Equivalent ionic fraction

Ion-exchange equilibrium data are reported in the form of isotherms with the help of the equivalent ionic fraction in the solution (Figure 7.2) ... 

Another important term in this discussion is the equivalent ionic fraction of Al which can be written as... 

They will be different in cell I and cell II. Equation 34.14b, used to define the selectivity coefficient, can now be rewritten in terms of the equivalent ionic fraction as follows ... 

The ion-exchange capacity of the membranes is determined using the standard protocols [36]. Equilibrium data for equivalent ionic fractions of Al " " and in the aqueous phase and the corresponding fraction in the membrane phase are then experimentally determined for a given total ionic concentration Ct expressed in eq/m. Average selectivity value is subsequently generated using Equation 34.14b. 

Some further nomenclature is now necessary to describe absorption equilibria in ion exchange systems. For a species i, m and C, represent the molal and molar concentrations respectively, whilst A and Xi denote the mole fraction and equivalent ionic fraction of i respectively. Single ion activity coefficients are denoted yj and mean ionic activity coefficients by yj . Whether the latter quantities refer to the molar or molal concentration scales is decided by the choice of units defining concentration. Thermodynamic activities and activity coefficients for the resin phase using the equivalent or mole fraction concentration scale (rational scale) are sometimes defined differently and are discussed in a later section. Finally, the exchanger and external solution phases are differentiated by subscripts r and s respectively. 

The relation between the molar selectivity coefficient and the equivalent ionic fractions of ions A and B in both phases may be derived as follows ... 

Assuming a linear relationship between conductivity and concentration for dilute solutions the equivalent ionic fraction of hydrogen ions in the external solution at equilibrium (A h) is given by ... 

Divalent Ion-Hydrogen Ion Selectivities. Selectivity coefficients determined at equivalent ionic fractions of 0.5 for the alkaline earth ions, Co2" ", and Zn " " are listed in Table II along with corresponding polymer water contents (7). Again, the normal order of selectivities is seen for the alkaline earth ions for a low charge density exchange site environment. The order of standard hydration free energies for these cations is Zn2" " > Co2" "... 

Often i( is desirable 10 use equivalent ionic fractions to represent concentrations in the solution and resin phases. Thus, in a binary system,... 

In the steady state, because J+, J are constant, the flux of diffusion can be calculated. Considering a 1 1 electrolyte, if y+y. = y 2, the equivalent ionic fraction is defined,... 

Interface coordinate in direction of motion of plane kinematic wave Equivalent ionic fraction of A in solution, Eq. (6.3.4)... 

FIGURE 21.7 Nitrate equivalent ionic fraction in the membrane versus nitrate equivalent ionic fraction in the solution (ACS Tokuyama Soda membrane, electrolyte temperature 25°C). (From Nwal Amang, D., Alexandrova, S., and Schaetzel, P., Desalination, 159, 237-271, 2003. With permission.)... 

The Equation (21.56) leads to a linear variation of the membrane electrical conductivity as a function of the equivalent ionic fraction of the nitrate ion in the membrane (Figure 21.8) [62]. 

The equivalent ionic fraction of counterion 1 in the strip side of the membrane is close to zero (yi,b 0). 

Thus, the mass transfer coefficient can be calculated with parameter setting of the curves representing the equivalent ionic fraction of the counterion 1 in the feed according to time (Equation 21.63). 

X equivalent ionic fraction in solution y equivalent ionic fraction in resin phase Zi valency of species i... 

Calculate the equivalent ionic fraction of sodium and magnesium ions in a cation exchanger whose selectivity coefficient is unity due to ideal behavior. (See problem 4.1.16.)... 

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