Vapor pressure coefficient determination

Example 4.5 2-Propanol (isopropanol) and water form an azeotropic mixture at a particular liquid composition that results in the vapor and liquid compositions being equal. Vapor-liquid equilibrium for 2-propanol-water mixtures can be predicted by the Wilson equation. Vapor pressure coefficients in bar with temperature in Kelvin for the Antoine equation are given in Table 4.113. Data for the Wilson equation are given in Table 4.126. Assume the gas constant R = 8.3145 kJ-kmol 1-K 1. Determine the azeotropic composition at 1 atm. 

If the vapor pressure is determined by measurements in the free-molecule regime, then evaporation rate measurements in the continuum regime permit the diffusion coefficient to be determined from a single experiment in the carrier gas of interest and at the temperature of interest. 

The accurate determination of relative retention volumes and Kovats indices is of great utility to the analyst, for besides being tools of identification, they can also be related to thermodynamic properties of solutions (measurements of vapor pressure and heats of vaporization on nonpolar columns) and activity coefficients on polar columns by simple relationships (179). 

Values for many properties can be determined using reference substances, including density, surface tension, viscosity, partition coefficient, solubihty, diffusion coefficient, vapor pressure, latent heat, critical properties, entropies of vaporization, heats of solution, coUigative properties, and activity coefficients. Table 1 Hsts the equations needed for determining these properties. 

Selection of Solubility Data Solubility values determine the liquid rate necessaiy for complete or economic solute recoveiy and so are essential to design. Equihbrium data generally will be found in one of three forms (1) solubility data expressed either as solubility in weight or mole percent or as Heniy s-law coefficients, (2) pure-component vapor pressures, or (3) equilibrium distribution coefficients (iC values). Data for specific systems may be found in Sec. 2 additional references to sources of data are presented in this section. 

Because of the difficulties in determining x, the thickness of the film between the two vapor pressures, an overall transfer coefficient is introduced. Based on the two film theory, the overall transfer coefficient is used. In the case of water evaporation, the gas film is the controlling mechanism and the resulting equation is... 

The environmental fate of chemicals is determined by both chemical/physical and biological processes in turn, the operation of these processes is dependent on the properties of the environmental chemicals themselves. Polarity, vapor pressure, partition coefficients, and chemical stability are all determinants of movement and... 

Thus, if the saturated vapor pressure is known at the azeotropic composition, the activity coefficient can be calculated. If the composition of the azeotrope is known, then the compositions and activity of the coefficients at the azeotrope can be substituted into the Wilson equation to determine the interaction parameters. For the 2-propanol-water system, the azeotropic composition of 2-propanol can be assumed to be at a mole fraction of 0.69 and temperature of 353.4 K at 1 atm. By combining Equation 4.93 with the Wilson equation for a binary system, set up two simultaneous equations and solve Au and A21. Vapor pressure data can be taken from Table 4.11 and the universal gas constant can be taken to be 8.3145 kJ-kmol 1-K 1. Then, using the values of molar volume in Table 4.12, calculate the interaction parameters for the Wilson equation and compare with the values in Table 4.12. 

The permeation technique is another commonly employed method for determining the mutual diffusion coefficient of a polymer-penetrant system. This technique involves a diffusion apparatus with the polymer membrane placed between two chambers. At time zero, the reservoir chamber is filled with the penetrant at a constant activity while the receptor chamber is maintained at zero activity. Therefore, the upstream surface of the polymer membrane is maintained at a concentration of c f. It is noted that c f is the concentration within the polymer surface layer, and this concentration can be related to the bulk concentration or vapor pressure through a partition coefficient or solubility constant. The amount... 

Equation (5) is equivalent to stating that sublimation and subsequent transport of 1 g of water vapor into the chamber demands a heat input of 650 cal (2720 J) from the shelves. The vial heat transfer coefficient, Kv, depends upon the chamber pressure, Pc and the vapor pressure of ice, P0, depends in exponential fashion upon the product temperature, Tp. With a knowledge of the mass transfer coefficients, Rp and Rs, and the vial heat transfer coefficient, Kv, specification of the process control parameters, Pc and 7 , allows Eq. (5) to be solved for the product temperature, Tp. The product temperature, and therefore P0, are obviously determined by a number of factors, including the nature of the product and the extent of prior drying (i.e., the cake thickness) through Rp, the nature of the container through Kv, and the process control variables Pc and Ts. With the product temperature calculated, the sublimation rate is determined by Eq. (4). 

The order of the mobilities of alachlor, butylate, and metolachlor in columns of various soils was metolachlor > alachlor > butylate. This correlates directly with the water solubilities and inversely to the adsorption coefficients and octanol/water partition coefficients of these compounds. Diffusion of these compounds in soil thin-layers was as follows butylate > alachlor > metolachlor, which correlates directly with the vapor pressures of these compounds. Significant soil properties affecting diffusion appeared to be bulk density and temperature. Soil moisture is also probably important, but its effect on the diffusion of these compounds was not determined. 

A wide variety of solubilities (in units of g/m3 or the equivalent mg/L) have been reported. Experimental data have the method of determination indicated. In other compilations of data the reported value has merely been quoted from another secondary source. In some cases the value has been calculated. The abbreviations are generally self-explanatory and usually include two entries, the method of equilibration followed by the method of determination. From these values a single value is selected for inclusion in the summary data table. Vapor pressures and octanol-water partition coefficients are selected similarly. 

Boublik, T., Fried, V., Hala, E. (1984) The Vapor Pressure of Pure Substances, 2nd revised Edition, Elsevier, Amsterdam, The Netherlands. Bowman, B. T., Sans, W. W. (1983) Determination of octanol-water partitioning coefficient (KqW) of 61 organophosphorus and carbamate insecticides and their relationship to respective water solubility (S) values. J. Environ. Sci. Health B18, 667-683. Bradley, R. S., Cleasby, T. G. (1953) The vapour pressure and lattice energy of some aromatic ring compounds. J. Chem. Soc. 1953, 1690-1692. 

Wasik, S. P., Miller, M. M., Tewari, Y. B., May, W. E., Sonnefeld, W. J., DeVoe, H., Zoller, W. H. (1983) Determination of the vapor pressure, aqueous solubihty, and octanol/water partition coefficient of hydrophobic substances by coupled generator column/ liquid chromatographic methods. Res. Rev. 85, 29 42. 

Several techniques are available for measuring values of interaction second virial coefficients. The primary methods are reduction of mixture virial coefficients determined from PpT data reduction of vapor-liquid equilibrium data the differential pressure technique of Knobler et al.(1959) the Bumett-isochoric method of Hall and Eubank (1973) and reduction of gas chromatography data as originally proposed by Desty et al.(1962). The latter procedure is by far the most rapid, although it is probably the least accurate. 

Predicting sorption coefficients and hence the mobility of organic pollutants in aqueous-solid systems requires complete knowledge and analysis of various physical and chemical properties of such pollutants. This includes properties such as solubility, equilibrium vapor pressure, Henry s law constant, partition coefficient, as well as pKa and pKb values. Such properties can initially help determine the sorption-desorption behavior of organic pollutants once they are released, directly and/or indirectly, to the aqueous environment and then are in direct contact with solid phases. The following sections briefly summarize these properties. 

In order to obtain the solution desired, a value of Ts is assumed, the vapor pressure of A is determined from tables, and mAs is calculated from Eq. (6.98). This value of mAs and the assumed value of Ts are inserted in Eq. (6.97). If this equation is satisfied, the correct Ts is chosen. If not, one must reiterate. When the correct value of Ts and mAs are found, BT or BM are determined for the given initial conditions Tx or mAco. For fuel combustion problems, mAcc is usually zero however, for evaporation, say of water, there is humidity in the atmosphere and this humidity must be represented as mAco. Once BT and BM are determined, the mass evaporation rate is determined from Eq. (6.87) for a fixed droplet size. It is, of course, much preferable to know the evaporation coefficient (5 from which the total evaporation time can be determined. Once B is known, the evaporation coefficient can be determined readily, as will be shown later. 

Fischer, R.G. and Ballschmiter, K. Prediction of the environmental distribution of alkyl dinitrates - Chromatographic determination of vapor pressure p°, water solubility Sh2o, gas-water partition coefficient Kgw (Henry s law constant) and octanol-water partition coefficient K , FreseniusJ. Anal Chem., 360 769-776, 1998. 

Equation (105) is the basis for the determination of gas-phase diffusion coefficients and ultra low vapor pressures using the methods proposed by Davis and Ray (1977), Ravindran et al. (1979), and Ray et al. (1979). Additional information can be gained by writing the Chapman-Enskog first approximation for the gas-phase diffusivity (Chapman and Cowling, 1970),... 

For this reason, additional studies on carbon tetrachloride flux rates into and out of surface water, as well as refined quantitative estimates of aquatic fate processes would be valuable. The chemical is expected to evaporate rapidly from soil due to its high vapor pressure and may migrate into groundwater due to its low soil adsorption coefficient. No data are available on biodegradation in soil. Additional studies to determine degradation rates and the extent to which adsorption has occurred would be useful. These data are also useful in evaluating the impact of carbon tetrachloride leaching from hazardous waste sites. 

In this study, a thermodynamic framework has been presented for the calculation of vapor-liquid equilibria for binary solvents containing nonvolatile salts. From an appropriate definition of a pseudobinary system, infinite dilution activity coefficients for the salt-containing system may be estimated from a knowledge of vapor pressure lowering, salt-free infinite dilution activity coefficients, and a single system-dependent constant. Parameters for the Wilson equation may be determined from the infinite dilution activity coefficients. 

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