Vapor pressure discussion

Normal Boiling Temperature The normal boiling temperature (point) is the temperature at which the vapor pressure equals exac tly 101,325 Pa (1 atmosphere). Caution shomd be taken in using values from older references, where the temperature may be reported for the prevaihng pressure (0.95-0.97 atm) rather than at 1 atmosphere. If at least two values of vapor pressure very close to 1 atmosphere are available, the normal boihng point can be interpolated or extrapolated on a plot of logP vs. l/T. Tme section on vapor pressure discusses this in more detail. 

P the other terms provide corrections which at low or moderate pressure are close to unity. To use Equation (2), we require vapor-pressure data and liquid-density data as a function of temperature. We also require fugacity coefficients, as discussed in Chapter 3. 

Enthalpies are referred to the ideal vapor. The enthalpy of the real vapor is found from zero-pressure heat capacities and from the virial equation of state for non-associated species or, for vapors containing highly dimerized vapors (e.g. organic acids), from the chemical theory of vapor imperfections, as discussed in Chapter 3. For pure components, liquid-phase enthalpies (relative to the ideal vapor) are found from differentiation of the zero-pressure standard-state fugacities these, in turn, are determined from vapor-pressure data, from vapor-phase corrections and liquid-phase densities. If good experimental data are used to determine the standard-state fugacity, the derivative gives enthalpies of liquids to nearly the same precision as that obtained with calorimetric data, and provides reliable heats of vaporization. 

An apparent systematic error may be due to an erroneous value of one or both of the pure-component vapor pressures as discussed by several authors (Van Ness et al., 1973 Fabries and Renon, 1975 Abbott and Van Ness, 1977). In some cases, highly inaccurate estimates of binary parameters may occur. Fabries and Renon recommend that when no pure-component vapor-pressure data are given, or if the given values appear to be of doubtful validity, then the unknown vapor pressure should be included as one of the adjustable parameters. If, after making these corrections, the residuals again display a nonrandom pattern, then it is likely that there is systematic error present in the measurements. ... 

These were converted from vapor pressure P to fugacity using the vapor-phase corrections (for pure components), discussed in Chapter 3 then the Poynting correction was applied to adjust to zero pressure ... 

Bikerman [179] has argued that the Kelvin equation should not apply to crystals, that is, in terms of increased vapor pressure or solubility of small crystals. The reasoning is that perfect crystals of whatever size will consist of plane facets whose radius of curvature is therefore infinite. On a molecular scale, it is argued that local condensation-evaporation equilibrium on a crystal plane should not be affected by the extent of the plane, that is, the crystal size, since molecular forces are short range. This conclusion is contrary to that in Section VII-2C. Discuss the situation. The derivation of the Kelvin equation in Ref. 180 is helpful. 

The present discussion is restricted to an introductory demonstration of how, in principle, adsorption data may be employed to determine changes in the solid-gas interfacial free energy. A typical adsorption isotherm (of the physical adsorption type) is shown in Fig. X-1. In this figure, the amount adsorbed per gram of powdered quartz is plotted against P/F, where P is the pressure of the adsorbate vapor and P is the vapor pressure of the pure liquid adsorbate. 

Physical Properties. Sulfur dioxide [7446-09-5] SO2, is a colorless gas with a characteristic pungent, choking odor. Its physical and thermodynamic properties ate Hsted in Table 8. Heat capacity, vapor pressure, heat of vaporization, density, surface tension, viscosity, thermal conductivity, heat of formation, and free energy of formation as functions of temperature ate available (213), as is a detailed discussion of the sulfur dioxide—water system (215). 

The Class I binary diagram is the simplest case (see Fig. 6a). The P—T diagram consists of a vapor—pressure curve (soHd line) for each pure component, ending at the pure component critical point. The loci of critical points for the binary mixtures (shown by the dashed curve) are continuous from the critical point of component one, C , to the critical point of component two,Cp . Additional binary mixtures that exhibit Class I behavior are CO2—/ -hexane and CO2—benzene. More compHcated behavior exists for other classes, including the appearance of upper critical solution temperature (UCST) lines, two-phase (Hquid—Hquid) immiscihility lines, and even three-phase (Hquid—Hquid—gas) immiscihility lines. More complete discussions are available (1,4,22). Additional simple binary system examples for Class III include CO2—hexadecane and CO2—H2O Class IV, CO2—nitrobenzene Class V, ethane—/ -propanol and Class VI, H2O—/ -butanol. 

Critical Pressure The critical pressure of a compound is the vapor pressure of the compound at the critical temperature. Below the critical temperature, any compound above its vapor pressure will be a liquid. The critical pressure is required for calculations discussed in the part of the section on critical temperature. 

Correlation Methods Vapor pressure is correlated as a function of temperature by numerous methods mainly derived from the Clapeyron equation discussed in the section on enthalpy of vaporization. The classic simple equation used for correlation of low to moderate vapor pressures is the Antoine S equation (2-27). 

Liquid viscosity is accurately correlated as a function of temperature by the modified Riedel equation previously discussed for correlation of vapor pressure and shown by Eq. (2-96). 

An alternate method for flash point prediction is the method of Gmehling and Rasmussen and depends on the lower flammabihty limit (discussed later). Vapor pressure as a function of temperature is also required. The method is generally not as accurate as the preceding method as flammability limit errors are propagated. The authors have also extended the method to defined mixtures of organics. 

Cavitation and Flashing From the discussion on pressure recoveiy it was seen that the pressure at the vena contracta can be much lower than the downstream pressure. If the pressure on a hquid falls below its vapor pressure (p,J, the liquid will vaporize. Due to the effect of surface tension, this vapor phase will first appear as bubbles. These bubbles are carried downstream with the flow, where they collapse if the pressure recovers to a value above p,. This pressure-driven process of vapor-bubble formation and collapse is known as cavitation. 

Toluene is a notoriously poor electrical conductor even in grounded equipment it has caused several fires and explosions from static electricity. Near normal room temperature it has a concentration that is one of the easiest to ignite and, as previously discussed, that generates maximum explosion effects when ignited (Bodurtha, 1980, p. 39). Methyl alcohol has similar characteristics, but it is less prone to ignition by static electricity because it is a good conductor. Acetone is also a good conductor, but it has an equihbrium vapor pressure near normal room temperature, well above UFL. Thus, acetone is not flammable in these circumstances. 

General. With simple instrumentation discussed here, it is not possible to satisfactorily control the temperature at both ends of a fractionation column. Therefore, the temperature is controlled either in the top or bottom section, depending upon which product specification is the most important. For refinery or gas plant distillation where extremely sharp cut points are probably not required, the temperature on the top of the column or the bottom is often controlled. For high purity operation, the temperature will possibly be controlled at an intermediate point in the column. The point where AT/AC is maximum is generally the best place to control temperature. Here, AT/AC is the rate of change of temperature with concentration of a key component. Control of temperature or vapor pressure is essentially the same. Manual set point adjustments are then made to hold the product at the other end of the column within a desired purity range. The technology does exist, however, to automatically control the purity of both products. 

Note that for this discussion now, Pim, just above and in equations to follow, refers to the pure component vapor pressure of the immiscible liquid being distilled [127], When steam is added to the still [127] ... 

Treatment of Solutions by Statistical Mechanics. Since the vapor pressure is directly connected with the free energy, in the thermodynamic treatment the free energy is discussed first, and the entropy is derived from it. In the treatment by statistical mechanics, however, the entropy is discussed first, and the free energy is derived from it. Let us first consider an element that consists of a single isotope. When the particles share a certain total energy E, we are interested in the number of recog-... 

The advantages of vapor pressure as an index of moisture have been discussed. At the present time very few vapor pressure data are available for foods. It would be of great interest to measure vapor pressure concurrently with the moisture content in order to determine the usefulness of the vapor pressure in studies on the stability of dehydrated foods. 

From the condition 21a it immediately follows that if the clathrate is formed in the presence of a number of compounds which are potential solutes, i.e., sufficiently small to have 0 for some i, all these compounds contribute to its stability. As has already been pointed out by Barrer and Stuart4 this at once explains the stabilizing influence of "Hilfsgase" such as air, C02, or H2S on the formation of gas hydrates discussed by Villard49 and von Stackelberg and Meinhold.47 If there is only one solute, Eq. 21a with the = sign determines the minimum vapor pressure fiA necessary to make the clathrate stable relative to Qa. Since all cavities contribute to the stabilization, one cannot say that this minimum pressure is controlled by a specific type of cavity. 

Use the Third Law to calculate the standard entropy, S°nV of quinoline (g) p — 0.101325 MPa) at T= 298,15 K. (You may assume that the effects of pressure on all of the condensed phases are negligible, and that the vapor may be treated as an ideal gas at a pressure of 0.0112 kPa, the vapor pressure of quinoline at 298.15 K.) (c) Statistical mechanical calculations have been performed on this molecule and yield a value for 5 of quinoline gas at 298.15 K of 344 J K l mol 1. Assuming an uncertainty of about 1 j K 1-mol 1 for both your calculation in part (b) and the statistical calculation, discuss the agreement of the calorimetric value with the statistical... 

Vapor pressures of phases in these systems were measured by the Knudsen effusion technique. Use of mass spectrometer-target collection apparatus to perform thermodynamic studies is discussed. The prominent sublimation reactions for these phases below 2000 K was shown to involve formation of elemental plutonium vapor. Thermodynamic properties determined in this study were correlated with corresponding values obtained from theoretical predictions and from previous measurements on analogous intermetallics. 

Now let s discuss the pressure computations. The observed reactor pressure is a sum of the partial pressures of nitrogen and the styrene monomer vapor. The vapor pressure of the styrene vapor is an increasing function of temperature and decreasing function of conversion. This is explained by the Flory-Huggins relationship ( ). 

Thermodynamic energy terms (and equilibrium constants) may differ for compounds containing different isotopic species of an element. This effect is described in theoretical detail by Urey (1947), and applications to geochemistry are discussed by Broecker and Oversby (1971) and Faure (1977). A good example is the case of the vapor/liquid equilibrium for water. The vapor pressure of a lighter isotopic species, H2 0, is higher relative to that of heavier species, (or HD O), and others. 

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