Constant ionic strength equilibrium

For solutions of fixed ionic strength, or, for example, where major ions in solution, e.g. conservative cations and anions, are present at concentrations several orders of magnitude greater than the species involved in the chemical equilibrium, e.g. A, B, C, and D in Equation (3.13), it can be assumed that the solute activity coefficients are also constants and can be incorporated into the equilibrium constant. The equilibrium constant for a fixed ionic strength aqueous solution is termed a constant ionic strength equilibrium constant, K. 

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 complexation of Pu(IV) with carbonate ions is investigated by solubility measurements of 238Pu02 in neutral to alkaline solutions containing sodium carbonate and bicarbonate. The total concentration of carbonate ions and pH are varied at the constant ionic strength (I = 1.0), in which the initial pH values are adjusted by altering the ratio of carbonate to bicarbonate ions. The oxidation state of dissolved species in equilibrium solutions are determined by absorption spectrophotometry and differential pulse polarography. The most stable oxidation state of Pu in carbonate solutions is found to be Pu(IV), which is present as hydroxocarbonate or carbonate species. The formation constants of these complexes are calculated on the basis of solubility data which are determined to be a function of two variable parameters the carbonate concentration and pH. The hydrolysis reactions of Pu(IV) in the present experimental system assessed by using the literature data are taken into account for calculation of the carbonate complexation. 

Note that when the concentration of added salt is very low, Debye length needs to be modified by including the charge contribution of the dissociating counterions from the polyelectrolytes. Because the equilibrium interaction is used, their theory predicts that the intrinsic viscosity is independent of ion species at constant ionic strength. At very high ionic strength, the intrachain electrostatic interaction is nearly screened out, and the chains behave as neutral polymers. Aside from the tertiary effect, the intrinsic viscosity will indeed be affected by the ionic cloud distortion and thus cannot be accurately predicted by their theory. 

The existence of such anion effects also implies that, if one wishes to do temperature studies, one cannot simply sit at a constant ionic strength and obtain meaningful activation parameters, because the equilibrium constant involving the association with the anion will also change, of course, as one varies the temperature. Thus, it is necessary to resolve out each rate constant at each temperature and then do the temperature dependencies on individual rate constants. 

G. Anderegg, The investigation of complex formation equilibrium at constant ionic strength, Talanta 40, 243-246 (1993). 

Equilibrium constants are defined at constant ionic strength. 

A measurement of the ability of a buffer system to limit the change in pH of a solution upon the addition of an increment of strong base. ft is the reciprocal of the slope of the pH-neutralization curve. Consider the simple equilibrium, HA H+ -h A where K = [H+][A ]/ [HA] in which K is a practical dissociation constant determined under conditions of constant ionic strength. In such systems the practical pK is equal to the pH of solution when there are equal concentrations of the two buffer species. Since the total concentration of the two... 

To examine the possibility that the different kinetic behaviors for series al, a3, and a5 may be due to differences in ionic strength, the solutions of series al and a3 were replaced by solutions of slighdy different compositions in which small amounts of sodium perchlorate were included. Extreme assumptions about the way that the sodium perchlorate would affect the equilibrium quotients for the bisulfate dissociation were used to calculate the detailed compositions of the new solutions in order to maintain constant ionic strength at 1.50, constant sulfate ion concentration at 0.276Af, and hydrogen ion concentrations close to those of solutions al and a3. No matter which of the assumptions was made in computing the compositions, the kinetic behaviors observed for the new solution series were very similar to those reported herein for series al and a3. 

We define equilibrium constants as concentration quotients, as in Equation (3) for A and /CK. Provided that the experiments are done at low and constant ionic strengths, /< 0.1 m, these can be converted to thermodynamic constants, Aa°, using known or estimated activity coefficients.16... 

All reactions of this type must be studied at constant ionic strength because of the considerable non-ideality of the solutions, and the equilibrium calculations should be given in terms of activities rather than concentrations. 

Planck s constant intensity of radiation initial intensity of radiation intensity of radiation absorbed moment of inertia ionic strength equilibrium constant... 

Since experiments are carried out at a constant ionic strength (I) and equilibrium concentrations of americium in solutions are found to be less than 10 4.8 M, all calculations are made on the... 

The effects of these factors can be illustrated by considering the formation of a 1 1 complex in a hypothetical soil solution at constant ionic strength in the presence of equimolar concentrations of the reactants, in the absence of competing cations and anions, and at pH = pKl = 4 for the dissociation of the monoprotic acid from which the complexing anion is derived (Fig. 9.1). Equilibrium modelling (using TITRATOR Cabaniss, 1987) indicates that >50% of the total cation concentration will not be complexed with the anion unless the pK for the formation of the species is approximately >7.7. The pK value is more than halved,... 

Figure 6. 51V NMR spectra of 0.5, 1.0, and 5.0 mM total vanadate in 150 mM imidazole at pH 8.0. The V2 (—555 ppm) and V4 (—579 ppm) resonances are indicated by arrows. The V2 resonance (—573 ppm) is upfield of the Vj and downfield of the V4 resonance, and the V5 resonance (—585 ppm) is furthest upfield. The H+-dependent equilibrium constants K12 and K14 are defined, and plots of [V2] as a function of [ V2]2 and [V4] as a function of [V2]4 are shown for a study carried out at constant ionic strength. The data shown in these plots were reported previously as assay conditions for studies of 6-phospho gluconate dehydrogenase from sheep liver (Data are from reference 35).

The equilibrium constants K = Kq K[ have been evaluated and the resulting values have been given in Table 4.5. The interaction of lanthanides with perchlorate is strong enough to warrant care in interpreting data on the stability constants in the presence of a large excess of perchlorate used to maintain constant ionic strength. 

Fig. 3.70 depicts the /i(pH) dependence of lyso PC films at po = 42 Pa, t = 30°C and constant ionic strength. In the pH range from 4.2. to 5.8, equilibrium silver-coloured films with mean h values of about 50 - 70 nm were formed. In some experiments, NBF of 7.6 nm thickness were formed, thus marking a fluctuation zone where both silver-coloured and NBF could be observed. Below pH = 4.1 only NBF formed. 

The details of the influence that electrostatic surface forces on the stability of foam films is discussed in Section 3.3. As already mentioned, the electrostatic disjoining pressure is determined (at constant electrolyte concentration) by the potential of the diffuse electric layer at the solution/air interface. This potential can be evaluated by the method of the equilibrium foam film (Section 3.3.2) which allows to study the nature of the charge, respectively, the potential. Most reliable results are derived from the dependence foam film thickness on pH of the surfactant solution at constant ionic strength. The effect of the solution pH is clearly pronounced the potential of the diffuse electric layer drops to zero at certain critical pH value. We have named it pH isoelectric (pH ). As already mentioned pH is an intrinsic parameter for each surfactant and is related to its electrochemical behaviour at the solution/air interface. Furthermore, it is possible to find conditions under which the electrostatic interactions in foam films could be eliminated when the ionic strength is not very high. 

Electrodes sensitive to one of the ion-pair partners in the so-called constant ionic strength cell [95] proved to be valuable to measure the free ion concentration and to determine the stoichiometric equilibrium constant. The latter has a clear thermodynamic meaning if the ionic strength of the medium is indicated, since in this approach, the reference standard state is not the usual infinite dilution of all species dissolved in the solvent (y-> 1, as c -> 0), but is the infinite dilution of the reacting species in the constant ionic medium (7—> 1, as c 0 at 1 = constant) [7]. Even if the constant ionic strength attenuates the variation of liquid junction potentials, the lower the association constant, the lower the consistency of the obtained constant. 

In many calculations the hydrogen ion concentration is more accessible than the activity. For example, the electroneutrality condition is written in terms of concentrations rather than activities. Also, from stoichiometric considerations, the concentrations of solution components are often directly available. Therefore, the hydrogen ion concentration is most readily calculated from equilibrium constants written in terms of concentration. When a comparison of hydrogen ion concentrations with measured pH values is required (in calculation of equilibrium constants, for example), an estimate of the hydrogen ion activity coeflScient can be made by application of the Debye-Huckel theory if necessary, an estimate of liquid-junction potentials also can be made. Alternatively, the glass electrode can be calibrated with solutions of known hydrogen ion concentration and constant ionic strength. " ... 

Pressure Transition-state theory accounts for pressure effects on solution reaction rates through the effect of pressure on the equilibrium constant K. At constant temperature and electrolyte concentration (constant ionic strength),... 

Hydrolysis equilibria can be interpreted in a meaningful way if the solutions are not oversaturated with respect to the solid hydroxide or oxide. Occasionally, it is desirable to extend equilibrium calculations into the region of oversaturation but quantitative interpretations for the species distribution must not be made unless metastable supersaturation can be demonstrated to exist. Most hydrolysis equilibrium constants have been determined in the presence of a swamping inert electrolyte of constant ionic strength (/ = 0.1, 1, or 3 M). As we have seen before, the formation of hydroxo species can be formulated in terms of acid-base equilibria. The formulation of equilibria of hydrolysis reactions is in agreement with that generally used for complex formation equilibria (see Table 6.2). 

The study of the variation of the solubility with the selenite concentration is stated to have been carried at the constant ionic strengths 0.01 and 0.3 M. How this was accomplished was not clear from the information in the paper. The data in the tables rather seem to indicate that the ionic strength varied and reached 0.03 and 0.5 M, respectively, in the solution with the highest selenite concentrations. The analysis of the data was made with an equilibrium model that comprised the solubility equilibrium and the formation of the complex 0(8003)2 T us the formation of CoSe03(aq) was not included in the model. The analysis led to values of the solubility product at the two ionic strengths that appear to be inconsistent with the value obtained from the solubility in water. This result together with the improbable model made the review reject the outcome of the equilibrium analysis. 

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