Ion exchange binary

The working capacity of a sorbent depends on fluid concentrations and temperatures. Graphical depiction of soration equilibrium for single component adsorption or binary ion exchange (monovariance) is usually in the form of isotherms [n = /i,(cd or at constant T] or isosteres = pi(T) at constant /ij. Representative forms are shown in Fig. I6-I. An important dimensionless group dependent on adsorption equihbrium is the partition ratio (see Eq. 16-125), which is a measure of the relative affinities of the sorbea and fluid phases for solute. 

In binary ion-exchange, intraparticle mass transfer is described by Eq. (16-75) and is dependent on the ionic self diffusivities of the exchanging counterions. A numerical solution of the corresponding conseiwation equation for spherical particles with an infinite fluid volume is given by Helfferich and Plesset [J. Chem. Phy.s., 66, 28, 418... 

Davis, M.T., Beierle, J., Bures, E.T., McGinley, M.D., Mort, J., Robinson, J.H., Spahr, C.S., Yu, W., Luethy, R., Patterson, S.D. (2001). Automated LC-LC-MS-MS platform using binary ion-exchange and gradient reversed-phase chromatography for improved proteomic analyses. J. Chromatogr. B Biomed Sci. Appl. 752, 281-291. 

In this chapter we shall treat some particular instances of the system (3.1.15) and the related phenomena. Thus in 3.2, we shall concentrate upon binary ion-exchange and discuss the relevant single nonlinear diffusion equation. It will be seen that in a certain range of parameters this equation reduces to the porous medium equation with diffusivity proportional to concentration. Furthermore, it turns out that in another parameter range the binary ion-exchange is described by the fast diffusion equation with diffusivity inversely proportional to concentration. It will be shown that in the latter case some monotonic travelling concentration waves may arise. 

Furthermore, in 3.3 we turn to reactive binary ion-exchange. An equilibrium binding reaction (adsorption) with a Langmuir-type isotherm is considered. Formation of sharp propagating concentration fronts is studied via an unconventional asymptotic procedure [1]. 

It was observed in the previous section that a certain limit case of non-reactive binary ion-exchange is described by the porous medium equation with m = 2 in other words, a weak shock is to be expected at the boundary of the support. Recall that this shock results from a specific interplay of ion migration in a self-consistent electric field with diffusion. Another source of shocks (weak or even strong in the sense to be elaborated upon below) may be fast reactions of ion binding by the ion-exchanger. 

Smith, T. G., and Dranoff, J. S. (1964). Film diffusion-controlled kinetics in binary ion exchange. Ind. Eng. Chem. Fundam. 3, 195-200. 

Zeolites behave as a salt and experience alkaline hydrolysis. That is, when a zeolite contacts water, the solution turns basic, that is, pH >7 this means that a proton exchange has occurred. It is necessary then to take into account proton concentration as a third component in binary ion exchange [37,38],... 

A large body of experimental research exists concerning two-component ion exchangers, whose behavior is described by Eq. 5.1 or 5.2.5 These systems thus exhibit binary ion exchange equilibria. The central problem in applying chemical thermodynamics to them is to derive equations that permit the calculation of and the activity coefficients of the two adsorbate species.6 Several approaches have been taken to solve this problem, each of which reflects a particular notion of how exchanger composition data can be utilized most effectively to calculate thermodynamic quantities. 

One conceptually simple approach is to express all binary ion exchange reactions as combinations of the special case of Eq. 4.3, in which the species Q is deleted and SR = SR, with the possibility that more than 1 mol of SR may combine with adsorptive ions to form the adsorbate species. This approach portrays ion adsorption formally as a complexation reaction and builds ion exchange reactions as combinations of these reactions.7 Since the adsorbate species may be formed from both cations and anions (cf. Eq. 4.3), ion exchange reactions involving charged complexes [e.g., CaCT(aq) as well as monatomic ions [e.g., Na (aq)J can be described. If the further simplification is made that adsorbate species activity coefficients do not depend on exchanger composition, then equilibrium spccialion calculations can be performed exactly as described... 

Stoichiometric capacity of the column, q0 PbV for adsorption, or Qpbv for simple binary ion exchange. This variable has been discussed in Section II, B. 

Linear equilibrium involves constant-separation-factor conditions, with the value of the factor r equal to unity. In binary ion exchange involving only one component in the feed, r = 1 corresponds to A = 1, a condition which may be approached but seldom is realized exactly. In ion exchange with a mixed feed, r tends toward unity as the feed mole-fraction of the exchanging component ca)0/C0] diminishes (Section III,... 

Abou-El-Leil M, Cooper AR. Analysis of field-assisted binary ion exchange. Journal of the American Ceramic Society. 1979 62(7-8) 390-395. DOI 10.1111/j. 1151-2916.1979.tbl9086.x. 

For a sinplified view of ion exchange equilibrium for binary ion exchange assume the equilibrium constant can be determined by the law of mass action. Let A represent the hydrogen ion and B the sodium ion. For monovalent ion exchange... 

I refers to either species A or B in a binary ion-exchange system... 

It has been emphasised already that accurate and reliable data are essential in the construction of adequate ion exchange models for the industrial applications of zeolite and other ion exchangers. In this section we will discuss ion exchange experimentation and its utility for industrial appHcations. We also discuss major pitfalls that may lead to unreliable results. Although industrial appHcations always involve more than two exchanging ions, seeing trends in the overaU equilibria under these circumstances may be difficult. Therefore, in this section, only binary ion exchange equilibria are considered in order to keep the major issues in focus. 

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