Critical properties volume

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. 

Critica.1 Properties. Several methods have been developed to estimate critical pressure, temperature, and volume, U). Many other properties can be estimated from these properties. Error propagation can be large for physical property estimations based on critical properties from group contribution methods. Thus sensitivity analyses are recommended. The Ambrose method (185) was found to be more accurate (186) than the Lyderson (187) method, although it is computationally more complex. The Joback and Reid method (188) is only slightly less accurate overall than the Ambrose method, and is more accurate for some specific substances. Other methods of lesser overall accuracy are also available (189,190) (T, (191,192) (T, P ),... 

Some of the other critical properties defined by the industry include volume resistivity, dielectric dissipation factor, insulative resistance and the like. 

Critical properties of gaseous compounds are useful in determining the P-V-T (Pressure-Volume-Temperalure) properties at nonideal conditions. The compressibility faetor Z is defined by the following relationship ... 

Upon completion of data collection, estimation of the critical properties for the remaining compounds was performed using the group contribution method of Joback as given by Reid, Prausnitz and Poling (24). A comparison of the estimates with experimental data was favorable with average absolute errors of only 0.9%, 6.3 %, and 4.4% for critical temperature (465 compounds), pressure (453 compounds) and volume (345 compounds). 

To model the solubility of a solute in an SCF using an EOS, it is necessary to have critical properties and acentric factors of all components as well as molar volumes and sublimation pressures in the case of solid components. When some of these values are not available, as is often the case, estimation techniques must be employed. When neither critical properties nor acentric factors are available, it is desirable to have the normal boiling point of the compound, since some estimation techniques only require the boiling point together with the molecular structure. A customary approach to describing high-pressure phenomena like the solubility in SCFs is based on the Peng-Robinson EOS [48,49], but there are also several other EOS s [50]. 

Critical Properties. The critical temperature, pressure and volume for methylamine, nitrous oxide and their binary mixtures were experimentally determined and have been previously reported (34). The critical temperatures of the mixtures are intermediate between those of the pure components (Tc methylamine = 156.9°C Tc nitrous oxide = 36.5°C). The critical pressure goes through a maximum between the pure component values (Pc methylamine = 7.43 bar Pc nitrous oxide = 72.4 bar). The maximum (92.5 bar) is observed at about 46 wt.% methylamine content. The extraction conditions reported in the present study are all above the critical T and P of the fluids used. 

Figure 14.7 Schematic representation of the different types of binary (liquid + liquid) phase equilibria, showing the effect of p, T, and x on the two-phase volume. Examples are known for all except figures (k), (o), and (s). Reproduced with permission from G. M. Schneider, High-pressure Phase Diagrams and Critical Properties of Fluid Mixtures , M. L. McGlashan, ed., Chapter 4 in Chemical Thermodynamics, Vol. 2, The Chemical Society, Burlington House, London, 1978.

Since pressure, volume, and temperature are related to the corresponding critical properties, the function connecting the reduced properties becomes the same for each substance. The reduced property is expressed as a fraction of the critical property. 

Calculate the volume using Kay s method. In this method, V is found from the equation V = ZRT/P, where Z, the compressibility factor, is calculated on the basis of pseudocritical constants that are computed as mole-fraction-weighted averages of the critical constants of the pure compounds. Thus, T = Z K, 71, and similarly for Pc and Z, where the subscript c denotes critical, the prime denotes pseudo, the subscript i pertains to the ith component, and Y is mole fraction. Pure-component critical properties can be obtained from handbooks. The calculations can then be set out as a matrix ... 

The bond graph method of network thermodynamics is widely used in studying homogeneous and heterogeneous membrane transport. Electroosmosis and volume changes within the compartments are the critical properties in the mechanism of cell membrane transport, and these properties can be predicted by the bond graph method of network thermodynamics. In another study, a network thermodynamics model was developed to describe the role of epithelial ion transport. The model has four membranes with series and parallel pathways and three transported ions, and simulates the system at both steady-state and transient transepithelial electrical measurements. 

The compilations of CRC (1-2), Daubert and Danner (3), Dechema (15), TRC (13-14), Vargaftik (18), and Yaws (19-36) were used extensively for critical properties. Estimates of critical temperature, pressure, and volume were primarily based on the Joback method (10-12) and proprietary techniques of the author. Critical density was determined from dividing molecular weight by critical volume. Critical compressibility factor was ascertained from application of the gas law at the critical point. Estimates for acentric factor were primarily made by using the Antoine equation for vapor pressure (11-12). 

The results are given in Table B. The initial entries in the table are physical and critical properties. This includes molecular weight, freezing point, boiling point, density, refractive index, and acentric factor for the physical properties. Critical temperature, pressure, volume, density, and compressibility factor are provided for the critical properties. 

Listed here for various chemical species are values for the molar mass (molecular weight), acentric factor >, critical temperature Tc, critical pressure Pc, critical compressibilityfactor Z., critical molar volume Vc, and normal boilingpoint T . Abstracted from Project 801, DIPPR , Design Institute for Physical Property Data of the American Institute of Chemical Engineers, they are reproduced with permission. The full data compilation is published by T. E. Daubert, R. P. Daimer, H. M. Sibul, and C. C. Stebbins, Physical and Thermodynamic Properties of Pure Chemicals Data Compilation, Taylor Francis, Bristol, PA, 1,405 chemicals, extant 1995. Included are values for 26 physical constants and regressed values of parameters in equations for the temperature dependence of 13 theniiodynamicand transport properties. 

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