Associated electrolytes

The deviation from Onsager s law is due to ion-ion interactions and is more pronounced for highly charged ions at high concentrations. The attractive interactions between opposite charged ions could yield to ion association, which is not exphcitly taken into account in the Onsager theory of conductivity. 

The simplest way to express the conductivity of associated electrolyte is the Otswald approach A = aK°, where a is the degree of dissociation of the electrolyte. Replacing a in equation (4.1) we obtain the following expression for Ka, 

This relationship can be rearranged to read (Hamed and Owen, 1958), 

This equation was used by Frantz and Marshall to obtain the dissociation constant of HCl above 400 °C (Frantz and 

Marshall, 1984) from data whose overall precision was estimated to be 1%. 

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For weakly and moderately associated electrolytes, 10< (A<104, no problem generally occurs in obtaining reliable values for KA and A0 from conductivity measurements. Strong association, however, as known for many salts in the solvent class 6, often entails unrealistic A ... 

Many attempts have been made by experiment or calculation to determine the absolute values of Galvani potentials at interfaces, particularly across the electrodeelectrolyte interface. Basically, if one knew the Galvani potential between one metal and the associated electrolyte and that at the interface between the metal and another metal, one could then find the Galvani potentials for all other interfaces from the data of OCV measurements with other galvanic cells. 

The total charge integrated over the entire interface comprising electrode and associated electrolyte is zero. 

Tan HL, Liew QY, Loo S, Hawkins R Severe hyperphosphatemia and associated electrolyte and metabolic derangement following the administration of sodium phosphate for bowel preparation. Anaesthesia 2002 57 478-483. 

The different techniques which have been applied to determine transport in polymer electrolytes are listed in Table 6.1. For a fully dissociated salt all the techniques yield the same values of t (small differences may arise due to second order effects such as long range ion interactions or solvent movement which may influence the different techniques in different ways). In the case of associated electrolytes, any of the techniques within one of the three groups will respond similarly, but the values obtained from different groups will, in general, be different. Space does not permit a detailed discussion of each technique, this is available elsewhere (see Bruce and Vincent (1989) and the references cited therein). However, we will consider one technique from each group to illustrate the differences. A solid polymer electrolyte containing an associated uni-univalent salt is assumed. 

The concept of mean spherical approximation (MSA, 3) in Chapter 2) has also been used to reproduce the conductivity data of electrolytes of fairly high concentration [23]. The MSA method applies to both associated and non-associated electrolytes and can give the values of association constant, KA. Although not described here,... 

The magnitude of the ohmic drop at a microelectrode can be evaluated quite readily for case 1 from a knowledge of the specific solution resistance (obtained from conductivity measurements such as in Table 12.1) and the expressions for the voltammetric current for the specific microelectrode employed. Case 2 is also straightforward if the free concentration of ions exceeds that of the electroactive species. However, the situation is somewhat more complicated for the third class. In this case, and in case 2 for fully associated electrolyte, migration as well as diffusion can affect the observed voltammetric signals. In all three cases, the situation may be further complicated by a change in structure of the double layer. However, this is ignored for now, and is considered in the section on very small electrodes. 

Diuretics such as thiazides, ethacrynic acid, and furosemide intensify the effects of nonpolarizing muscle relaxants, possibly because of a diuresis-induced reduction in the volume of distribution and an associated electrolyte imbalance, such as hypokalemia. 

Sometimes, the conductivity of the solution may decrease due to the formation of electroneutral ion pairs. Under these conditions, the Fuoss-Onsager equation can be used to calculate the molar conductivity (A) of associated electrolytes [57] ... 

Simonin, J.P., Bernard, O., and Blum, L. Real ionic solutions in the mean spherical approximation 3 osmotic and activity coefficients for associating electrolytes in the primitive model. 7. Phys. Chem.B. 1998, 102,4411 417. 

The most elaborate treatment of the dissociation of electrolytes in solutions is the one given by Fuoss and Onsager (9, 10). The so-called F.O. equation, applied to I-I associated electrolytes is... 

The results obtained also are useful for the calculation of the ionic conductivity of nonaqueous electrolyte solutions. Several attempts exist for the calculation of the molar conductivity of associating electrolytes beyond the limiting law at the level of the MSA [3, 32, 33], where, however, only ion pairs were taken into account. Ion pairs and tetramers are electrically neutral, nonconducting species in the solution, by contrast to the ion trimers. The total concentration of charged particles is given by,... 

Vlachy, V., Ichiye, T., and Haymet, A.D.J. Symmetrical associating electrolytes - gcmc simulations and integral-equation theory. Journal of the American Chemical Society, 1991, 113, No. 4, p. 1077-1082. 

Electric-conductivity measurements in acetonitrile show it to be a 1 1 (associated) electrolyte.5,8 The crystal structure has been determined.9... 

Experimental activity coefficients are always quoted as stoichiometric values, ]/j, based on stoichiometric concentrations and ionic strengths. This is still the case for associated electrolytes. However, when association occurs the actual ionic strength will be less than the stoichiometric ionic strength, and it then becomes vital to distinguish between based on the actual concentration and the actual ionic strength, and based on the stoichiometric concentration and the stoichiometric ionic strength. 

What this argument shows is that removal of ions due to association and non-ideality will both independently cause the activity to be less than the stoichiometric concentration. For an associated electrolyte, both association and non-ideality will be involved and both factors will contribute to bring Oobserved down more extensively than either of them would do in the absence of the other. 

Since Oobserved < Cstoich this can be quantified as flobserved = (f " )observed stoich, and will manifest itself in a (yf " )observed being less than would be expected for a corresponding obeying the Debye-Hiickel equation. For an associated electrolyte logicobserved (l + plots Will therefore approach the Debye-... 

Figure 12.1 A schematic graph of Aobsvd vs. y Cstoich for an associated electrolyte, with the limiting Debye-Hiickel-Onsager slope drawn in.

Figure 12.2 Cross-over diagram for a 1-1 and a 2-2 unassodated electrolyte and a 2-2 associated electrolyte.

Within the range of concentrations for which the Fuoss-Onsager equation is expected to be valid, this equation accounts well for the effects of non-ideality in solutions of symmetrical electrolytes in which there is no ion association. It can thus be taken as a base-line for non-associated electrolytes and any deviations from this predicted behaviour can be taken as evidence of ion association (see Section 12.12). 

It may seem surprising that these two forms of the conductance equation for associated electrolytes are so similar. There is, however, no mistake here. Neither equation is exact, and the difference between the two equations is of the order of terms such as or c logc which... 

Determination of A°, Afassodation and a using the Fuoss-Onsager equation for associated electrolytes... 

Nonetheless, the Fuoss-Onsager 1957 equations for unassociated and associated electrolytes cope with non-ideality extremely well, provided the concentration range is limited to up to ... 

In the period between 1957 and 1978 various modifications and extensions were made to the Fuoss-Onsager equations for unassociated and associated electrolytes, but there were no major changes in the model. All that these studies had done was to produce modified conductance equations. 

TAM] Tamamushi, R., A method for determining the degree of dissociation of symmetrical associated electrolytes fi om conductivity and activity data. Bull. Chem. Soc. Jpn., 48, (1975), 705-706. Cited on pages 182, 184,375. 

Eq. (6 a) is valid for both completely and partially dissociated (or associated) electrolytes if the activity coefficient is written as follows... 

Only the free ions in tlte solution are supposed to transport charges in the applied external field. For associating electrolytes Eq. (34) is transformed into the set of equations... 

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