Activity coefficient relations

This example is based on the model description of Sec. 3.3.4, and involves a multicomponent, semi-batch system, with both heating and boiling periods. The compositions and boiling point temperatures will change with time. The water phase will accumulate in the boiler. The system simulated is based on a mixture of n-octane and n-decane, which for simplicity will be assumed to be ideal but which has been simulated using detailed activity coefficient relations by Prenosil (1976). 

Can the species activity coefficients be calculated accurately An activity coefficient relates each dissolved species concentration to its activity. Most commonly, a modeler uses an extended form of the Debye-Hiickel equation to estimate values for the coefficients. Helgeson (1969) correlated the activity coefficients to this equation for dominantly NaCl solutions having concentrations up to 3 molal. The resulting equations are probably reliable for electrolyte solutions of general composition (i.e., those dominated by salts other than NaCl) where ionic strength is less than about 1 molal (Wolery, 1983 see Chapter 8). Calculated activity coefficients are less reliable in more concentrated solutions. As an alternative to the Debye-Hiickel method, the modeler can use virial equations (the Pitzer equations ) designed to predict activity coefficients for electrolyte brines. These equations have their own limitations, however, as discussed in Chapter 8. 

The first term in parentheses on the right side of equation 5.213 is the distribution coefficient (K ), and the second groups activity coefficients related to the mixing behavior of components in the two phases. The equilibrium constant is thus related to the interaction parameters of the two phases at equilibrium. For example, the equilibrium between two regular mixtures is defined as... 

Moreover, with the increase in the ionic strength a larger fraction of water molecules is bound to ion hydration sleeves, whereby a strong reduction of the concentration of free water molecules occurs and therefore the activity or the activity coefficient, related to 1kg of free water molecules, increases correspondingly. 

Note Equations like (2.6) and (2.8) can also be put in a form where molarity, molality, or some other concentrative unit is used rather than mole fraction. This means that /ie has another value, but—more important—it also affects the value of the (apparent) activity coefficient. For a very dilute solution, the differences tend to be negligible, but in other cases, the concentrative unit to which the activity coefficient relates should be stated. Naturally, the various kinds of concentration can be recalculated into each other see Appendix A.7. 

Next we can finally see how the activity coefficient relates to the Margules equations for this case. Recall from Chapter 9 that the partial molar quantity of one component in a binary solution can be obtained graphically from the tangent (as with the chemical potentials /j,b and /ta in the coexisting solutions of Figure 15.3a). From equation (9.6), the partial molar free energy or chemical potential of component A in a solution of A and B is given by... 

Separation Processes Equipment for Multiphase Contacting Thermodynamic Equilibrium Diagrams Phase Equilibria from Equations of State Equilibrium Properties from Activity Coefficient relations... 

How are activity coefficients related to the minimum work needed to separate a mixture into its pure components ... 

Here the N b denote the mole fraction of glycine in water and benzene, respectively, and the fs denote proportionality constants, (activity coefficients) relating activity to mole fraction. One of these constants may be arbitrarily chosen it is convenient to make the choice so that = 1 in a very dilute aqueous solutionf. At equilibrium (o ), = ag)g, and hence from (2) ... 

Medium effect (/" ) For solvents other than water the medium effect is the activity coefficient related to the standard state in water at zero concentration. It reflects differences in the electrostatic and chemical interactions of the ions with the molecules of various solvents. Solvation is the most significant interaction. 

Yc.i, Ym.i, and Yx,i are the activity coefficients related to concentrations expressed in molarities, molalities, and mole fractions, respectively. 

The infinite dilution activity coefficient relations for other common activity coefficient equations are shown in [1, p. 182]. 

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