Vapor pressure estimating from

Two estimates will be made using vapor pressure data from the CRC Handbook [63] and the integrated form of Clausius-Clapeyron equation ... 

The constants in this equation differ slightly from those in the reference because more data were used to obtain the latter. Vapor pressure estimates do not differ greatly, however 7.39 X 10"3mm. for 2,4-D methyl ester and 1.61 X 10 3 for n-propyl 2,4,5-T. 

Biomass tars are known to be very complex mixtures which contain significant amounts of polar compounds that can potentially form hydroxyl bonds. This means that current vapor pressure estimation techniques are not only difficult to apply, but are inaccurate for mixtures with significant oxygen functionalities. Therefore we have chosen to approach this problem from an experimental standpoint. 

Using the Antoine equation for vapor pressure, estimate the acentric factor for isobutane from Equation (4-68) and compare it to the value tabulated in Appendix I. 

If the chemical of interest is a solid, it sublimates to pose its vapor pressure. The sublimation process can be viewed as the sum of processes of a hypothetical fusion (melting) to liquid and vaporization from liquid to gas at given temperature and pressure. Such liquid, of course, is hypothetical because it may not exist at the given condition. The vapor pressure of this hypothetical liquid, Pp, rather than the true vapor pressure of the solid, Pg, is often generated by various vapor pressure estimation models. Pg can be converted to liquid vapor pressure Pp using the fugacity ratio F ... 

When a vapor pressure estimate is not available from the literature, it can be estimated approximately using Trouton s rule, which is that the entropy of vaporization is 21.2 times the boiling temperature (K) in cal/mol, i.e., the entropy of vaporation at the normal boiling point is 21.2 cal/mol K. An integrated form of... 

Therefore, the average deviations are less important for a vapor pressure estimation method than the number of substances where the method fails completely. In this area, a simple estimation procedure based on the vapor pressure equation of Hoffmann and Florin [34] has proved to be more appropriate than various methods from the literature [35-37] that are based on corresponding states or group contributions. The equation of Hoffmann-Florin is based on the charts developed by Cox [38]. Cox charts are constructed in a way that for some reference fluids the scale of the abscissa is adjusted to make the vapor pressure curve in a log P -T-diagram a straight line. The Hoffmann-Florin equation has two adjustable parameters o and P ... 

Figure 5.12 Estimated normal boiling point temperatures, of [C Cjim][Nty ionic liquids as a function of alkyl side chain length, n. O, 3" using the Eotvos equation with the data under discussion [26] , using the Guggenheim equation with the data under discussion [26] A, using the Guggenheim equation with data from [1] , using the Clausius-Clapeyron relation with experimental vapor pressure values from [33-35].

We might try to estimate the Henry s law constant by extrapolating the vapor-pressure curve from the critical point, but the extrapolation is so large and thus uncertain that instead we normally use the experimental concentration values for dissolved gases, plotted as in Figure 3.9 this topic is discussed again in Chapter 9. 

This example illustrates the advantages and disadvantages of the C-C equation. Using it, one can very easily make useful vapor-pressure estimates. This example shows a 30-fold extrapolation from the input pressure (100 psia) with only an 11% error. For many applications, this is adequate. 

The accentric factor is used exclusively in making corresponding-states estimates of PvT, EOSs that estimate PvT, and other thermodynamic properties derived from PvT. It is almost never used in making vapor-pressure estimates, and will not be used again in this chapter. 

Mathematical Consistency. Consistency requirements based on the property of exact differentials can be apphed to smooth and extrapolate experimental data (2,3). An example is the use of the Gibbs-Duhem coexistence equation to estimate vapor mole fractions from total pressure versus Hquid mole fraction data for a binary mixture. 

In order to ensure thermodynamic consistency, in almost all cases these properties are calculated from Tr. and the vapor pressure and liquid density correlation coefficients listed in those tables. This means that there will be slight differences between the values listed here and those in the DIPPR tables. Most of the differences are less than 1%, and almost all the rest are less than the estimated accuracy of the quantity in question. 

Critical temperature and pressure are reqmred and can be estimated from the methods of this section. Vapor pressure is predicted by the methods of the next section. Experimental values should be used if available. The acentric factor is used as a third parameter with and... 

When criticals cannot he estimated with reasonable accuracy, the method of Maxwell and BonnelP is recommended. The normal boiling point and the specific gravity at 60 F (15.5 C) are required inputs. According to what vapor pressure range is expected, the vapor pressure is calculated from Eqs. (2-34), (2-35), or (2-36). If the wrong range is selected, the procedure will need to be repeated. 

An analytical method for the prediction of compressed liquid densities was proposed by Thomson et al. " The method requires the saturated liquid density at the temperature of interest, the critical temperature, the critical pressure, an acentric factor (preferably the one optimized for vapor pressure data), and the vapor pressure at the temperature of interest. All properties not known experimentally maybe estimated. Errors range from about 1 percent for hydrocarbons to 2 percent for nonhydrocarbons. 

Single-Effect Evaporators The heat requirements of a singleeffect continuous evaporator can be calculated by the usual methods of stoichiometry. If enthalpy data or specific heat and heat-of-solution data are not available, the heat requirement can be estimated as the sum of the heat needed to raise the feed from feed to product temperature and the heat required to evaporate the water. The latent heat of water is taken at the vapor-head pressure instead of at the product temperature in order to compensate partiaUv for any heat of solution. If sufficient vapor-pressure data are available for the solution, methods are available to calculate the true latent heat from the slope of the Diihriugliue [Othmer, Ind. Eng. Chem., 32, 841 (1940)]. 

The iC values (vapor-liquid equihbrium ratios) in Equation (13-123) are estimated from the same equation-of-state or aclivity-coefficient models that are used with equilibrium-stage models. Tray or packed-section pressure drops are estimated from suitable correlations of the type discussed by Kister (op. cit.). 

The vapor pressure (VP) can be used in conjunction with a measured LEE to estimate flash point. When this is done it is usually found that the calculated flash point is less than the measured value owing to limitations in the flash point test technique (5-1.1.1). Conversely, the LEE can be estimated only approximately from the flash point. The VP can also be used to replace the 10... 

Since a portion of the liquid was vaporized to the vapor space, the hq uid will have lost some of its lighter components. This effectively changes the composition of the liquid and yields a slightly lower s apor pressure than the true vapor pressure of the liquid at 100°F. Figure 6-6 can be used to estimate true vapor pressure at any temperature from a known RVP. 

To estimate the desired composition of the bottom liquid, the vapor pressures of the different components at 100°F can be assumed to be a measure of the volatility of the component. Thus, if a split of n-C4 is assumed, the mole fraction of each component in the liquid can be estimated from ... 

Eq values may be calculated from Figure 8-29 or assumed at 20 to 50% as an estimating value for hydrocarbon oil and vapors, pressures atmospheric to 800 psig, and temperatures of 40°F to 130°F (see Thble 8-11). 

Carbon was estimated by a variation of the Van Slyke method.(2) A 30-100 mg sample was heated for 30 minutes with 0.5 g K2Cr207, lg KIOj, 10 mL 20% fuming H2S01( and 5 mL HjPO in a closed flask swept by a purified N2 stream. The N2 stream carried the evolved C02 to an absorption solution of 0.5M Na0H-0.3M N H. After the wet combustion, the absorbed C02 was released from an aliquot of the NaOH solution with lactic acid in a manometric apparatus. Corrections were applied for the vapor pressure of water and for reagent blank. 

---