Ion association constant

The determination of accurate and precise limiting conductivities and ion association constants requires care in the design and use of the conductance apparatus, and in the purification and handling of solvents and salts. For this reason attention is given initially here to experimental aspects of conductance measurements. This is followed by a tabulation of selected data, primarily in dipolar apro-tic solvents, and a brief discussion of data taken in one solvent, acetonitrile, which is intended to show the scope of interpretation possible at the present time. 

Small ion association constants (down to 5 or so) can be determined with relatively high precision by conductance techniques. The magnitude of these constants is related to many of the factors that determine mobilities. 

Dissertation Washington University St. Louis, 1979]. From data for the analogous cobalt(III) complex with perchlorate and hexafluorophosphate as anions, he found association constants of about 900 and 300, with distances of closest approach of 5 or 6 8, respectively. These values seem reasonable. For the iron(II) compound with the hexafluorophosphate or perchlorate, the ion association constants were too small to measure (< - 50). 

We have recently completed a study of the isomerization, racemization, and chloride exchange rates of ds-[Co en2 C1J+ in methanol in the presence of only small quantities of chloride. We found that the rate depended upon chloride concentration when it was low and became independent of chloride concentration in the higher region studied by Brown et al. The rate constants are plotted in Figure 1 as function of chloride ion concentration (8). These observations are very similar to those of Basolo et al. for the substitution by azide and can be explained in the same way, i.e., by invoking ion association. The kinetic curves can be reproduced by an ion association constant, K, for the equilibrium,... 

Table II. Ion Association Constants and First-Ordor Rato Constants for Chloride Exchange of Isomerisation of cis- and trans-[Co en2 Cl2]+...

This approach applies only when we are certain that the substrate is mainly in the form of the free ion at the lowest anion concentrations. This is true in the chloride exchange of cw-[Co en2 Cl2]+ in methanol and we can safely conclude that the mechanism is unimolecular (8, 9. 10, 11, 26, 27). This condition did not exist when we studied the displacement of water in trans-[Co en2N02H20]+2 by anions where, because of the large ion association constants, none of the substrate was in the free ion form under reaction conditions. However, in the reaction between trans-[Co en2N02Br]+ and thiocyanate in sulfolane, the substrate was mainly in the free ion form. The observed second-order kinetic form was fully consistent with assigning a bimolecular mechanism to the rearrangement of the ion pair. 

With the decrease in permittivity, however, complete dissociation becomes difficult. Some part of the dissolved electrolyte remains undissociated and forms ion-pairs. In low-permittivity solvents, most of the ionic species exist as ion-pairs. Ion-pairs contribute neither ionic strength nor electric conductivity to the solution. Thus, we can detect the formation of ion-pairs by the decrease in molar conductivity, A. In Fig. 2.12, the logarithmic values of ion-association constants (log KA) for tetrabutylammonium picrate (Bu4NPic) and potassium chloride (KC1) are plotted against (1 /er) [38]. 

Fig. 2.12 Relationship between the ion association constants (log KA) and the reciprocal of solvent permittivity (1 /er) (solid line) and between the degree of ion association (a) and log (c/(A) (dotted curve), (open circles Bu4NPic in AN, NB, MeOH, Ac, Py, DCE, o-dichlorobenzene, acetic acid, chlorobenzene and benzene closed squares KCI in ethanolamine, MeOH, EtOH, acetic acid and H20-dioxane mix-tures). The solid line was obtained using a Eq. (2.19) for 0 = 0.6 nm.

An alternative approach to ion association was proposed by Fuoss. He defined the ion-pair as two oppositely charged ions that are in contact, i.e. at a distance of r=a, and derived the following equation for the ion association constant ... 

Moreover, as schematically shown in Fig. 2.15, three different types of ion-pairs, i.e. solvent-separated (A+SSB-), solvent-shared (A+SB-) and contact (A+B-) types, may be formed depending on the strength of ion-solvent interactions, complicating the treatment of ion association. If we consider the following multi-step equilibrium, the total ion-association constant (KA) is expressed by Eq. (2.21) ... 

Table 1.3. Values of ion association constants for common major ions (as log Ka).

The use of DMSO as a mechanistic tool is not restricted to rate variation effects (Section 4). Advantage can also be taken of its unique molecular properties which enable it to stabilize certain types of structures, such as the anionic intermediates in SnAt reactions. Moreover, as a consequence of its influence on ion association constants, it is found to affect the product distribution and the stereochemical course of bimolecular olefin-forming eliminations. These two illustrative systems which have been chosen for discussion are intended to demonstrate the versality of this solvent in mechanistic studies and may suggest other avenues of investigation. 

Dissociation of a salt in a solvent can similarly be treated taking into account ion pair formation. An ion association constant associated with the equilibrium established between ion pairs and dissociated ions is derived in the -> Bjerrum theory of ion pairs. 

The ion pair IP has no net charge and therefore does not contribute to the solution conductance. The ion association constant is expressed as... 

Ion-Association Constant Extent to Which Ion-Pair Formation Occurs... 

Calculate the ion association constant of CsCl in ethanol e = 24.3) according... 

Raman spectra are related to the concentration of the species that give rise to them and offer a tool by which one may perform quantitative evaluations of ion-pair equilibria. For example, the ion association constant for ion pairing between Ag and... 

The ion-association constants are shown as logarithmic values in Fig.l and were expressed by the equation 3... 

The ion-association constants of the perchlorate of [Co(phen)3]3+ are larger than those of [Co(bpy)3]3+ while the K/ values of their chlorides are similar to each other. This indicates that the [Co(phen)3]3+ ion is somewhat more hydrophobic although the difference in dln(A °° slight. 

The momentary association of simple ions is a well-known phenomenon that has been treated in a number of ways. For example, the ion association constant of Bjerrum has received much experimental support. However, the association of simple electrolytes is considered to be shortlived and has been included in the Debye-Hiickel electrostatic theory as correction constants to the concentration. On the contrary, the hydration of the ions may be long-lived. This may be accounted for by considering additionally the ionic interaction ... 

It must be emphasised that the values selected in this review for formation of NiHPjO, and NiPjO, should not be used for solutions more than 0.01 M in alkali metal ions unless explicit values are introduced for the pyrophosphate-alkali metal ion association constants (the values of De Stefano et al. [94STE/FOT] may be useful, cf. Appendix A for that reference). 

Investigations on various salts in these solvents show that competition between ion-ion and ion-solvent interactions with increasing salt concentration leads to comparable states of the different solutions at their respective maximum conductance i.e. the maximum specific conductance for every solution is obtained when the conductance-determining effects have established a critical energy barrier which depends almost exclusively on solvent and temperature and not on the solute. As an important consequence, in spite of large ion-ion association constants, the maximum specific conductance can be found at unexpectedly high K a,(-values in solvents of low permittivity This feature can be used advantageously for technical... 

In this table, all units are based on the molar scale and was obtained from the temperature dependence of the overall formation constant Based on the differences in these quantities with the two supporting electrolytes, the ion-association constant for LiCl was estimated as 10 -, which is in good agreement with the value 10 obtained from conductivity data. In PC-H2O mixtures up to [H2O] = 3.57 molar, the various equilibrium constants are given by... 

One cannot neglect of course the changes in solvation of the ion aggregate itself but these changes are small and variations in the ion-association constant for this type of aggregate are largely a reflection of changes in activity of the parent ions and in particular the anion. ... 

The true constant of ion association is a ratio of ionic associate concentration Cat An to ion concentration product. If ionic associate concentration is unknown (as is true in many cases), ion association constant is calculated from the analytical concentration of dissolved substance ... 

The general theory of ionic equilibrium leads to the conclusion that ion association constant in universal or conditionally universal media, in accordance to flic equation [9.53a], depends exponentially on reciprocal value of permittivity ... 

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