Vapor pressure, corresponding-state expression

The explicit formula pxr — I = (1 — Pr)0 for reduced saturation density as a function of reduced pressure is proposed for the entire liquid-vapor saturation boundary. The expression A 1 depends on Pr p 0.35 depends weakly on Pr, corresponding at Pr = 1 to the critical exponent pc. The parameters A and ft can be related to the Pitzer factor o>. Special cases include the power law pr — 1 = C(1 — Tr)0c. . . and the low-pressure vapor equation prx0 = p0Pr The function A — Ac = g(Pr) is found from data to be a universal function for nonpolar substances. If Ac is correlated with o>, the formula takes on the corresponding-states form pr = /o,(Pr, to). This form predicted the density of saturated liquid and vapor with 0.4% and 0.9% accuracy, respectively, for 38 substances. 

It is important to note that in these calculations, it is assumed that the solute is in a dissolved form in both phases i.e., it is not present in sorbed, micelle, or colloidal forms. The concentrations must, of course, be less than the saturation values, which correspond to the solubility of the substance in the water phase and to the vapor pressure in the atmosphere. A convenient method of calculating Henry s constants is to express H as the ratio of the solute s saturation vapor pressure P as obtained from handbooks, to the solute s aqueous solubility C It is important that the state of the two phases (i.e., solid or liquid) be the same for both data. This has caused problems with PCBs in which the available solubility data tend to be those of the pure solid isomers, whereas the vapor pressure data are obtained by extrapolation from vapor pressures of liquid mixtures. It is essential that the two sets of data apply to the same solute physical condition. 

We have seen that a liquid exerts a characteristic vapor pressure [W Section 12.2]. When a nonvolatile solute (one that does not exert a vapor pressure) is dissolved in a liquid, the vapor pressure exerted by the liquid decreases. The difference between the vapor pressure of a pure solvent and that of the corresponding solution depends on the concentration of the solute in the solution. This relationship is expressed by Raoult s law, which states that the partial pressure of a solvent over a solution, Pu is given by the vapor pressure of the pure solvent. Pf, times the mole fraction of the solvent in the solution, X -... 

For a given temperature, pressure, and composition, the corresponding density and Z factor given by the equation of state is needed. The vapor root is found by solving the truncated virial equation of state (see Table 14-8) for Z, and for small values of BP/RT, the expression so obtained reduces to Z = 1 + BP/RT, that is,... 

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