Rate of ion exchange

The rates of ion exchange are generally determined by diffusion processes the ratedetermining step may either be that of diffusion across a boundary film of solution or... 

Variances in resin performance and capacities can be expected from normal annual attrition rates of ion-exchange resins. Typical attrition losses that can be expected include (1) Strong cation resin 3 percent per year for three years or 1,000,000 gals/ cu.ft (2) Strong anion resin 25 percent per year for two years or 1,000,000 gals/ cu.ft (3) Weak cation/anion 10 percent per year for two years or 750,000 gals/ cu. ft. A steady falloff of resin-exchange capacity is a matter of concern to the operator and is due to several conditions ... 

Quantification and Elucidation of Rate-Limiting Steps 109 Chemical Reaction and Diffusion 112 Rates of Ion Exchange on Soils and Soil Constituents 113 Mineralogical Composition 114 Ion Charge and Radius 116 Binary Cation and Anion Exchange Kinetics 117... 

However, researchers later found (Boyd et al., 1947) that the rate of ion exchange increased with decreasing particle size of the exchanger. This showed that mass-transfer phenomena and not chemical reaction were rate-controlling. 

Rates of Ion Exchange on Soils and Soil Constituents TABLE 5.2 Examples of Ion Exchange with Reaction"... 

The rates of ion exchange on soils range from a few seconds to days, depending on a number of factors. These include type and quantity of inorganic and organic constituents, ion charge and radius, and kinetic methodology (Chapter 3). 

Rates of ion exchange on kaolinite, smectite, and illite are usually quite rapid. Sawhney (1966) found that sorption of cesium on illite and smectite was rapid, while on vermiculite, sorption had not reached an equilibrium even after 500 h (Fig. 5.5). Sparks and Jardine (1984) found that potassium adsorption rates on kaolinite and montmorillonite were rapid, with an apparent equilibrium being reached in 40 and 120 min, respectively. However, the rate of potassium adsorption on vermiculite was very slow. Malcom and Kennedy (1969) studied Ba-K exchange rates on kaolinite, illite, and montmorillonite using a potassium ion-specific electrode to monitor the kinetics. They found >75% of the exchange occurred in 3 s, which represented the response time of the electrode. The rate of Ba-K exchange on vermiculite was characterized by a rapid and slow rate of exchange. 

The ionic radius can also affect the rate of ion exchange. An example of this is shown in the work of Sharma et al., (1970), who studied the rate of exchange of La3+, Tb3+, and Lu3+ in HC1 using a flow system (Fig. 5.6). Calculated D values are shown in Table 5.4, along with data on ion size. Lanthanum has the largest ionic crystal radius, while Lu3+ has the smallest. The hydrated size of the ions is in the order Lu3+ > Tb3+ > La3+. 

Most of the studies involving ion exchange kinetics on soil constituents have been concerned with inorganic components such as clay minerals, oxides, etc., as just discussed. Rates of ion exchange on humic substances, while extremely important, have not been extensively studied. 

Carman (C6) described the successful development and application to a uranium resin-in-pulp process of a continuous countercurrent ion-exchange pilot plant. This new technique is based on the observation that the resins at the correct level of air agitation float in close proximity to the surface of the pulp. So long as the resin beads are able to move about gently but freely in the surface layer, a satisfactory rate of ion exchange is possible. Under this condition, the mechanical damage to the resin due to attrition is negligible. 

The mass-transfer rate is slow in CIEC. By increasing temperature this parameter is sizably enhanced and the rate of ion exchange becomes more rapid. The increase in temperature, however, may cause the evolution of gas bubbles from the solution and result in their entry into column systems. The gases are formed in chemical reactions and are due to the air dissolved in the solutions employed. They can influence the stability of fluid flow, distort the bandshape, and even promote the formation of cavities in the exchange bed, thereby disturbing the separation process. Because the bubbles rise while the fluid flow is down in a column, it is difficult to remove these bubbles in CIEC. 

Conventionally, the rates of ion exchange are presented in terms of the fractional attainment U(t) of equilibrium. This quantity is defined for the ion-exchanger phase as... 

Elimination of c and Cb from Eq. (18) with help of Eqs. (21) and (26) yields the system of n differential equations, that describe the rate of ion exchange in each fraction i of the heterogeneous mixture as... 

These n nonlinear differential equations have to be solved simultaneously and numerically to obtain the rate of ion exchange of each fraction in the mbcture. Once all X, are known as a function of time, the concentration C ... 

To investigate the rates of ion exchange Cs /H, the resin beads in the form were added to the CsCl solution (again 0.0001 M), labeled with Cs. When the two size fraction samples were placed individually in the solution (V = 50 mL) for separate study, the rate curves shown in Fig. 6 were obtained. The quantities Q of ion exchanger used were 0.34 and 0.30 mequiv for the 0.04- and 0.08-cm fraction, respectively. The separation factor (see Eq. (15)) obtained for both size fractions was = 3.5 for the equilibrium uptake of Cs by the exchanger. To obtain the... 

To project first the rate of ion exchange if each of the 11 size fractions (5 mequiv each) were present individually in the above solution (c,o, = 0.001 M), U(t) is calculated for each fraction by using Eq. (22). The rate curves obtained are illustrated in Fig. 9. They show that even the largest particles (fraction 11) reach 95% of their equilibrium state already after 500 s. Increasing or decreasing c, , by a factor of 10 barely changes the rate curves in Fig. 9. 

The rates of ion exchange for heterogeneous mixtures of ion exchanger may also be investigated in a stirred-flow cell. For a better understanding of the characteristics of the stirred-flow method, however, the results obtained for homogeneous systems are discussed briefly first [28]. This... 

Because it is assumed that Elm diffusion is rate controlling, the rate of ion exchange, i.e., X (t) in Eq. (40) is given by Eq. (18) and the rate coefficient R by Eq. (19) with is again the equivalent separation factor. Because the ion exchanger is also in equilibrium with the influent solution for t -> 00, is given by... 

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