Vapor Pressure in Binary Mixtures

After this short, general discussion, which will have given an idea of the orders of magnitude involved, it is time to pass on to the treatment of vapor pressure and osmotic pressure, their origin and measurement and the interpretation of the results obtained in this field. 

In accordance with the accepted concepts and mathematical methods of treatment discussed in the previous section, we must turn our attention particularly to the following question  

How does the fugacity (the tendency to escape) of the various components of a mixture change with the composition This fugacity / expresses quite generally the tendency to leave the liquid phase and to enter the gaseous one it is caused by the kinetic energy of the molecules and expresses to what extent the thermal motion has been able to overcome the forces which hold the liquid phase together.  

If we confine ourselves to a mixture of two components the theory requires that, in the state of equilibrium. 

In this equation Ni and Ns denote the mol fractions of the two components, while Fi and Fs are the partial molar free energies, 

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Smith, V.L. et al. (1980) Temporal variations in trihalomethane content of drinking water. Environ. Sci. Technol. 14, 190-196. Smyth, C.P., Enge., E.W. (1929) Molecular orientation and the partial vapor pressures of binary mixtures. I. Systems composed of normal liquids. J. Am. Chem. Soc. 51, 2646-2660. 

The phase diagrams shown in Figures 9.4—9.7 all have T and P monotonic in the compositions of both phases. Consequently, at any fixed pressure the mixture boiling points are bounded by the pure-component boiling points, and at any fixed temperature the mixture pressures are bounded by the pure-component vapor pressures. But binary mixtures can have T and P pass through extrema with composition. Consider the slope of an isothermal Px curve for a binary mixture in VLE,... 

Igoudjilene, O. Ait-Kad, A. Jose, J. Static measurements of the total vapor pressure of binary mixtures of butan-2-one with 1,1,2-trichloroethane or 1,2-dichloroethane in the temperature range from 263 K to 343 K ELDATA Int. Electron. J. Phys.-Chem. Data 1999,5, 135-142... 

D. Rectification in vertical wetted wall column with turbulent vapor flow, Johnstone and Pigford correlation =0.0.328(Wi) Wi P>vP 3000 < NL < 40,000, 0.5 < Ns. < 3 N=, v,.gi = gas velocity relative to R. liquid film = — in film -1 2 " [E] Use logarithmic mean driving force at two ends of column. Based on four systems with gas-side resistance only, = logarithmic mean partial pressure of nondiffusing species B in binary mixture. p = total pressure Modified form is used for structured packings (See Table 5-28-H). 

The normal boiling point of a binary liquid mixture is the temperature at which the total vapor pressure is equal to 1 atm. If we were to heat a sample of pure benzene at a constant pressure of 1 atm, it would boil at 80.1°C. Similarly, pure toluene boils at 110.6°C. Because, at a given temperature, the vapor pressure of a mixture of benzene and toluene is intermediate between that of toluene and benzene, the boiling point of the mixture will be intermediate between that of the two pure liquids. In Fig. 8.37, which is called a temperature-composition diagram, the lower curve shows how the normal boiling point of the mixture varies with the composition. 

Verevkin, S.R et al.. Thermodynamic properties of mixtures containing ionic liquids. Vapor pressures and activity coefficients of n-alcohols and benzene in binary mixtures with l-methyl-3-butyl-imidazolium bis(trifluoromethyl-sulfonyl)imide. Fluid Phase Equilib., 236, 222, 2005. 

Bamberger, A.G. Sieder, and G. Maurer. 2000. High-pressure (vapor + liquid) equilibrium in binary mixtures of (carbon dioxide + water or acetic acid) at temperatures from 313 to 353 K. /. Supercrit. Fluids 17 97-110. 

In Section A.l, the general laws of thermodynamics are stated. The results of statistical mechanics of ideal gases are summarized in Section A.2. Chemical equilibrium conditions for phase transitions and for reactions in gases (real and ideal) and in condensed phases (real and ideal) are derived in Section A.3, where methods for computing equilibrium compositions are indicated. In Section A.4 heats of reaction are defined, methods for obtaining heats of reaction are outlined, and adiabatic flame-temperature calculations are discussed. In the final section (Section A.5), which is concerned with condensed phases, the phase rule is derived, dependences of the vapor pressure and of the boiling point on composition in binary mixtures are analyzed, and properties related to osmotic pressure are discussed. 

If the components of a binary mixture are immiscible, the vapor pressure of the mixture is the sum of the vapor pressures of the two components, each exerted independently and not as a function of their relative concentrations in the liquid. This property is employed in steam distillation, a process particularly applicable to the separation of high boiling substances from non-volatile impurities. The steam forms a cheap and inert carrier. The principles of the process also apply to other immiscible systems. 

A modified local composition (LC) expression is suggested, which accounts for the recent finding that the LC in an ideal binary mixture should be equal to the bulk composition only when the molar volumes of the two pure components are equal. However, the expressions available in the literature for the LCs in binary mixtures do not satisfy this requirement. Some LCs are examined including the popular LC-based NRTL model, to show how the above inconsistency can be eliminated. Further, the emphasis is on the modified NRTL model. The newly derived activity coefficient expressions have three adjustable parameters as the NRTL equations do, but contain, in addition, the ratio of the molar volumes of the pure components, a quantity that is usually available. The correlation capability of the modified activity coefficients was compared to the traditional NRTL equations for 42 vapor—liquid equilibrium data sets from two different kinds of binary mixtures (i) highly nonideal alcohol/water mixtures (33 sets), and (ii) mixtures formed of weakly interacting components, such as benzene, hexafiuorobenzene, toluene, and cyclohexane (9 sets). The new equations provided better performances in correlating the vapor pressure than the NRTL for 36 data sets, less well for 4 data sets, and equal performances for 2 data sets. Similar modifications can be applied to any phase equilibrium model based on the LC concept. 

We shall now give a brief account of critical phenomena in the vaporization of a binary mixture. In this case it is convenient to consider the T, p diagram at constant composition (c/. fig. 16.5). For a pure substance we obtain simply the line AG which terminates at the critical point C. For a mixture of constant composition we have to consider two pressures, one corresponding to the liquid, and the other to the vapour at the same composition and temperature. These two pressures correspond to the points in fig. 13.6 where an ordinate at constant composition e.g. Xj FE) cuts the vaporization curve (G) and the condensation curve (H). (The vapour and liquid are not of course in equilibrium). As the temperature is raised the shape of the lenticular area of fig. 13.6 varies and finally decreases to zero. We thus obtain the curve FGKH of fig. 16.5 of which the branch from F to K corresponds to liquid and K to H to the vapour. The point K is the critical point at which the two phases are identical. Near to K there will also... 

The vapor pressure of pure zinc chloride was measured by Meyer et al. (1989). However, a more accurate value for vapor pressure at 450 C, i.e. 55.5 Pa, was given by Anthony and Bloom (1975), who determined the vapor pressure in the temperature range 450-625°C. Bloom et al. (1970) had determined that the addition of NaCl or KCl reduces the vapor pressure of ZnCl2. The vapor pressure of these binary mixtures was used to determine the activity coefficients of zinc chloride and alkali chloride. Haver et al. (1976) reported the weight loss of the bath for different electrolyte compositions and observed that when pure ZnCl2 was used, there was more loss the weight loss decreases with additions of FiCl, NaCl, and KCl. 

The Txy diagram is a convenient graphical method for summarizing vapor-liquid equilibrium (VLE) data at a particular pressure. For binary mixtures, we usually denote the mole fraction of the more volatile component as X in the liquid phase as as y in the vapor phase. For this particular choice of x and y, the Txy diagram will always slope downward as shown at right. 

Several types of pressure measurements can be taken. These include absolute pressure, where one side of the capsule is exposed to 0 psia in a sealed chamber. Gauge pressure is measured with one side of the capsule vented to atmosphere. Vapor pressure transmitter seals one side of the capsule, filling it with the chemical composition of the vapor to be measured. The vapor pressure in the sealed chamber is compared with the process pressure (at the same temperature). Ifequal, the compositions are inferred to be equal. This technique is used primarily for binary mixtures as multicomponent compositions have too many degrees of freedom. 

Dragoescu, D. Barhala, A. Vilcu, R. Isothermal vapor-liquid equilibria in binary mixtures of cyclohexane + propylbenzene by static total pressure method at temperatures from 303.15 K to 323.15 K ELDATA Int. Electron. J. Phys.-Chem. Data 1997, i, 85-90... 

Kaplan, S. L Monakhova, Z. D. Equilibrium in solutions. IV. Boiling temperatures at atmospheric pressure and vapor composition of binary mixtures of the chlorides of methane and ethane [Russ]. Zh. Obshch. Khim. 1937, 7, 2499-2512. 

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