Constants ion pairs

By analogy, one can define an association constant ion-pair formation. Thus, one can consider an equilibrium between free ions (the positive M" ions and the negative A ions) and the associated ion pairs (symbolized IP)... 

Some interesting conductance studies of protein-nonaqueous solvent systems have been carried out. Greenberg and Larson (1935), for example, found that gelatin, casein, and edestin dissolved in glacial formic acid (D = 56.5 at 16°C) showed marked increases of conductivity over that of the solvent, whereas no conductivity increment was observed with the same proteins dissolved in glacial lactic or acetic (D = 6.15 at 20°C) acids. This is in accord with the conclusions reached in Section IV,B,1, that in solvents of low dielectric constant, ion-pairing (in these cases, of the protein cations to lactate and acetate counterions) is essentially complete. Con-... 

Because methylene chloride is a solvent of low dielectric constant, ion pairing occurs detectably even for rather large cations and anions. We will discuss ion-pairing studies involving these compounds before the effects of solvent upon X, because it is... 

The explanation of these results proposed by Kraus and Fuoss21 in a series of papers, is based on two assumptions. The first of these is that electrolytes that are completely dissociated in water or any other solvents of high dielectric constant will be more or less associated into ion pairs in solvents of low dielectric constants. Ion pairs, AB, are considered to form entirely by electrostatic forces from the charged ions A+ and B , and the complexes are assumed to take no part in the conduction. Though no sharp division has been made experimentally these ion pairs are considered to differ from the undissociated portion of a weak electrolyte in that no electron shift has occurred in their formation. The second assumption is that, as the concentration of the ion pairs increases, a proportion of them will combine with ions by electrostatic forces, to form triple ions. ... 

The process of association of ions and ion pairs does not necessarily stop with the formation of ion pairs. In solvents of very low dielectric constants ion pairs may react to form complex molecules according to the equation... 

Generally, when determining association constants (ion-pair or... 

One can write acid-base equilibrium constants for the species in the inner compact layer and ion pair association constants for the outer compact layer. In these constants, the concentration or activity of an ion is related to that in the bulk by a term e p(-erp/kT), where yp is the potential appropriate to the layer [25]. The charge density in both layers is given by the algebraic sum of the ions present per unit area, which is related to the number of ions removed from solution by, for example, a pH titration. If the capacity of the layers can be estimated, one has a relationship between the charge density and potential and thence to the experimentally measurable zeta potential [26]. 

The rate constants for the catalysed Diels-Alder reaction of 2.4g with 2.5 (Table 2.3) demonstrate that the presence of the ionic group in the dienophile does not diminish the accelerating effect of water on the catalysed reaction. Comparison of these rate constants with those for the nonionic dienophiles even seems to indicate a modest extra aqueous rate enhancement of the reaction of 2.4g. It is important to note here that no detailed information has been obtained about the exact structure of the catalytically active species in the oiganic solvents. For example, ion pairing is likely to occur in the organic solvents. 

If this electrostatic treatment of the substituent effect of poles is sound, the effect of a pole upon the Gibbs function of activation at a particular position should be inversely proportional to the effective dielectric constant, and the longer the methylene chain the more closely should the effective dielectric constant approach the dielectric constant of the medium. Surprisingly, competitive nitrations of phenpropyl trimethyl ammonium perchlorate and benzene in acetic anhydride and tri-fluoroacetic acid showed the relative rate not to decrease markedly with the dielectric constant of the solvent. It was suggested that the expected decrease in reactivity of the cation was obscured by the faster nitration of ion pairs. 

The general formula for the initiator species can be written H B, where the degree of separation or ion pairing depends on the polarity of the medium and the possibility of specific solvation interactions. If we represent the equilibrium constant for the reactions in (6.DD) and (6.EE) by K, the initiator concentration can be written as... 

Ionic polymers may exist as undissociated, unsolvated ion pairs undissociated ion pairs solvated to some extent solvated ions dissociated to some extent or some combination of these. The propagation rate constant kp and the dissociation equilibrium constant K of the lithium salt of anionic... 

Studies have shown that, in marked contrast to carbanionic polymerisation, the reactivity of the free oxonium ion is of the same order of magnitude as that of its ion pair with the counterion (6). On the other hand, in the case of those counterions that can undergo an equiUbrium with the corresponding covalent ester species, the reactivity of the ionic species is so much greater than that of the ester that chain growth by external attack of monomer on covalent ester makes a negligible contribution to the polymerisation process. The relative concentration of the two species depends on the dielectric constant of the polymerisation medium, ie, on the choice of solvent. 

The physical picture in concentrated electrolytes is more apdy described by the theory of ionic association (18,19). It was pointed out that as the solutions become more concentrated, the opportunity to form ion pairs held by electrostatic attraction increases (18). This tendency increases for ions with smaller ionic radius and in the lower dielectric constant solvents used for lithium batteries. A significant amount of ion-pairing and triple-ion formation exists in the high concentration electrolytes used in batteries. The ions are solvated, causing solvent molecules to be highly oriented and polarized. In concentrated solutions the ions are close together and the attraction between them increases ion-pairing of the electrolyte. Solvation can tie up a considerable amount of solvent and increase the viscosity of concentrated solutions. 

Table 1. Anion Extraction Constants Eq, of Tetra-n-Butylammonium Ion Pairs Between Water and Chloroform...

EA Carter, JT Elynes. Solute-dependent solvent force constants for ion pairs and neutral pairs m a polar solvent. J Phys Chem 93 2184-2187, 1989. 

In the discussion of the relative acidity of carboxylic acids in Chapter 1, the thermodynamic acidity, expressed as the acid dissociation constant, was taken as the measure of acidity. It is straightforward to determine dissociation constants of such adds in aqueous solution by measurement of the titration curve with a pH-sensitive electrode (pH meter). Determination of the acidity of carbon acids is more difficult. Because most are very weak acids, very strong bases are required to cause deprotonation. Water and alcohols are far more acidic than most hydrocarbons and are unsuitable solvents for generation of hydrocarbon anions. Any strong base will deprotonate the solvent rather than the hydrocarbon. For synthetic purposes, aprotic solvents such as ether, tetrahydrofuran (THF), and dimethoxyethane (DME) are used, but for equilibrium measurements solvents that promote dissociation of ion pairs and ion clusters are preferred. Weakly acidic solvents such as DMSO and cyclohexylamine are used in the preparation of strongly basic carbanions. The high polarity and cation-solvating ability of DMSO facilitate dissociation... 

The ionization eonstant should be a function of the intrinsic heterolytic ability (e.g., intrinsic acidity if the solute is an acid HX) and the ionizing power of the solvents, whereas the dissoeiation constant should be primarily determined by the dissociating power of the solvent. Therefore, Ad is expeeted to be under the eontrol of e, the dieleetrie eonstant. As a consequenee, ion pairs are not deteetable in high-e solvents like water, which is why the terms ionization constant and dissociation constant are often used interchangeably. In low-e solvents, however, dissociation constants are very small and ion pairs (and higher aggregates) become important species. For example, in ethylene chloride (e = 10.23), the dissociation constants of substituted phenyltrimethylammonium perchlorate salts are of the order 10 . Overall dissociation constants, expressed as pArx = — log Arx, for some substanees in aeetie acid (e = 6.19) are perchloric acid, 4.87 sulfuric acid, 7.24 sodium acetate, 6.68 sodium perchlorate, 5.48. Aeid-base equilibria in aeetie acid have been earefully studied beeause of the analytical importance of this solvent in titrimetry. 

Sn2 reactions with anionic nucleophiles fall into this class, and observations are generally in accord with the qualitative prediction. Unusual effects may be seen in solvents of low dielectric constant where ion pairing is extensive, and we have already commented on the enhanced nucleophilic reactivity of anionic nucleophiles in dipolar aprotic solvents owing to their relative desolvation in these solvents. Another important class of ion-molecule reaction is the hydroxide-catalyzed hydrolysis of neutral esters and amides. Because these reactions are carried out in hydroxy lie solvents, the general medium effect is confounded with the acid-base equilibria of the mixed solvent lyate species. (This same problem occurs with Sn2 reactions in hydroxylic solvents.) This equilibrium is established in alcohol-water mixtures ... 

The dissociation constant for the first process is only 1.1 X 10 lmol at 25°C this corresponds to pKa 2.95 and indicates a rather small free hydrogen-ion concentration (cf. CICH2CO2H, p ffl 2.85) as a result of the strongly H-bonded, undissociated ion-pair [(H30)" F ]. By contrast, K2 = 2.6 X 10 lmol pK2 0.58), indicating that an appreciable number of the fluoride ions in the solution are coordinated by HF to give HF2 rather than by H2O despite the very much higher concentration of H2O molecules. 

When diazomethane is slowly added to excess lactam, the anions formed can interact with unreacted lactam by means of hydrogen bonds to form ion pairs similar to those formed by acetic acid-tri-ethylamine mixtures in nonpolar solvents. The methyldiazonium ion is then involved in an ion association wdth the mono-anion of a dimeric lactam which is naturally less reactive than a free lactam anion. The velocity of the Sn2 reaction, Eq. (7), is thus decreased. However, the decomposition velocity of the methyldiazonium ion, Eq. (6a), is constant and, hence, the S l character of the reaction is increased which favors 0-methylation. It is possible that this effect is also involved in kinetic dependence investigations have shown that with higher saccharin concentrations more 0-methylsaccharin is formed. 

In ionic polymerizations, reaction rates are faster in solvents with high dielectric constants, which promote the separation of the ion pair. 

A criterion for the presence of associated ion pairs was suggested by Bjerrum. This at first appeared to be somewhat arbitrary. An investigation by Fuoss,2 however, threw light on the details of the problem and set up a criterion that was the same as that suggested by Bjerrum. According to this criterion, atomic ions and small molecular ions will not behave as strong electrolytes in any solvent that has a dielectric constant less than about 40. Furthermore, di-divalent solutes will not behave as strong electrolytes even in aqueous solution.2 Both these predictions are borne out by the experimental data. 

In the case of a sparingly soluble substance, if each of the quantities in (64) is divided by Avogadro s constant, we confirm the statement made above— namely, that, if AS at per ion pair is added to the contribution made to the entropy of the crystal by each ion pair, in this way we evaluate the contribution made by one additional ion pair to the entropy of the saturated solution and it is important to grasp that this contribution depends only on the presence of the additional pair of ions in the solution and does not depend on where they have come from. They might have been introduced into the solution from a vacuum, instead of from the surface of a solid. In (64) the quantities on the right-hand side refer to the solution of a crystal, but the quantity (S2 — Si) does not it denotes merely a change in the entropy of a solution due to the presence of additional ions, which may have come from anywhere. When Si denotes the entropy of a sufficiently large amount of solution, (S2 — Si) is the partial molal entropy of the solute in this solution. 

The molecular weight of H2O being 18.0, 1 mole of water at room temperature occupies 18.0 cm. If several water molecules are added to a quantity of water, the increment in volume per molecule added will be 18.0 cm3 divided by Avogadro s constant. In other words, omitting Avogadro s constant, the increment will be 18.0 cms/mole. As we shall be interested in ion pairs, we may remark that the increment in volume per pair of H2O molecules will be 3G cma/mole and we may use this value as a basis of comparison for a pair of atomic ions. 

An alternative to the formation of neutral metal chelates for solvent extraction is that in which the species of analytical interest associates with oppositely charged ions to form a neutral extractable species.6 Such complexes may form clusters with increasing concentration which are larger than just simple ion pairs, particularly in organic solvents of low dielectric constant. The following types of ion association complexes may be recognised. 

Conductivity measurements yield molar conductivities A (Scm2 mol-1) at salt concentration c (mol L-1). A set of data pairs (Af, c,), is evaluated with the help of non linear fits of equations [89,93,94] consisting of the conductivity equation, Eq. (7), the expression for the association constant, Eq. (3), and an equation for the activity coefficient of the free ions in the solution, Eq.(8) the activity coefficient of the ion pair is neglected at low concentrations. 

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