Fugacity enhancement factor

The fugacity coefficient of thesolid solute dissolved in the fluid phase (0 ) has been obtained using cubic equations of state (52) and statistical mechanical perturbation theory (53). The enhancement factor, E, shown as the quantity ia brackets ia equation 2, is defined as the real solubiUty divided by the solubihty ia an ideal gas. The solubiUty ia an ideal gas is simply the vapor pressure of the sohd over the pressure. Enhancement factors of 10 are common for supercritical systems. Notable exceptions such as the squalane—carbon dioxide system may have enhancement factors greater than 10. Solubihty data can be reduced to a simple form by plotting the logarithm of the enhancement factor vs density, resulting ia a fairly linear relationship (52). 

The enhancement factor contains three terms supercritical phase, ideal behaviour of the pure component 2 in the vapour phase at the sublimation pressure, and the Poynting factor that describes the influence of the pressure on the fugacity of pure solid 2. 

The solubility data for naphthalene in ethylene and in CO2 are consistent with the data in Figure 3. The proper way to make the comparison is to use the enhancement factor instead of the solubility. The enhancement factor equals y2P/P2 which is simply the actual solubility divided by the solubility in an ideal gas. The enhancement factor removes the effect of vapor pressure which is useful for comparing fluids at constant reduced temperature but at different actual temperatures. In terms of the fugacity coefficient of the solute, 2, the enhancement factor is given by... 

Eqs. (l)-(3) show that the solubilities of sohds in an SCF depend among others on their fugacity coefficients (pf (pf and the calculations indicated that these coefficients were responsible for the large solubilities of solids in supercritical solvents. These solubilities are much larger than those in ideal gases, and enhancement factors of 10" -10 are not uncommon [1] they are, however, still relatively small and usually do not exceed several mole percent. Consequently, these supercritical solutions can be considered dilute and the expressions for the fugacity coefficients in binary and ternary supercritical mixtures simplihed accordingly. 

Note that the enhancement factor E has contributions from both the Poynting factor and the vapor-phase fugacity coefficient, both of which are important at high pressure, and that —> 1 as 7 —> 7 . 

The solubility and the enhancement factor are dependent on the interactions in the supercritical phase, but are also dependent on the properties in the solid phase. Equating the fugacities of the solid compound in both phases, and using the convention that component 2 is the solid solute. 

The numerator quantifies the effect of hydrostatic pressure on the fugacity of the solid phase. The exponential term is known as the Poynting correction (17). The denominator quantifies the fluid phase intermolecular interactions and density effects. Note that the enhancement factor is dependent on the solid volume as well as the interactions in the supercritical fluid. A solute with a large solid molar volume will have a larger enhancement factor than a solute with a smaller solid molar volume at the same temperature and pressure when the interactions in the supercritical phase are identical. To further understand the molecular interactions in supercritical fluids, it is interesting to decompose the enhancement factor into these two effects. We may define a fluid enhancement factor, Ep, and a Poynting enhancement factor, Ep,... 

Figure 12.12 Supercritical enhancement of the solubility of solid methane(l) in fluid hydro-gen(2) at 76 K. Points are experimental data of Hiza and Herring [8]. Solid line is from the ideal-gas law dashed line is the ideal-gas result corrected by a Poynting factor dash-dot line is the approximation (12.2.14) with the fugacity coefficient computed from the simple virial equation via (12.2.16). Figure after Chueh and Prausnitz [7].

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