Ion exchange isotherms for

Box 11.2 General Derivation of Ion Exchange Isotherms for Cationic Organic Compound (/ = BH+). 

Figure 12 Ion-exchange isotherms for alkali cation exchange with Zr(HP04)2 H20. (Reprinted with permission from Ref 66. 1981 American Chemical Society)...

Figure 14 The ion-exchange isotherms for uni-univalent ion-exchange reactions (left) and the In dependence (right) of various types of reaction on X, (a) Langmuir type, (b) selectivity reversal, (c) anti-Langmuir type, (d) incomplete exchange, (e) hysteresis loop. (From M. Abe, in Ion Exchange Processes Advances and plications (A. Dyer, M. J. Hudson, and P. A. Williams, eds.). The Royal Society of Chemistry, Science Park, Cambridge, UK, p. 199, 1993. With permission.)...

Ion exchange isotherms for PAN-KCoFC/Cs, KCoFC/Cs systems and PAN-zeolite 4A/Sr, zeolite 4A/Sr systems were obtained to evaluate the equilibrium parameters such as ion exchange capacity and equilibrium constant for kinetic calculations. The experimental data were modeled by Langmuir equation given by... 

Figure 6.10 Ion-exchange isotherms for the La3+-NaYsystem at 25, 82.2, 100, and 180°C. Reproduced with permission from [17] and [18], Copyright (1980) Chemical Journal of Chinese Universities...

Fig. 2 Ion-exchange isotherm for Ca /Na exchange showing selectivity reversal at high solution concentration.

Figure 2. Ion exchange isotherms for 1200 EW Nafion at 25° C, 0.01 M ionic strength (10). Closed symbols normal form open symbols expanded form of polymer. Symbols are the same as those in Figure 1.

Phillipsite-like phases have been synthesized at 80 °C, treating rhyohtic pumice in a mixed Na -K alkaline envirorunent, having different Na /K molar ratios [02C1]. Ion-exchange isotherms for the cation pairs Na/NH4, Na/Ba, Na/K, and Na/Ca have also been obtained and the relevant thermodynamic eqirihbriirm constants calculated. The phillipsites revealed a good selectivity for Ba, NHi, and K and a substantial nonselectivity for Ca [02C1]. 

Fig 9 7 Comparison of calculated and measured ammonium ion exchange isotherms for clinoptilobte samples A and B... 

In absence of any selectivity, the amount of each cation adsorbed in the cell wall must be exactly proportional to the amount of each cation present in the treatment solution. For example, the proportions of two bivalent cations adsorbed in the cell wall must be the same as in the equilibrium solution. In other words, the ion exchange isotherm must be diagonal. 

Typical exchange isotherms for the reactions Ca2+ + 2 Na+ R Ca2+ R + 2 Na+. In dilute solutions the exchanger shows a strong preference for Ca2+ over Na+. This selectivity decreases with increasing ion concentration. The 45° line represents the isotherm with no selectivity. 

Lead ion-exchange isotherms are plotted in Figures 1 and 2. The data in Figure 1 for the Pb(N03)2-Na-A system show that Na-A is extremely selective for Pb2+ and that this selectivity increases with temperature over the range of 50°C. Comparison of this system with the Pb(CH3COO)2 Na-A system (Figure 2) shows... 

We have obtained part of a CdCl -Na-A ion-exchange isotherm in 0.1N solution at 25°C to check the results obtained by Gal and coworkers (1). These data, shown in Figure 3 as crosses, indicate that the preference of Na-A for Cd2+ ions varies with coion according to the series... 

Here, nickel is extracted with a di(2-ethylhexyl) phosphoric acid in its H-form (HDEHP) and two protons are set free. This causes a pH-shift during extraction, which can be avoided if the ion exchanger is, for example, in the Na-form. Typical extraction isotherms are depicted in Fig. 10.2. At the indicated pH-value no nickel, but more than 80 % cobalt, can be extracted in one equilibrium stage. During cobalt... 

FIGURE 7.4 Characteristic ion-exchange isotherms of zeolites (a) Regular system with selectivity for cation A, (b) incomplete ion exchange of cation A, (c) irregular system with selectivity reversal, (d) regular system with selectivity for cation B, and (e) irregular system with selectivity reversal. 

The data for the ion exchange isotherms were obtained from batch experiments conducted in a constant temperature agitated system utilizing tightly sealed polypropylene bottles. Conventional chemical analyses were used to obtain the cation distribution data in both zeolite and exchange solution phases. Most of the exchanges were carried out at ambient temperature for 24-72 hours. Preliminary tests had shown that equilibrium was essentially reached within a few hours. 

The application of the composite isotherms enables us to model the ion exchange on heterogeneous surfaces, such as rocks and soils. When the structure and composition of the sorbent is well known, we can choose the most probable site affinity distribution function. If not, it is desirable to fit the composite isotherm by different models. The just-described four isotherms provide an opportunity for this. In addition, when adsorption and ion exchange can take place simultaneously, adsorption and ion-exchange isotherms and site distribution functions can be combined (Cernik et al. 1996). 

The transformation of the equilibrium (or selectivity) constants and the ion-exchange isotherms can easily be made only for homovalent ion exchange because the ion-exchange isotherms usually do not take into consideration the heterovalent character of the ion exchange. This causes additional serious problems in the evaluation of isotherm parameters. It is shown for the exchange of monovalent and divalent cations that... 

Adsorption and ion exchange, for example, can be treated by an adsorption or ion-exchange isotherm (Sections 1.3.4.1 and 1.3.4.2). The ion-exchanged quantity, for example, can be expressed from Equation 1.95 and substituted into Equation 1.129. In real geological conditions, the volume of the solution (V) is substituted by the free pore volume (w). Taking into account that the humidity (0) and the density of the solid matrix (p) remain constant, the differential equation can be further simplified. The result is as follows ... 

By this method, the ion-exchange isotherms and selectivity coefficients can precisely be determined in a wide surface concentration range, which allows the construction of the ion-exchange isotherm and selectivity function, and the integration of the selectivity function (Chapter 1, Section 1.3.4.2.1, Equation 1.81). An example of a cation-exchange isotherm and isotherm parameters is shown in Figure 2.2 for the cation exchange of cobalt ions and calcium-montmorillonite. 

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