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As the concentration of the ion-exchanger ion is constant in the membrane phase, it holds that cBl+(m) + cB2+(m) = cA)-(m) (6.3.6) For the potential difference & </) (cf. Eqs 3.2.48 and 6.3.6) we have
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Similarly, A^0 is given as
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(6.3.8)
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The EMF of cell (6.3.1) can be written as E = EISB-ETef (6.3.9) where the 'potential of the ion-selective electrode, I S E' is expressed by collecting the variables related to test solution 1 in one term and the variables related to the membrane, the internal solution of the ion-selective electrode and the internal reference electrode in another constant term so that in view of (6.3.2), (6.3.7) and (6.3.8) F yB2() RT = O,,SE + -j In [ , (!) + A:^ 3 2 + a B 2 + (l)]
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(6.3.10)
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428 The quantity K^iB2+ is termed the selectivity coefficient for the determinand B ^ with respect to the interferent B 2 + . Obviously, for a B l + (l) ^BT+,B2+ B2+(1)5 Eq. (6.3.9) is converted to Eq. (6.3.3), often expressed by stating that the potential of the ion-selective electrode depends on the logarithm of the activity of the determinand ion with Nernstian slope. A similar dependence is obtained for the ion B 2 + when a B l + (l) K^i,B2+0B2+(1) Equation (6.3.10) is termed the Nikolsky equation. Among cations, potassium, acetylcholine, some cationic surfactants (where the ion-exchanger ion is the p-chlorotetraphenylborate or tetraphenylborate), calcium (long-chain alkyl esters of phosphoric acid as ion-exchanger ions), among anions, nitrate, perchlorate and tetrafluoroborate (long-chain tetraalkylammonium cations in the membrane), etc., are determined with this type of ion-selective electrodes. 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 A^ + 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. 6.3.2 Ion -selective electrodes with fixed ion -exchanger sites This type of membrane consists of a water-insoluble solid or glassy electrolyte. One ionic sort in this electrolyte is bound in the membrane structure, while the other, usually but not always the determinand ion, is mobile in the membrane (see Section 2.6). The theory of these ion-selective electrodes will be explained using the glass electrode as an example; this is the oldest and best known sensor in the whole field of ion-selective electrodes. The membrane of the glass electrode is blown on the end of a glass tube. This tube is filled with a solution with a constant pH (acetate buffer, hydrochloric acid) and a reference electrode is placed in this solution (silver chloride or calomel electrodes). During the measurement, this whole system is immersed with another reference electrode into the test solution. The membrane potential of the glass electrode, when the internal and analysed
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