Vapor phases

The PH2(PD2) radical was first detected by its electronic absorption bands between 3600 (3800) and 5500 A during flash photolysis of phosphane, PH3(PD3), with quartz UV [1, 2] (the bands represent a progression in the upper-state (A a ) behding frequency vi and were erroneously ascribed to emission in Phosphor C, 1965, p. 6). Many physical and chemical methods of H abstraction from PH3 have been applied since then together with various PH2 detection methods. These investigations are gathered in a table below. For PHD and PD2 formation, see the remarks below the table  

A few examples are given in the table below of reactions of PH3 with other atoms or radicals and of ion-molecule reactions, where PHg was not detected but was assumed to have been formed (abbreviations k = rate constant, f = vibrational excitation, MW = microwave, UHF = ul-trahlgh frequency, FP=flash photolysis, LIF=laser-induced fluorescence, MS=mass spectrometry, ICR = ion cyclotron resonance, FA = flowing afterglow). 

Another PHg source is benzylphosphane CgHsCHgPHg. Its thermal decomposition starts at 650 C [49] or 600°C [50] and was approximately complete at SSO C [49] or 800 C [50]. The PHg fragment was mass-spectrometrically detected following either electron impact [49] or photoionization with the Lyman-a line [50]. The formation of PHg was confirmed by its reaction with CH3 (from the simultaneous pyrolysis of ethyl nitrite) to CH3PH2 which was mass-spectrometrically detected [49]. 

The reaction of elemental phosphorus with hydrogen was also used for PH2 production. H atoms from MW-discharged H2 were passed over the red modification, and the resulting PH2 was detected by LIF [51, 52], IMF (intermodulated fluorescence) [27], or MW spectroscopy [14]. The reaction of phosphorus vapor with atomic or molecular hydrogen did not lead to any PH2 electronic emission [18]. Emission bands, which had been observed during the reaction of elemental P with atomic H, were first attributed to PH2 [53,54], but they were later shown to be due to HPO [55]. 

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The method proposed in this monograph has a firm thermodynamic basis. For vapo/-liquid equilibria, the method may be used at low or moderate pressures commonly encountered in separation operations since vapor-phase nonidealities are taken into account. For liquid-liquid equilibria the effect of pressure is usually not important unless the pressure is very large or unless conditions are near the vapor-liquid critical region. 

The detailed techniques presented here are based on particular models for the vapor phase (Hayden-O Connell) and for the liquid phase (UNIQUAC). However, our discussion of these techniques is sufficiently general to allow the use of other models, whenever the user prefers to do so. 

In vapor-liquid equilibria, if one phase composition is given, there are basically four types of problems, characterized by those variables which are specified and those which are to be calculated. Let T stand for temperature, P for total pressure, for the mole fraction of component i in the liquid phase, and y for the mole fraction of component i in the vapor phase. For a mixture containing m components, the four types can be organized in this way ... 

In vapor-liquid equilibria, it is relatively easy to start the iteration because assumption of ideal behavior (Raoult s law) provides a reasonable zeroth approximation. By contrast, there is no obvious corresponding method to start the iteration calculation for liquid-liquid equilibria. Further, when two liquid phases are present, we must calculate for each component activity coefficients in two phases since these are often strongly nonlinear functions of compositions, liquid-liquid equilibrium calculations are highly sensitive to small changes in composition. In vapor-liquid equilibria at modest pressures, this sensitivity is lower because vapor-phase fugacity coefficients are usually close to unity and only weak functions of composition. For liquid-liquid equilibria, it is therefore more difficult to construct a numerical iteration procedure that converges both rapidly and consistently. 

In Chapter 2 we discuss briefly the thermodynamic functions whereby the abstract fugacities are related to the measurable, real quantities temperature, pressure, and composition. This formulation is then given more completely in Chapters 3 and 4, which present detailed material on vapor-phase and liquid-phase fugacities, respectively. 

The calculation of vapor and liquid fugacities in multi-component systems has been implemented by a set of computer programs in the form of FORTRAN IV subroutines. These are applicable to systems of up to twenty components, and operate on a thermodynamic data base including parameters for 92 compounds. The set includes subroutines for evaluation of vapor-phase fugacity... 

For a vapor phase (superscript V) and a liquid phase (superscript L), at the same temperature, the equation of equilibrium... 

Equation (1) is of little practical use unless the fuga-cities can be related to the experimentally accessible quantities X, y, T, and P, where x stands for the composition (expressed in mole fraction) of the liquid phase, y for the composition (also expressed in mole fraction) of the vapor phase, T for the absolute temperature, and P for the total pressure, assumed to be the same for both phases. The desired relationship between fugacities and experimentally accessible quantities is facilitated by two auxiliary functions which are given the symbols (f... 

A rigorous relation exists between the fugacity of a component in a vapor phase and the volumetric properties of that phase these properties are conveniently expressed in the form of an equation of state. There are two common types of equations of state one of these expresses the volume as a function of... 

Equation (12), applicable at low or moderate pressures, is used in this monograph for typical vapor mixtures. However, when the vapor phase contains a strongly dimerizing component such as carboxylic acid. Equation (7) is not applicable and... 

In the calculation of vapor-liquid equilibria, it is necessary to calculate separately the fugacity of each component in each of the two phases. The liquid and vapor phases require different techniques in this chapter we consider calculations for the vapor phase. 

At pressures to a few bars, the vapor phase is at a relatively low density, i.e., on the average, the molecules interact with one another less strongly than do the molecules in the much denser liquid phase. It is therefore a common simplification to assume that all the nonideality in vapor-liquid systems exist in the liquid phase and that the vapor phase can be treated as an ideal gas. This leads to the simple result that the fugacity of component i is given by its partial pressure, i.e. the product of y, the mole fraction of i in the vapor, and P, the total pressure. A somewhat less restrictive simplification is the Lewis fugacity rule which sets the fugacity of i in the vapor mixture proportional to its mole fraction in the vapor phase the constant of proportionality is the fugacity of pure i vapor at the temperature and pressure of the mixture. These simplifications are attractive because they make the calculation of vapor-liquid equilibria much easier the K factors = i i ... 

The fugacity fT of a component i in the vapor phase is related to its mole fraction y in the vapor phase and the total pressure P by the fugacity coefficient ... 

The fugacity coefficient is a function of temperature, total pressure, and composition of the vapor phase it can be calculated from volumetric data for the vapor mixture. For a mixture containing m components, such data are often expressed in the form of an equation of state explicit in the pressure... 

Two additional illustrations are given in Figures 6 and 7 which show fugacity coefficients for two binary systems along the vapor-liquid saturation curve at a total pressure of 1 atm. These results are based on the chemical theory of vapor-phase imperfection and on experimental vapor-liquid equilibrium data for the binary systems. In the system formic acid (1) - acetic acid (2), <() (for y = 1) is lower than formic acid at 100.5°C has a stronger tendency to dimerize than does acetic acid at 118.2°C. Since strong dimerization occurs between all three possible pairs, (fij and not... 

Vapor-Phase Mole Fraction Propionic Acid... 

Conclusion Effect of Independent Variables on Vapor-Phase Nonideality... 

While vapor-phase corrections may be small for nonpolar molecules at low pressure, such corrections are usually not negligible for mixtures containing polar molecules. Vapor-phase corrections are extremely important for mixtures containing one or more carboxylic acids. 

As discussed in Chapter 3, at moderate pressures, vapor-phase nonideality is usually small in comparison to liquid-phase nonideality. However, when associating carboxylic acids are present, vapor-phase nonideality may dominate. These acids dimerize appreciably in the vapor phase even at low pressures fugacity coefficients are well removed from unity. To illustrate. Figures 8 and 9 show observed and calculated vapor-liquid equilibria for two systems containing an associating component. 

Figure 4-8. Vapor-liquid equilibria for a binary system where both components solvate and associate strongly in the vapor phase.

Using UNIQUAC, Table 2 summarizes vapor-liquid equilibrium predictions for several representative ternary mixtures and one quaternary mixture. Agreement is good between calculated and experimental pressures (or temperatures) and vapor-phase compositions. ... 

To illustrate calculations for a binary system containing a supercritical, condensable component. Figure 12 shows isobaric equilibria for ethane-n-heptane. Using the virial equation for vapor-phase fugacity coefficients, and the UNIQUAC equation for liquid-phase activity coefficients, calculated results give an excellent representation of the data of Kay (1938). In this case,the total pressure is not large and therefore, the mixture is at all times remote from critical conditions. For this binary system, the particular method of calculation used here would not be successful at appreciably higher pressures. 

Figure 13 presents results for a binary where one of the components is a supercritical, noncondensable component. Vapor-phase fugacity coefficients were calculated with the virial... 

In Equation (24), a is the estimated standard deviation for each of the measured variables, i.e. pressure, temperature, and liquid-phase and vapor-phase compositions. The values assigned to a determine the relative weighting between the tieline data and the vapor-liquid equilibrium data this weighting determines how well the ternary system is represented. This weighting depends first, on the estimated accuracy of the ternary data, relative to that of the binary vapor-liquid data and second, on how remote the temperature of the binary data is from that of the ternary data and finally, on how important in a design the liquid-liquid equilibria are relative to the vapor-liquid equilibria. Typical values which we use in data reduction are Op = 1 mm Hg, = 0.05°C, = 0.001, and = 0.003... 

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. 

Figure 3 presents results for acetic acid(1)-water(2) at 1 atm. In this case deviations from ideality are important for the vapor phase as well as the liquid phase. For the vapor phase, calculations are based on the chemical theory of vapor-phase imperfections, as discussed in Chapter 3. Calculated results are in good agreement with similar calculations reported by Lemlich et al. (1957). ... 

Finally, Table 2 shows enthalpy calculations for the system nitrogen-water at 100 atm. in the range 313.5-584.7°K. [See also Figure (4-13).] The mole fraction of nitrogen in the liquid phase is small throughout, but that in the vapor phase varies from essentially unity at the low-temperature end to zero at the high-temperature end. In the liquid phase, the enthalpy is determined primarily by the temperature, but in the vapor phase it is determined by both temperature and composition. 

The computation of pure-component and mixture enthalpies is implemented by FORTRAN IV subroutine ENTH, which evaluates the liquid- or vapor-phase molar enthalpy for a system of up to 20 components at specified temperature, pressure, and composition. The enthalpies calculated are in J/mol referred to the ideal gas at 300°K. Liquid enthalpies can be determined either with... 

This chapter presents quantitative methods for calculation of enthalpies of vapor-phase and liquid-phase mixtures. These methods rely primarily on pure-component data, in particular ideal-vapor heat capacities and vapor-pressure data, both as functions of temperature. Vapor-phase corrections for nonideality are usually relatively small. Liquid-phase excess enthalpies are also usually not important. As indicated in Chapter 4, for mixtures containing noncondensable components, we restrict attention to liquid solutions which are dilute with respect to all noncondensable components. 

Two generally accepted models for the vapor phase were discussed in Chapter 3 and one particular model for the liquid phase (UNIQUAC) was discussed in Chapter 4. Unfortunately, these, and all other presently available models, are only approximate when used to calculate equilibrium properties of dense fluid mixtures. Therefore, any such model must contain a number of adjustable parameters, which can only be obtained from experimental measurements. The predictions of the model may be sensitive to the values selected for model parameters, and the data available may contain significant measurement errors. Thus, it is of major importance that serious consideration be given to the proper treatment of experimental measurements for mixtures to obtain the most appropriate values for parameters in models such as UNIQUAC. 

The sum of the squared differences between calculated and measures pressures is minimized as a function of model parameters. This method, often called Barker s method (Barker, 1953), ignores information contained in vapor-phase mole fraction measurements such information is normally only used for consistency tests, as discussed by Van Ness et al. (1973). Nevertheless, when high-quality experimental data are available. Barker s method often gives excellent results (Abbott and Van Ness, 1975). 

At low pressures, it is often permissible to neglect nonidealities of the vapor phase. If these nonidealities are not negligible, they can have the effect of introducing a nonrandom trend into the plotted residuals similar to that introduced by systematic error. Experience here has shown that application of vapor-phase corrections for nonidealities gives a better representation of the data by the model, oven when these corrections... 

Figure 7-1. Incipient equilibrium vapor-phase compositions calculated with subroutine BUDET.

Convergence is usually accomplished in 2 to 4 iterations. For example, an average of 2.6 iterations was required for 9 bubble-point-temperature calculations over the complete composition range for the azeotropic system ehtanol-ethyl acetate. Standard initial estimates were used. Figure 1 shows results for the incipient vapor-phase compositions together with the experimental data of Murti and van Winkle (1958). For this case, calculated bubble-point temperatures were never more than 0.4 K from observed values. 

Cases 3 and 4 show strong vapor-phase nonidealities as well. 

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