Selectivity coefficient determination

From the parameter estimation, C can easily be determined (note, however, that this value has an uncertainty due to linear curve fitting). Then, substituting the concentrations (aMel and c s) into Equation 2.24, the selectivity coefficients can be determined. The selectivity coefficients determined this way can be plotted as a function of the surface equivalent fraction of any ions (e.g., hydrogen ion). Similarly, the selectivity coefficients can directly be calculated from the experimental data, and the values can also be determined as a function of the surface equivalent fraction of the ions. Thus, two selectivity functions can be obtained (Figure 2.7). 

Divalent Ion-Hydrogen Ion Selectivities. Selectivity coefficients determined at equivalent ionic fractions of 0.5 for the alkaline earth ions, Co2" ", and Zn " " are listed in Table II along with corresponding polymer water contents (7). Again, the normal order of selectivities is seen for the alkaline earth ions for a low charge density exchange site environment. The order of standard hydration free energies for these cations is Zn2" " > Co2" "... 

K+, 18 Cs+, 10.0 (26). This change in order of selectivity can be ascribed to increased electrostatic interactions between exchange sites and alkali metal ions as ionic radius increases and solvation energy decreases (2, 3). Therefore the selectivity coefficients determined for Nafion in methanol are a further indication of the much lower charge density on the sulfonate exchange site compared to conventional sulfonate polymers. 

We mentioned that selectivity coefficients determined using the Nicolsky equation often vary, depending on relative concentrations and measurement conditions, and the equation does not dpply if the response is non-Nemstian (often the case with secondary ions). The matched potential method is an attempt to deal with this. Bakker and co-workers introduced a new formulism that provides a.clear interpretation of the matched potential method, elegantly deriving an equation based on ion exchange in which the last term in Equation 13.49 becomes where... 

The selectivity coefficient is easy to calculate if kj and kj can be independently determined. It is also possible to calculate Ka,i by measuring Sjamp in the presence and absence of known amounts of analyte and interferent. 

Even if a method is more selective for an interferent, it can be used to determine an analyte s concentration if the interferent s contribution to Sjamp is insignificant. The selectivity coefficient, Ka,i> was introduced in Chapter 3 as a means of characterizing a method s selectivity. 

In a particular analysis the selectivity coefficient, Xa.i, is 0.816. When a standard sample known to contain an analyte-to-interferent ratio of 5 1 is carried through the analysis, the error in determining the analyte is +6.3%. (a) Determine the apparent recovery for the analyte if Rj = 0. (b) Determine the apparent recovery for the interferent if Ra = 1 ... 

The amount of calcium in a sample of urine was determined by a method for which magnesium is an interferent. The selectivity coefficient, Rca.Mg> for the method is 0.843. When a sample with a Mg/Ca ratio of 0.50 was carried through the procedure, an error of-3.7% was obtained. The error was +5.5% when a sample with a Mg/Ca ratio of 2.0 was used. 

Plot of cell potential versus the log of the analyte s concentration In the presence of a fixed concentration of Interferent, showing the determination of the selectivity coefficient. 

Selectivity As described earlier, most ion-selective electrodes respond to more than one analyte. For many ion-selective electrodes, however, the selectivity for the analyte is significantly greater than for most interfering ions. Published selectivity coefficients for ion-selective electrodes (representative values are found in Tables 11.1 through 11.3) provide a useful guide in helping the analyst determine whether a potentiometric analysis is feasible for a given sample. 

Creager and colleagues designed a salicylate ion-selective electrode using a PVC membrane impregnated with tetraalkylammonium salicylate. To determine the ion-selective electrode s selectivity coefficient for benzoate,... 

At equdibrium, the selectivity coefficient ) for B over A is determined from the fodowing equation ... 

The main chemico-analytical properties of the designed ionoselective electrodes have been determined. The work pH range of the electrodes is 1 to 5. The steepness of the electrode function is close to the idealized one calculated for two-charged ions (26-29 mV/pC). The electrode function have been established in the concentration range from 0.1 to 0.00001 mole/1. The principal advantage of such electrodes is the fact that thiocyanate ions are simultaneously both complexing ligands and the ionic power. The sensitivity (the discovery limits), selectivity (coefficient of selectivity) and the influence of the main temporal factors (drift of a potential, time of the response, lifetime of the membranes) were determined for these electrodes. 

The so-called potentiometric selectivity coefficient K " reflects the non-ideal behavior of ion-selective membranes and determines the specificity of this electro-... 

Calcium activities as low as 5 x 10 7 M can be measured, with selectivity coefficients ACaMg and ACaK of 0.02 and 0.001, respectively. Such potential response is independent of the pH over the pH range from 5.5 to 11.0. Above pH 11, Ca(OH)+ is formed, while below pH 5.5, protons interfere. Because of its attractive response characteristics, the calcium ISE has proved to be a valuable tool for the determination of calcium ion activity in various biological fluids. 

Discuss the significance of the selectivity coefficient of an ISE. How would you determine its value ... 

The conclusion above is valid for ideally selective membranes. Real membranes in most cases have limited selectivity. A quantitative criterion of membrane selectivity for an ion to be measured, relative to another ion M +, is the selectivity coefficient The lower this coefficient, the higher the sefectivity wifi be for ions relative to ions An electrolyte system with an imperfectly selective membrane can be described by the scheme (5.16). We assume, for the sake of simplicity, that ions and have the same charge. Then the membrane potential is determined by Eq. (5.17), and the equation for the full cell s OCV becomes... 

Especially sensitive and selective potassium and some other ion-selective electrodes employ special complexing agents in their membranes, termed ionophores (discussed in detail on page 445). These substances, which often have cyclic structures, bind alkali metal ions and some other cations in complexes with widely varying stability constants. The membrane of an ion-selective electrode contains the salt of the determined cation with a hydrophobic anion (usually tetraphenylborate) and excess ionophore, so that the cation is mostly bound in the complex in the membrane. It can readily be demonstrated that the membrane potential obeys Eq. (6.3.3). In the presence of interferents, the selectivity coefficient is given approximately by the ratio of the stability constants of the complexes of the two ions with the ionophore. For the determination of potassium ions in the presence of interfering sodium ions, where the ionophore is the cyclic depsipeptide, valinomycin, the selectivity coefficient is Na+ 10"4, so that this electrode can be used to determine potassium ions in the presence of a 104-fold excess of sodium ions. 

E. Bakker, Determination of improved selectivity coefficients of polymer membrane ion-selective electrodes by conditioning with a discriminated ion. J. Electrochem. Soc. 43, L83—L85 (1996). 

Results of analogous permeation studies for the hydrophobic toluene molecule are shown in Fig. 20. Now the opposite selectivity pattern is observed i.e., toluene is preferentially transported in the R = -CieHjj membranes. This can be illustrated by defining the alternative selectivity coefficient aci6/0H (Table 3). As was the case for aoH/cia. the acie/on values increase with decreasing tubule diameter. In addition to toluene, acie/on values were determined for p-xylene and naphthalene in the i.d. = 1.9 nm membranes. The following acu/on values were obtained 2.8 for toluene, 6.2 for j9-xylene, and 16 for naphthalene. 

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