Equilibrium ionic strength dependence

If the rate equation contains the concentration of a species involved in a preequilibrium step (often an acid-base species), then this concentration may be a function of ionic strength via the ionic strength dependence of the equilibrium constant controlling the concentration. Therefore, the rate constant may vary with ionic strength through this dependence this is called a secondary salt effect. This effect is an artifact in a sense, because its source is independent of the rate process, and it can be completely accounted for by evaluating the rate constant on the basis of the actual species concentration, calculated by means of the equilibrium constant appropriate to the ionic strength in the rate study. 

Raman and Brubaker have also examined reduction by chelates of Fe(II) and explain the ionic strength dependence in terms of a pre-equilibrium ionpairing. 

Marshall s extensive review (16) concentrates mainly on conductance and solubility studies of simple (non-transition metal) electrolytes and the application of extended Debye-Huckel equations in describing the ionic strength dependence of equilibrium constants. The conductance studies covered conditions to 4 kbar and 800 C while the solubility studies were mostly at SVP up to 350 C. In the latter studies above 300°C deviations from Debye-Huckel behaviour were found. This is not surprising since the Debye-Huckel theory treats the solvent as incompressible and, as seen in Fig. 3, water rapidly becomes more compressible above 300 C. Until a theory which accounts for electrostriction in a compressible fluid becomes available, extrapolation to infinite dilution at temperatures much above 300 C must be considered untrustworthy. Since water becomes infinitely compressible at the critical point, the standard entropy of an ion becomes infinitely negative, so that the concept of a standard ionic free energy becomes meaningless. 

The rate constants for the reaction of a pyridinium Ion with cyanide have been measured in both a cationic and nonlonic oil in water microemulsion as a function of water content. There is no effect of added salt on the reaction rate in the cationic system, but a substantial effect of ionic strength on the rate as observed in the nonionic system. Estimates of the ionic strength in the "Stern layer" of the cationic microemulsion have been employed to correct the rate constants in the nonlonic system and calculate effective surface potentials. The ion-exchange (IE) model, which assumes that reaction occurs in the Stern layer and that the nucleophile concentration is determined by an ion-exchange equilibrium with the surfactant counterion, has been applied to the data. The results, although not definitive because of the ionic strength dependence, indicate that the IE model may not provide the best description of this reaction system. 

The specific ion interaction approach is simple to use and gives a fairly good estimate of activity factors. By using size/charge correlations, it seems possible to estimate unknown ion interaction coefficients. The specific ion interaction model has therefore been adopted as a standard procedure in the NEA Thermochemical Data Base review for the extrapolation and correction of equilibrium data to the infinite dilution standard state. For more details on methods for calculating activity coefficients and the ionic medium/ ionic strength dependence of equilibrium constants, the reader is referred to Ref. 40, Chapter IX. 

The pH dependence of Ks/Km is similar for step 1 and step 2 reactions as shown in Fig. 26b, but this similarity in the pH curves indicate only that the same titratable groups on the free enzyme and/or free substrate are involved in the two steps. As discussed explicitly by Usher et al. (522) the roles of the two histidines could be reversed and this would make no difference since the ratio of HE EH where these are the two singly protonated species is independent of pH. Similar ks and Ka curves for the two steps would also fail to prove identical roles for the two histidines. Since a pentacovalent species—whether it is a transient activated complex or a more stable intermediate—is common to the various alternatives, pK shifts deduced from ka curves could be the same. Both substrates are monovalent anions with low pK values so that 1 /Km, whether interpreted as an equilibrium binding value or as a function of the kinetic parameters mirroring the total occupancy of all the stable intermediates, could also be the same for both steps. The values for the reverse of step 2 would behave differently since the pj of 3 -CMP, for example, is 5.9. It should also be noted that ks/Km curves should be and are ionic strength dependent (508) in the same way that the His 12 and His 119 pK values are as observed by NMR (280). 

Unsymmetrical inert electrolyte binding leads to semantic problems even at pristine conditions PZC becomes ionic strength dependent, the surface potential is not equal to zero at the PZC. etc., cf. Eqs. (3.2) and (3.3). Fortunately such problems are encountered in modeling exercises with unsymmetrical electrolyte binding, but not in reality. Anyway, this modification is not recommended. Ultimately a TLM with seven adjustable parameters (equilibrium constants of reactions (5.32), (5.33), (5.46), and (5.47) are unrelated) can be used to model raw titration data (the charging curves were not shifted to produce PZC = CIP) [66], but physical meaning of such model exercises is questionable. 

Ciavatta obtained [90CIA] an average deviation of 0.05 kg-mol" between s estimates according to Eqs. (B.22) and (B.23) and the e values at 25°C obtained from ionic strength dependency of equilibrium constants. 

Since this equilibrium constant involves concentrations it is, by definition, a non-ideal constant, and in principle may show an ionic strength dependence. Generally the experimental measurement is the pH, found either directly from the pH of the given solution, or, more accurately, from a pH titration. The rigorous definition of pH is ... 

Using the methylviologen cation radical (MV +) formed by pulse radiolysis, monophasic kinetics of cytochrome reduction are observed with a rate constant of 4.5 X 108 M 1/s (1.1 X 108 M 1/s on a per heme basis) at pH 8.0 with the Hildenborough cytochrome (36). This very fast second-order process approaches the diffusion controlled limit. Moreover, the reverse reaction can be estimated to be 7.8 X 104 M-1/s, which suggests that the reaction takes place primarily with the highest potential heme (the A E 0 between heme I and MV + is 190 mV, consistent with an equilibrium constant of approximately 103). Interestingly, the kinetics with MV + are ionic strength dependent, which is consistent with a plus-plus interaction,... 

Figure 7-5 The ionic strength dependence of the monomer/dimer equilibrium of P. denitrificans cytochrome C550- Cytochrome csso (2.3 nmol) dissolved in 10 mM Hepes, pH 8.0, containing the appropriate NaCl concentration, were passed down a Superdex 75 column equilibrated in the same buffer. The elution volume was compared with a set of standards (serum albumin, ovalbumin, carbonic anhy-drase, myoglobin and cytochrome c) in order to obtain a value of Mr. O, oxidized cytochrome C550 , cytochrome C550 reduced with 1 mM ascorbate.

In a few cases we have used the equilibrium constants for minor species to estimate their ionic strength dependence and to show the charge and size systematics of ion interaction coefficients. 

The specific interaction parameter b is also different from the corresponding Ae value because of the different Debye-Htickel terms. Up to the review of Baes and Mesmer [1976BAE/MES], there were no data available to model the ionic strength dependence of the equilibrium constants for polynuclear species in one of the ionic media. The common method to estimate equilibrium constants at zero ionic strength was to use an experimental value at finite ionic strength and then to use only the Debye-Htickel term to estimate the value at zero ionic strength. 

To conclude, this paper does not provide a useful method to estimate the ionic medium / ionic strength dependence of equilibrium constants and all equilibrium constants at zero ionic strength deduced by the approach in [1973MIL] are rejected by the present review. 

Table 6 lists association constants between porphyrins and nucleic acids. Equilibrium constants between Hi(TMpyP-4) (52) and Cu(TMpyP-4) (88) with a synthetic polymer poly(dG-dC) were estimated to be 7.7 x lO M and 8.0 x 10 M, respectively, based on McGhee-von Hippel analysis.The equilibrium constants were ionic-strength dependent. It was observed that at 2 M ionic strength, the Free-base poqrhyrin 52 almost completely dissociates from DNA, poly(dA-dT) and poly(dG-dC). Therefore electrostatic interactions are the important driving force. Kinetic studies were carried out for the above system... 

For low MW salts, K eC nd its ionic strength dependence are primarily determined by solute-substrate interactions, usually electrostatic, including the Donnan equilibrium between the mobile phase and the gel phase. Deviation from Kv ec = 1 can be attributed with confidence to such effects. For polyions, the "ideal" or "unperturbed" value of K jeC ( °eC difficult to identify furthermore, because of intrapolymer repulsion and concommitant chain expansion (30), itself is dependent on ionic strength. Consequently, derivations from ideal SEC due to charge interactions may go undetected, and possibly only the more dramatic cases are recognized in the literature. 

The ionic strength depends not only on the concentration of Ag" and Cl ions but also on all the other ions. Thus, for example, the addition of nitric acid HNO3, which adds H" " and NOJ ions to the system, will change the activity coefficient. But the equilibrium constant, which is a function of Tonly (8.3.19), remains constant if T is constant. As a result, the value of m (or solubility in molal) will change with the ionic strength I. If the concentration of nitric acid (which dissociates completely) is mnNOs. the ionic strength will be... 

If the rate law involves the concentration of a species involved in a pre-equilibrium before the rate-determining step of a reaction, then the concentration of this species may depend upon the ionic strength, from which the reaction rate may also show an ionic strength dependence. This effect is known as the secondary salt effect. To some extent this effect is an artefact, since it does not really affect the rate constant of the reaction, but changes the concentration of the reactants. The correct rate constant can be determined using the true concentration of the species, calculated using the appropriate equilibrium constant for the pre-equilibrium step determined at the experimental ionic strength. 

In determining the values of Ka use is made of the pronounced shift of the UV-vis absorption spectrum of 2.4 upon coordination to the catalytically active ions as is illustrated in Figure 2.4 ". The occurrence of an isosbestic point can be regarded as an indication that there are only two species in solution that contribute to the absorption spectrum free and coordinated dienophile. The exact method of determination of the equilibrium constants is described extensively in reference 75 and is summarised in the experimental section. Since equilibrium constants and rate constants depend on the ionic strength, from this point onward, all measurements have been performed at constant ionic strength of 2.00 M usir potassium nitrate as background electrolyte . 

The pH will depend upon the ionic strength of the solution (which is, of course, related to the activity coefficient — see Section 2.5). Hence, when making a colour comparison for the determination of the pH of a solution, not only must the indicator concentration be the same in the two solutions but the ionic strength must also be equal or approximately equal. The equation incidentally provides an explanation of the so-called salt and solvent effects which are observed with indicators. The colour-change equilibrium at any particular ionic strength (constant activity-coefficient term) can be expressed by a condensed form of equation (4) ... 

At a finite distance, where the surface does not come into molecular contact, equilibrium is reached between electrodynamic attractive and electrostatic repulsive forces (secondary minimum). At smaller distance there is a net energy barrier. Once overcome, the combination of strong short-range electrostatic repulsive forces and van der Waals attractive forces leads to a deep primary minimum. Both the height of the barrier and secondary minimum depend on the ionic strength and electrostatic charges. The energy barrier is decreased in the presence of electrolytes (monovalent < divalent [Pg.355]

Thus, the dissociation equilibrium is affected by the ionic strength, temperature and dielectric constant of the solvent as well as by the parameter h (involved in AGf,). On the other hand, the term dG /dn does not depend on the degree of polymerization (except for very small values of n). The degree of polymerization does not affect, for example, the course of the potentiometric titration of a poly acid. 

---