Activity coefficient, calculation

To illustrate calculations for a binary system containing a supercritical, condensable component. Figure 12 shows isobaric equilibria for ethane-n-heptane. Using the virial equation for vapor-phase fugacity coefficients, and the UNIQUAC equation for liquid-phase activity coefficients, calculated results give an excellent representation of the data of Kay (1938). In this case,the total pressure is not large and therefore, the mixture is at all times remote from critical conditions. For this binary system, the particular method of calculation used here would not be successful at appreciably higher pressures. 

Mixture property Define the model to be used for liquid activity coefficient calculation, specify the binary mixture (composition, temperature, pressure), select the solute to be extracted, the type of phase equilibrium calculation (VLE or LLE) and finally, specify desired solvent performance related properties (solvent power, selectivity, etc.)... 

A comparison of trace mean activity coefficients calculated by the methods of Johnson and Pytkowicz (2) and Pitzer and Kim (8j. ... 

The individual activity coefficients calculated from (4.12), suitable for calibration of ISEs for chloride ions, the alkali metal and alkaline earth ions, are given in tables 4.1 and 4.2. Ion activity scales have also been proposed for KF [141], choline chloride [98], for mixtures of electrolytes simulating the composition of the serum and other biological fluids (at 37 °C) [106,107], for alkali metal chlorides in solutions of bovine serum albumine [132] and for mixtures of electrolytes analogous to seawater [140]. 

Fig. 39. Activity coefficients calculated from the data of Fig. 37 and from an additional set of data obtained from a duplicate run compared with the Gibbs-Duhem equation. Reprinted with permission from Allen, T. M., Taflin, D. C, and Davis, E. J., Ind. Eng. Chem. Res. 29, 682-690, Copyright 1990, American Chemical Society.

The Ga-In-Sb liquidus is examined in a similar way at 573°K. We assume x2 = X to be near unity and approximate the activity coefficients calculated... 

Figure 3. Activity coefficients calculated from polarized spheres model (T = 25 °C, D = 78.54)...

Figure 4. Recovery of the cube-root law activity coefficients calculated from polarized sphere model using coulombic and induced dipole terms.

To use activity coefficients, first solve the equilibrium problem with all activity coefficients equal to unity. From the resulting concentrations, compute the ionic strength and use the Davies equation to find activity coefficients. With activity coefficients, calculate the effective equilibrium constant K for each chemical reaction. K is the equilibrium quotient of concentrations at a particular ionic strength. Solve the problem again with K values and find a new ionic strength. Repeat the cycle until the concentrations reach constant values. 

Organic Matter (SOM) Phase Activity Coefficients Calculated from UNIFAC and ELBRO-FV... 

The values of some total ion activity coefficients calculated from different models can be checked when a solid composed of the same ions is equilibrated with a solution without substantially changing its composition. Under these circumstances the activity coefficient product can be determined by dividing the thermodynamic solubility product by the observed equilibrium concentration product. 

Example 5. Use the Raoult s law reference activity coefficients calculated for chloroform in Example 1 to calculate the activity coefficient of acetone at xchl = 0.508 in a chloroform-acetone solution. 

The other approach recommended by Mackay (2000) is a group contribution method to derive the molar activity coefficient, calculating the solubility (the AQUAFAC method, Myrdal et al. [1992 1993 1995]). 

Note the use of activities, as well as of an equilibrium constant based on activities. The kinetic constants for autocatalyzed and catalyzed reactions, k and k, were determined from initial reaction rates with liquid activity coefficients calculated by UNIQUAC. Near chemical equilibrium the fCT is about 6, while Kx is about 5. Table 8.7 gives activation energies and pre-exponential factors obtained by nonlinear regression. The simulation shows tbat the autocatalysis effect is neghgible below 150 °C, but it might increase to 20% at 180 °C. 

Since a molal activity coefficient has been calculated for the solute in the polymer phase and a molar activity coefficient calculated for the liquid phase Eq. (4-45) should be used to calculate the polymer/liquid partition coefficient ... 

TABLE 2.3. Single-Ion Activity Coefficients Calculated from the Extended Debye-Huckel Equation at 25°C... 

Compute logarithms of the activity coefficients from experimental X-Y data. Assuming an ideal vapor phase, the activity coefficients are given as y, = P 7, / X, P( > and y2 = PY2/X2 P2. The natural logarithms of the activity coefficients calculated using the preceding equations are shown in cols. 7 and 8 of Table 1.11. 

Calculate the Wilson constants for the ethanol/water system using the infinite-dilution activity coefficients calculated in the preceding example y,00 = 5.75 and y2°° = 2.48, with subscript 1 pertaining to ethanol. 

Table 1.12 Activity coefficient calculations for butanol(1)-water(2) system at 1 atm...

At 7 = 0.064 mol the single-ion activity coefficient calculated by the DH model is 8% lower than that calculated by the extended DH model. Now consider a solution which has an ionic strength of only 0.001 mol L . ... 

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