Critical point data, table

Table 14.8 Interaction Parameter Values from Binary Critical Point Data...

Tests of this prediction against experimental critical-point data of Table 2.4 reveal large deviations (e.g., an approximately 20% error even in the most favorable case of He) that reflect serious quantitative defects of the Van der Waals description. This is but one of many indications that the Van der Waals equation, although a distinct improvement over the ideal gas equation, is still a significantly flawed representation of real fluid properties. 

Ethanol takes part in a reaction at 300°C, with a partial pressure of 30 atm. Table 10.1 gives the critical point data, which are Tc=516 K, and Pc=63 atm. What is the fugacity under these conditions In this case we have reduced temperatuie=777 =573/516= 1.11, and reduced pressurc=/y/Jce=30/63=0.48. From Fig 7.7, we find y=f/P=0.92. Thus / =yP=27.6atm. 

We are interested in using the BACK equation for hydrogen mixtures. Therefore we have determined equation constants for hydrogen, and these are included in Table I. PVT data (7) at temperatures of 111-2778 K and pressures up to 1020 atm are used in this determination. Neither vapor-pressure nor critical-point data are used to avoid complications owing to quantum effects. It is found necessary to adopt an unusual value of the constant C of 0.241. With this C value the calculated pressure shows a relative root-mean-squared deviation of 0.5% and a relative bias of less than 0.1%. 

The naive model is not adequate. However, a bit more can be extracted from it. Table 2.6 quotes measurements of rj and x. Included are three estimates of d, two calculated from transport data using the expression for fj and X of Table 2.2. The third is determined from critical point data via the van der Waals boi since Vc = 3boand = iAo(4jrrf /3) then d = vJlnNo). In addition the mean free path is evaluated using (2.12) with the value of d determined from viscosity data. The estimates of d from transport and critical point data differ considerably. Nonetheless they are of the same order of magnitude, which suggests that the model is not unreasonable. 

Table 3.1 provides some theoretical correction factors for the van der Waals EOS, calculated based on the critical-point data. Although inconvenient to use, improved accuracy can be achieved by using empirically derived correction factors, rather than the theoretical values determined from Eqs. (3.3) and (3.4). Such data are available for many species but are rarely, if ever, needed in the study of fuel cells. 

Properties of Light and Heavy Hydrogen. Vapor pressures from the triple point to the critical point for hydrogen, deuterium, tritium, and the various diatomic combinations are Hsted in Table 1 (15). Data are presented for the equiUbrium and normal states. The equiUbrium state for these substances is the low temperature ortho—para composition existing at 20.39 K, the normal boiling point of normal hydrogen. The normal state is the high (above 200 K) temperature ortho—para composition, which remains essentially constant. 

Values converted and mostly rounded off from those of Goodwin, NBSIR 77-860, 1977. t = triple point c = critical point. The notation 3.O.—9 signifies 3.0 X 10 . Later tables for the same temperature range for saturation and for the superheat state from 0.1 to 1000 har, 85.5 to 600 K, were published by Younglove, B. A. and J. F. Ely, J. Fhys. Chem. Ref. Data, 16, 4 (1987) 685-721, but the lower temperature saturation tables contain some errors. 

Values converted from tables of Sbank, Theimodynarmc Propeities of UCON 245 Refiigerant, Union Carbide Corporation, New York, 1966. See also Sbank, ] Chem. Eng. Data, 12, 474 80 (1967). c = critical point. Tbe notation 6.46.—4 signifies 6.46 X 10" ... 

Values interpolated and converted from tables of Kang, McKetta, et al.. Bur. Eng. Res. Repr. 59, University of Texas, Austin, 1961. See also J. Chem. Eng. Data, 6 (1961) 220-227 and Am. Inst. Chem. Eng. ]., 7 (1961) 418. c = critical point. The notation 6.189.—4 signifies 6.189 X 10 . The AIChE publication contains a Mohier diagram to 4500 psia, 480 F, while the reprint contains saturation and superheat tables. 

Critical ( -values for p - 0.05 are available. " - In lieu of using these tables, the calculated -values can be divided by the appropriate Student s t(f, 0.05) and V2 and compared to the reduced critical -vdues (see Table 1.12), and data file QRED TBL.dat. A reduced -value that is smaller than the appropriate critical value signals that the tested means belong to the same population. A fully worked example is found in Chapter 4, Process Validation. Data file MOISTURE.dat used with program MULTI gives a good idea of how this concept is applied. MULTI uses Table 1.12 to interpolate the cutoff point for p = 0.05. With little risk of error, this table can also be used fo = 0.025 and 0.1 (divide q by t(/, 0.025) /2 respectively t f, 0.1) V 2, as appropriate. 

Table 5. Topological characteristics of the electron density in Ge at the bond (3,-1), cage (3,+3) and ring (3,+l) critical points. First row presents the ED results, second row presents the calculations based on model parameters, obtained by LAPW data. Characteristics of the...

If the potential parameters for the pure components are not found in the tables given in (Hll) and (Bll), and if viscosity and second virial data are not available for their determination, then for the Lennard-Jones (6-12) potential it is possible as a last resort to estimate these parameters from the properties of the substance at its critical point c, its melting point m, or its boiling point b these relations give /k in °K. and a in Angstrom units (1 A. = 10-3 cm.) ... 

Table 10.5 provides performance data regarding the SCWO process. Typical destruction efficiencies (DEs) for a number of compounds are also summarized in Table 10.5, which indicates that the DE could be affected by various parameters such as temperature, pressure, reaction time, oxidant type, and feed concentration. Feed concentrations can slightly increase the DE in supercritical oxidation processes. For SCWO, the oxidation rates appear to be first order and zero order with respect to the reactant and oxygen concentration, respectively. Depending upon reaction conditions and reactants involved, the rate of oxidation varies considerably. Pressure is another factor that can affect the oxidation rate in supercritical water. At a given temperature, pressure variations directly affect the properties of water, and in turn change the reactant concentrations. Furthermore, the properties of water are strong functions of temperature and pressure near its critical point. 

To this point we have applied the critical temperature to both viscosity and density calculations. Already this critical property Tc is seen as valued data to have for any hydrocarbon discrete single component or a mixture of components. It is therefore important to secure critical temperature data resources as much as practical. I find that a simple table listing these critical properties of discrete components is a valued data resource and should be made available to all. I therefore include Table 1.3 listing these critical component properties for 21 of our more common components. A good estimate can be made for most other components by relating them to the family types listed in Table 1.3. 

Table 3.3 Tpp data for liquid n-heptane along the saturation curve from the normal boiling point to the critical point. http //webbook.nist.gov/chemistry...

Supercritical fluids (SCFs) have long fascinated chemists and over the last 30 years this interest has accelerated. There is even a journal dedicated to the subject— the Journal of Supercritical Fluids. These fluids have many fascinating and unusual properties that make them useful media for separations and spectroscopic studies as well as for reactions and synthesis. So what is an SCF Substances enter the SCF phase above their critical pressures P and temperatures (Tc) (Figure 4.1). Some substances have readily accessible critical points, for example for carbon dioxide is 304 K (31 °C) and is 72.8 atm, whereas other substances need more extreme conditions. For example for water is 647 K (374 °C) and P is 218 atm. The most useful SCFs to green chemists are water and carbon dioxide, which are renewable and non-flammable. However, critical data for some other substances are provided for comparison in Table 4.1. In addition to reactions in the supercritical phase, water has interesting properties in the near critical region and carbon dioxide can also be a useful solvent in the liquid phase. Collectively, carbon dioxide under pressurized conditions (liquid or supercritical) is sometimes referred to as dense phase carbon dioxide. 

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