Exchange isotherms

Ion-exchange isotherms assume different shapes depending on the selectivity factor and the variations in with the level of exchange The rational selectivity coefficient includes the ionic charge and is given by... 

Fig. 8. Ion-exchange isotherm. The separation factor is given by the ratio of area 1/area II (1). See text.

External Heat Exchanger Isothermal Heating Medium... 

BATCH HEATING EXTERNAL HEAT EXCHANGER, ISOTHERMAL HEATING MEDIUM... 

Fig ure 7-28. Batch heating through an external heat exchanger, isothermal heating medium. 

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. 

Such a study has been performed on a model plant system, the Nitella flexilis cell wall [1, 2, 3]. This freshwater alga has giant intemodal cells whose easily isolated cell walls constitute a simplified model of higher plant cell walls it has no lignin and its pectin is not methylesterified. Isolated cell walls are cut in pieces and distributed in different lots over the whole exchange isotherm to reduce variability between experimental points. 

Fig. 2. The logarithm of the selectivity coefficients of a calcium-copper (a) or a calcium-potassium (b) exchange isotherm is plotted as a function of the proportion of the preferred ions adsorbed in the cell walls.

In the simplest case, a linear relationship may exist between solutes in soil solution and those on the solid pha.se, such that C, = hCr, where C, is the. solute concentration on the solid phase and h defines the buffer power. In perhaps more typical situations, the relationship might be defined by a more complicated, concentration-dependent relationship such as a Freundlich or Langmuir expression here the instantaneous buffer power may be defined as the tangent to the exchange isotherm i.e., h = dCJdCi. Some care is needed when defining this buffer power (7). 

In Fig. 4.19 the mol fraction of Ca2+ on the exchanger is plotted as a function of the mol fraction of Ca2+ in the solution. For a hypothetical exchange with no selectivity, the exchange isotherm is represented by the dashed line. In such a case the ratio... 

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. 

Only few data are available for this kind of analysis. In addition to the above-presented data, exchange isotherms have been measured for Th and for -zeolite An experimental result for potassium zeolite L suspended in water and exchanged at room temperature with is shown in Fig. 6. For... 

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

The Exchange Isotherm. For adsorption at constant pH the amount of selenite on the surface is related to the solution concentration by an equation of the Langmuir type (Equation 1). 

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... 

ION-EXCHANGE ISOTHERMAL SUPERSATURATION CONCEPT, PROBLEMS, AND APPLICATIONS Dmitri N. Muraviev and Ruslan Khamizov... 

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