Ion exchange calculations

Ion exchange calculated from the difference in Versenate calcium titration between a sample contacted with 0.1N NaCl and one contacted with distilled water. 

IUPAC recommendations for defining D are [7] distribution coefficient, D the ratio of the total (analytical) amount of a solute per gram of dry ion exchanger to its analytical concentration (total amount per cm ) in the solution concentration distribution ratio, D the ratio of the total (analytical) concentration of a solute in the ion exchanger to its concentration in the external solution (dimensionless) the concentrations are calculated per cm of the swollen ion exchanger and cm of the external solution volume distribution coefficient, D, the ratio of the total (analytical) concentration of a solute in the ion exchanger calculated per cm of the column or bed volume to its concentration (total amount per cm ) in the external solution. 

With an arbitrary definition of KNaX as equal to unity, thus establishing a reference half reaction, the equilibrium constant for any other half reaction can be determined from measured selectivity coefficients. The Gapon equation can be readily implemented in this manner. Implementation of the Vanselow equation, however, requires modification of the general equilibrium models to account for the more complex dependence of mole fractions on the molar concentrations. An example ion-exchange calculation using the half reaction approach to represent the Gapon equation is presented in Appendix 2. 

Ion exchange and titration Extraction and ion exchange Calculated from other values NMR... 

Hardness can also be calculated by summation of the individually deterrnined alkaline earths by means of atomic absorption analysis. Basic samples must be acidified, and lanthanum chloride must be added to minimise interferences from phosphate, sulfate, and aluminum. An ion-selective electrode that utilizes ahquid ion exchanger is also available for hardness measurement however, this electrode is susceptible to interferences from other dissolved metal ions. 

Example 2 Calculation of Variance In mixed-hed deionization of a solution of a single salt, there are 8 concentration variables 2 each for cation, anion, hydrogen, and hydroxide. There are 6 connecting relations 2 for ion exchange and 1 for neutralization equilibrium, and 2 ion-exchanger and 1 solution electroneiitrahty relations. The variance is therefore 8 — 6 = 2. 

The physical nature of the sulfate complexes formed by plutonium(III) and plutonium(IV) in 1 M acid 2 M ionic strength perchlorate media has been inferred from thermodynamic parameters for complexation reactions and acid dependence of stability constants. The stability constants of 1 1 and 1 2 complexes were determined by solvent extraction and ion-exchange techniques, and the thermodynamic parameters calculated from the temperature dependence of the stability constants. The data are consistent with the formation of complexes of the form PuSOi,(n-2)+ for the 1 1 complexes of both plutonium(III) and plutonium(IV). The second HSO4 ligand appears to be added without deprotonation in both systems to form complexes of the form PuSOifHSOit(n"3) +. ... 

Before releasing a process column for chromatography, it is advisable to perform some test to measure efficiency, such as calculating height equivalent theoretical plates (HETP), both to forestall any problems in the column bed and to provide a benchmark by which to measure column reproducibility and predict degradation of the bed or material. Examples of compounds that are relatively innocuous for use in pharmaceutical applications are 1% NaCl (for gel filtration), concentrated buffer solutions (for ion exchange), and benzyl alcohol and parabens for reverse phase LC.10... 

The ion exchange system will be capable of processing 200,000 lb/hr. A two-bed ion exchange unit will be specified. The minimum resin volume is 200 ft3. This was calculated on the basis of 2 GPM/ft3 resin.62 During the summer the extra wash water will be sent directly to the river. It does not appear to be warm enough to justify a cooling tower and should contain no pollutants. 

Downing, D.G. Calculating Minimum Cost Ion-Exchange Units, Chemical Engineering, Dec. 6, 1965, p. 170. 

The sizes of the voids decrease in order Cs, Rb, Na, K These differences are ascribed to the different influence of cation on the surrounding reactive species that changes the nature of alkali cation - aluminosilicate anion complexes. On the other hand, in the case that the cations are introduced in the matrix by ion exchange, (procedure b) the r3 lifetimes are approximately the same for all the cations (Table 2) and the size of cation does not have such pronounced influence. The calculated radii are shown in Table 4. 

For an N-species system, with N c"s (or n s) known, the N n°s (or c s) can be found by simultaneous solution of the N — 1 independent i.j combinations for Eq. (16-45) using Eq. (16-44a) one nj/cl is assumed, the other values can be calculated using Eq. (16-45), and the sum of the trial n s (or c s) is compared with Eq. (16-44h). Because an N-component system has N — 1 independent concentrations, a three-component equilibrium can be plotted in a plane and a four-component equilibrium in a three-dimensional space. Figure 16-8 shows a triangular plot of c contours in equilibrium with the corresponding n coordinates. Improved models for ion-exchange equilibria are in Smith and, SJk... 

Figure 2 illustrates the variation of the first-order rate constants, kv, with [CTABr] for reactions of benzoic anhydride with 0.01 M NaOH and with 0.02 M sodium formate. The lines are calculated using the ion-exchange treatment with the following parameters Ks = 650 M (3 = 0.75, Kgr = 10 for X = OH- and HCO 2 and kM = 200 and 0.06 s 1 for OH" and HCO 2 respectively. Similar values of the rate constants were used in fitting the data... 

Fig. 2 Reactions of benzoic anhydride in CTABr , 0.01 M NaOH , 0.02 M HC02Na. The lines are calculated using the ion-exchange model. (Reprinted with permission of the American Chemical Society)...

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