Correlation of Vapor Pressure Data

The starting point for this purpose is the Clapeyron equation, developed in Chapter 4 (commonly referred to as the Clausius-Clapeyron equation)  

AV difference between saturated vapor and liquid molar volumes  

If we make the simple assumption that the group AHy/Az) is independent of temperature, then  

2 suggests that if a limited number of vapor pressure data is available, a linear plot of InP versus (l/T) can be used for inter- and extrapolation purposes. 

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This suggests that a plot of P against 1/T should yield a line having a local slope of (-A, /R). A straight line is obtained only when is nearly constant, i.e., over a narrow range of temperatures. An integrated version of the Clausius-Clapeyron equation finds use in correlation of vapor pressure data ... 

Myers, H.S., Fenske, M.R. (1955) Measurement and correlation of vapor pressure data for high boiling hydrocarbons, hid. Eng. Chem. 47, 1652-1658. 

More specific analysis of tars and correlations of vapor pressure data as a function of molecular weight or/and some chemical characteristics were beyond the scope of this presentation, although these are important considerations. Detailed pyrolysis models [Chen et al., 1998 Serio et al., 1994] include a tar vaporization step and use... 

Knowledge Required (1) The meaning of term vapor pressure. (2) The correlation of vapor pressure data with other physical properties. 

Correlation and compilation of vapor-pressure data for pure fluids. Normal and low pressure region. 

Compilation of vapor-pressure data for organic compounds data are correlated with the Antoine equation and graphs are presented. 

The correlations were generated by first choosing from the literature the best sets of vapor-pressure data for each fluid. 

Vapor pressure data tend to be, in general, accurate at pressures above 0.1 atm. At lower pressures the uncertainty increases. Thus at 1 mm Hg and below, errors of 10% and higher are typical. For a method of screening a large number of vapor pressure data and correlating them with see Wilsak and Thodos (1984) and for the latter only, Reid et al. 

An overview of some basic mathematical techniques for data correlation is to be found herein together with background on several types of physical property correlating techniques and a road map for the use of selected methods. Methods are presented for the correlation of observed experimental data to physical properties such as critical properties, normal boiling point, molar volume, vapor pressure, heats of vaporization and fusion, heat capacity, surface tension, viscosity, thermal conductivity, acentric factor, flammability limits, enthalpy of formation, Gibbs energy, entropy, activity coefficients, Henry s constant, octanol—water partition coefficients, diffusion coefficients, virial coefficients, chemical reactivity, and toxicological parameters. 

Mathematical Consistency Requirements. Theoretical equations provide a method by which a data set s internal consistency can be tested or missing data can be derived from known values of related properties. The abiUty of data to fit a proven model may also provide insight into whether that data behaves correctiy and follows expected trends. For example, poor fit of vapor pressure versus temperature data to a generally accepted correlating equation could indicate systematic data error or bias. A simple sermlogarithmic form, (eg, the Antoine equation, eq. 8), has been shown to apply to most organic Hquids, so substantial deviation from this model might indicate a problem. Many other simple thermodynamics relations can provide useful data tests (1—5,18,21). 

Corresponding states have been used in other equations. For example, the Peng-Robinson equation is a modified RedHch-Kwong equation formulated to better correlate vapor—Hquid equiHbrium (VLE) vapor pressure data. This equation, however, is not useful in reduced form because it is specifically designed to calculate accurate pressure data. Reduced equations generally presuppose knowledge of the pressure. 

Vapor pressure is the most important of the basic thermodynamic properties affec ting liquids and vapors. The vapor pressure is the pressure exerted by a pure component at equilibrium at any temperature when both liquid and vapor phases exist and thus extends from a minimum at the triple point temperature to a maximum at the critical temperature, the critical pressure. This section briefly reviews methods for both correlating vapor pressure data and for predicting vapor pressure of pure compounds. Except at very high total pressures (above about 10 MPa), there is no effect of total pressure on vapor pressure. If such an effect is present, a correction, the Poynting correction, can be applied. The pressure exerted above a solid-vapor mixture may also be called vapor pressure but is normallv only available as experimental data for common compounds that sublime. 

Figures 9-32A and B [98] illustrate the correlation of wet pressure drop and system vapor rate at various liquid rates for No. 2 Nutter rings however, other available data indicate that other sizes of Nutter rings, Pall rings, and selected other packing shapes correlate in the same manner.

Correlating ln(Pc /Pc), with vapor pressure data For isotopomer pairs with the vapor pressure and VPIE established near Tc, a thermodynamic consistency test between ln(Tc7Tc) and ln(Pc /Pc), and calculation of ln(Pc7Pc) from ln(Tc7Tc) is possible. The critical pressure of the heavier isotopomer at its critical temperature, Pc(Tc), can be calculated from the lighter, Pc,(Tc7 provided the vapor pressure of the lighter between Tc and Tc, the VPIE, and Tc and Tc are known. For Tc < Tc ... 

Isobaric data reduction is complicated by the fact that both composition and temperature vary from point to point, whereas for isothermal data composition is the only significant variable. (The effect of pressure on liquid-phase properties is assumed negligible.) Because the activity coefficients are strong functions of both liquid composition and T, which are correlated, it is quite impossible without additional information to separate the effect of composition from that of T. Moreover, the Pi sat values depend strongly on T, and one must have accurate vapor-pressure data over a temperature range. 

It often happens that tabulated vapor pressure data are not available at temperatures of interest, or they may not be available at all for a given species. One solution to this problem is to measure p at the desired temperatures. Doing so is not always convenient, however, especially if a highly precise value is not required. An alternative is to estimate the vapor pressure using an empirical correlation for p" T). Reid, Prausnitz, and Poling summarize and compare vapor pressure estimation methods, several of which are given in the paragraphs that follow. 

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. 

Balaban, A.T. and Feroiu, V. (1990). Correlation Between Structure and Critical Data of Vapor Pressures of Alkanes by Means of Topological Indices. Rep.Mol. Theory, 1,133-139. 

Ambrose, D., The Correlation and Estimation of Vapor Pressures, in Proceedings NPL Conference Chemical Thermodynamic Data on Fluids and Fluid Mixtures, September 1978, Guildford UK, p. 193, IPC Science Technology Press, 1979. 

If experimental vapor-pressure data are available for a span of temperatures, or a correlation is available, dp Jd can be evaluated in the vicinity of T. Furthermore, (Vg Vi) can be estimated solely from Vg if we neglect VJ hence for a nonideal gas... 

Inorganic molecules The simple correlation r = 1.64Ti, is recommended if the normal boiling point is known. Critical pressure is best obtained by extrapolating vapor pressure data to r , and is best obtained from a correlation of liquid density extrapolated to T. ... 

Expected uncertainty Varies significantly with temperature and with the quality and temperature range of the vapor pressure data used in the correlation. 

From the standpoint of physicochemical measurements, family and isothermal plots are useful for the determination of vapor pressures (and, in addition, recalling Equations 13 and 16, heats of vaporization as well) from the retention data obtained from just a few chromatographic runs (33). Furthermore, the GC technique is ideally suited to instances in which the solutes are available only in minute quantities or are substantially impure, where each of these constraints ordinarily precludes bulk vapor-pressure measurements by conventional static procedures. For example, Heath and Tumlinson (34) employed log(retention) plots to determine the vapor pressures of trace acetate ingredients used in pheromone formulations. An important aspect of their work was that family correlations were obtained with a chiral-nematic stationary phase, cholesteryl p-chlorocinnamate. 

Ktihne et al. [105] used MP and 23 structural parameters to correlate the vapor pressure of 1838 hydrocarbons and halogenated hydrocarbons. The neural network model was built using 1200 compounds and provided a mean absolute error of 0.13 log units for the test set of 638 compounds. It should be noted that the authors predicted vapor pressure as a function of the temperature and total number of data points for model development was 8148. The MP and BP are also used in MPBPVP program developed by Syracuse Research Inc [101]. 

PRSV equation for the substances considered here are given in Table 3.1.1 k of the PRSV equation is obtained by fitting pure component saturation pressure (P p) versus temperature data, A computer program to optimize k for a set of T versus / P data is provided on the diskette accompanying this monograph, and the program details are presented in Appendix D. The effect of this parameter on the accuracy of vapor pressure correlations for several fluids is shown in Figure 3.1.1. 

The Soave equation uses an additional parameter, the acentric factor, to correlate vapor pressure data. The acentric factor, co, had been deflned in earlier work as a parameter that correlates the deviation of the reduced vapor pressure of a particular compound from that of simple molecules. The reduced vapor pressure is correlated with the reduced temperature as follows ... 

This equation (Peng and Robinson, 1976) was developed with the goal of overcoming some of the deficiencies of the Soave equation, namely its inaccuracy in the critical region and in predicting liquid densities. The equation is similar to the Soave equation in that it is cubic in the volume, expresses its parameters in terms of the critical temperature, critical pressure, and acentric factor, and is based on correlating pure-component vapor pressure data. The equation is written as... 

An important consideration when using either method for VLE is the importance of correct prediction of the pure-component vapor pressures. For activity-coefficient models, this requires the direct use of a correlation for for EOS models, it may require (especially for polar fluids) fitting the a T) term in the EOS to vapor-pressure data. 

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