function of temperature, according...

The vapour pressure of liquid selenium was measured by a static method in the temperature range 823 to 1173 K. The total vapour pressure at equilibrium was given as log j(/i/bar) = 5.203 -4987 T. A third law evaluation by this review of the enthalpy... 

Fig. 4.4. Logarithm of the vapour pressure of liquid n-butane as a function of reciprocal temperature.

From determinations of the vapour pressures of liquid white phosphorus and of solid violet phosphorus, it was found that the vapour... 

Smits and Bokhorst, Proc. K, Akad. Wetensch. Amsterdam, 1914, 16, 1174 1914-15, 17, 678, 962, 973 1916, 18, 106 Z. physikal. Chem., 1916, 91, 249. Compare Jolibois, Compt. rend., 1909, 149, 287 1910, 151, 382. The vapour pressure of liquid white phosphorus in die range of temperature 44°-150° has been determined by Macrae and Voorhis (/. Amer. Chem. Soc, 1921, 43, 547), and the values found can be represented by the expression logic P (mm. Hg) 7 9542 — 2757 5 T, The values obtained are much lower than those extrapolated from the vapour-ptessure curve of Smits and Bokhorst. 

From a study of the vapour pressure of liquid methanol (Berka, L.H., Kildahl, N.K, Bergin, S.J. and Bums D.S. J. Chem. Ed., 71,441 (1994)) students observed the following results ... 

The vapour pressure of liquid radon at temperatures extending up to the critical temperature was measured by Whjdlaw-Gray and Ramsay (J. Chem. Soc. 1909, 95, 1073). These measurements are recorded in table 1. The last entry relates to the critical temperature Tg and pressure p. ... 

Figure 6 LaPlace equation for the vapour pressure of liquids and small radii...

Berzelius suggested that measurements of the pressures of water vapour over alkalis or hydroxides of alkaline earths, and comparison with the vapour pressures of liquid water, might provide a means to express every chemical affinity in numbers and compare it with the general measure, the weight, of a mechanical force . 

There exist three solid forms of SO3 called A, B and C. Only the A-form is stable, while B and C are not stable. The melting point of the A-form is 62°C, at which temperature the vapour pressure of liquid SO3 is 2.5 atmospheres. However, it appears that the A-form never crystallises from the liquid phase, that only forms if B crystals are present initially. These B-form crystals will in time (which might be very long) transform into A, therefore it is essential to prevent the formation of B crystals. 

We consider now the possibility of the presence of an additional phase, namely, liquid zinc. If the temperature of the reaction system is raised above T the pressure will rise above 1 atm. It is found that the displacement to the right in the chemical reactions causes the partial pressure of the zinc vapour to rise more rapidly, with increasing temperature, than the vapour pressure of liquid zinc. The vapour... 

Make an estimate of the vapour pressure of liquid carbon dioxide at 0 and indicate sources of incK curacy in the method used. 

A liquid X consists of an equilibrium mixture of a monomer, and a dimer, B, 2A B, At a particular temperature T the vapour pressure of liquid X, which may be assumed due to the monomer only, is and the equilibrium constant expressed in mole fraction units is K. At the same temperature the vapour pressure of a solvent C is pj. 

Solution According to Eq.(4.7b), the vapour pressure of liquid zinc may be expressed as... 

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