Pure-fluid saturation curve

In the context of van der Waals theory, a and b are positive parameters characterizing, respectively, the magnitude of the attractive and repulsive (excluded volume) intermolecular interactions. Use this partition function to derive an expression for the excess chemical potential of a distinguished molecule (the solute) in its pure fluid. Note that specific terms in this expression can be related to contributions from either the attractive or excluded-volume interactions. Use the Tpp data given in Table 3.3 for liquid n-heptane along its saturation curve to evaluate the influence of these separate contributions on test-particle insertions of a single n-heptane molecule in liquid n-heptane as a function of density. In light of your results, comment on the statement made in the discussion above that the use of the potential distribution theorem to evaluate pff depends on primarily local interactions between the solute and the solvent. 

Figures. Stability fields, calculated by the Anderko andPitzer equation of state of the HzO-NaCl system in a pressure-temperature diagram. Solid lines the saturation curve (LG) of pure water and the spinodal isopleths of p[fD-NaCl fluids (numbers refer to the mole fractions of NaCl). Dotted lines the liquid spinodal curve Sp(L, Hfd) and gas. spinodal curve Sp(G, HfJ) of pure water.

For a ptue substance, the fugadty depends on temperature, piessme, and phase. The locus of saturated liquid and saturated vapor states that satisfy both (8.2.18) and (8.2.19) forms the vapor-liquid saturation curve (also called the vapor pressure curve). Pure-fluid vapor pressures P increase with increasing T. But along the liquid branch... 

These conditions identify both vapor-liquid and liquid-liquid critical points. For vapor-liquid equilibria, they are satisfied when the spinodal coincides with the vapor-liquid saturation curve. However, that point need not occur either at the maximum in the saturation envelope or at the maximum in the spinodal see Figure 8.12. Along a spinodal the one-phase metastable system is balanced on the brink of an instability at a critical point that balance coincides with a two-phase situation and the resulting fluctuations cause critical opalescence, just as they do at pure-fluid critical points. 

For pure fluids, it is most common to represent the saturated vapor and saturated liquid transport properties as simple polynomial functions in temperature, although polynomials in density or pressure could also be used. Exponential expansions may be preferable in the case of viscosity (Bmsh 1962 Schwen Puhl 1988). For mixtures, the analogous correlation of transport properties along dew curves or bubble curves can be similarly regressed. In the case of thermal conductivity, it is necessary to add a divergent term to account for the steep curvature due to critical enhancement as the critical point is approached. Thus, a reasonable form for a transport property. 

Critical point For a pure substance, the upper limit of the vapor-liquid saturation curve where the equilibrium vapor and liquid phases become identical and the compressibility of the fluid becomes infinite. For water, the critical point occurs at a temperature of approximately 374°C and a pressure of approximately 22 MPa. 

Similarly, for the case when z— the two lines 6 and (R become a single line which is the curve of tensions of saturated vapor of fluid 2 in the pure state this line ends at the critical point C, of the fluid 2. 

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