Zero ionic strength

Data reported for the protolysis constant of water at zero ionic strength are listed in Table 5.7. The data cover a wide range of temperature, and a number of data are available at most temperatures where data have been reported. The average of the data, at a given temperature, has been determined together with an uncertainty at a 95% confidence level, and these average values are used subsequently in this work. Data that have not been accepted have been determined statistically to be outliers. 

The equations of Bandura and Lvov (2006) are complex functions of temperature. Undertaking the necessary algebra to determine the expressions for enthalpy, entropy and heat capacity leads to even more complex functions (not presented here). Use of these equations to derive the enthalpy, entropy and heat capacity values as a function of temperature gives values that follow the same trends as measured values, but the absolute values are often outside the 95% confidence limit of the measured data. Consequently, it is felt that the measured data provide a better estimate of these thermodynamic data than expressions developed from the equations of Bandura and Lvov (2006). 

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The data in the tables generally refer to temperatures of about 20 to 25°C. Most of the values in Table 8.12 refer to zero ionic strength, but those in Table 8.13 often refer to a finite ionic strength. 

In this experiment the equilibrium constant for the dissociation of bromocresol green is measured at several ionic strengths. Results are extrapolated to zero ionic strength to find the thermodynamic equilibrium constant. Equilibrium Constants for Calcium lodate Solubility and Iodic Acid Dissociation. In J. A. Bell, ed. Chemical Principles in Practice. Addison-Wesley Reading, MA, 1967. 

Directions are provided in this experiment for determining the dissociation constant for a weak acid. Potentiometric titration data are analyzed by a modified Gran plot. The experiment is carried out at a variety of ionic strengths and the thermodynamic dissociation constant determined by extrapolating to zero ionic strength. 

This experiment describes the determination of the stability (cumulative formation) constant for the formation of Pb(OH)3 by measuring the shift in the half-wave potential for the reduction of Pb + as a function of the concentration of OH . The influence of ionic strength is also considered, and results are extrapolated to zero ionic strength to determine the thermodynamic formation constant. 

Source All values are from Martell, A. E. Smith, R. M. Critical Stability Constants, Vol. 1-4. Plenum Press New York, 1976. Unless otherwise stated, values are for 25 °C and zero Ionic strength. Values In parentheses are considered less reliable. 

The following substituents listed in Table IV were omitted in the determination of p S-SOs", 4-SOs", 3-C02", and 4-CO2". For these ionic substituents a strong dependence of the a-values calculated on ionic stren h was observed, and it was impossible to extrapolate to zero ionic strength cf. H. Zollinger, W. Btichler, and C. Wittwer, Helv. Chim. Acta 36, 1711 (1953). 

Flo. 33. Extrapolation to zero ionic strength of the equilibrium constant of acetic acid in aqueous solution at 25°C. 

Experience shows that solutions of other electrolytes behave in a manner similar to the examples we have used. The conclusion we reach is that the Debye-Hiickel equation, even in the extended form, can be applied only at very low concentrations, especially for multivalent electrolytes. However, the behavior of the Debye-Hiickel equation as we approach the limit of zero ionic strength appears to give the correct limiting law behavior. As we have said earlier, one of the most useful applications of Debye-Hiickel theory is to... 

In the case of the monofluorocomplexes of quadrivalent plutonium, it is obvious that the lower values obtained in chloride and nitrate media are due to complexing by these ions these results will not be discussed further. In HCIO4 media the data for the first two fluoride complexes are quite self-consistent and well within the same order of magnitude as these reported for the other quadrivalent actinides (12, 89). An extensive comparison would extend beyond the scope oT tKTs paper. In the case of PuF3+, extrapolation of bi to zero ionic strength is not warranted as such in view of the limited number of data. However, in the case of ThF3+ where the data extend over a very wide range of ionic... 

More recently, a value of 3x 10 l.mole . sec has been calculated for the exchange rate coefficient at 10 °C and zero ionic strength by Campion et al. using the Marcus theory and rate coefficients for the reactions... 

Campion et ai have calculated a value for the exchange coefficient (10 °C, zero ionic strength) of 1 x 10 l.mole sec from the observed rate coefficients for the reactions... 

The reductions by ferrous ion and mono- and bis-bipyridyl complexes of Fe(II) are also simple second-order with (for the Fe reaction at zero ionic strength ). 2 = TO X 10 exp(—12.1 X 10 /Rr) l.mole . sec . This reaction generates an intermediate capable of oxidising ethanol but the effect is suppressed by addition of Cl , Br and acrylonitrile, the latter being polymerised. 

Ferrocyanide reduces persulphate, the reaction being second-order in a fairly saline medium (0.5 M K2S04) with /c2 = 3.2x 10 exp(—11.9 x lO /Hr) l.mole . sec. The rate is strongly influenced by the presence of potassium ions and this has been shown not to be merely an ionic strength effect" . Consideration of all possible modes of ion-pairing led to the conclusion that the two reactants are [K(Fe(CN)6] and [KS20g] . At zero ionic strength, E = 9.6 kcal.mole and AS = —34.7 eu. Kershaw and Prue have measured the specific effects of many other cations on the rate of this reaction. 

If several buffer concentrations are used, extrapolation can be carried out to zero ionic strength, and the pKa can be determined. For initial studies, however, a pK in... 

The solubility product is measured by determining the ion concentrations by a suitable analytical method and the results are extrapolated to zero ionic strength, where P — P. 

The relationships of the type (3.1.54) and (3.1.57) imply that the standard electrode potentials can be derived directly from the thermodynamic data (and vice versa). The values of the standard chemical potentials are identified with the values of the standard Gibbs energies of formation, tabulated, for example, by the US National Bureau of Standards. On the other hand, the experimental approach to the determination of standard electrode potentials is based on the cells of the type (3.1.41) whose EMFs are extrapolated to zero ionic strength. 

The pK of Ca2+aq (204), 12.6 at zero ionic strength, rising to over 13 as ionic strength increases, means that concentrations of CaOH+aq will be negligible in body fluids (lpolluted waters, and under all conditions of biological relevance, from the very low pHs of 0.5 (Thiobacillus thiooxidans) to 1.5 at which bacteria used for oxidative metal extraction operate (205), through acid soils and acid rain (pH 3 to 6), streams, rivers, and oceans (pH 6 to 8), soda lakes (pH 10), up to the pHs of 11 or more in Jamaican Red Mud slurry ponds (206) (cf. Section II.C.l below). 

Changes in solubility product are one means of experimentally determining a value of activity coefficient, because we can independently determine the concentrations (e.g. via a titration) and the values of all y will be one at zero ionic strength. 

The small difference between the successive pK values (cf. values below) of tungstic acid was previously explained in terms of an anomalously high value for the first protonation constant, assumed to be effected by an increase in the coordination number of tungsten in the first protonation step (2, 3, 55). As shown by the values of the thermodynamic parameters for the protonation of molybdate it is actually the second protonation constant which has an abnormally high value (54, 58). An equilibrium constant and thermodynamic quantities calculated for the first protonation of [WO, - pertaining to 25°C and zero ionic strength (based on measurements from 95° to 300°C), namely log K = 3.62 0.53, AH = 6 13 kJ/mol, and AS = 90 33 J, are also consistent with a normal first protonation (131) (cf. values for molydate, Table V). 

It should be possible to obtain EV2 for unpaired ions either by Fleischmann s technique [13] (which was published too late for the Keele Research Group, now dispersed, to make use of it), or by extrapolating EV2 obtained conventionally with varying concentrations of supporting electrolyte, to zero ionic strength. 

Dankwerts and McNeil ( 3) have employed the method of Van Krevelen et al. to predict the partial pressure of carbon dioxide over carbonated alkanolamine solutions. The central feature of this model is the use of pseudo-equilibrium constants and their dependence on ionic strength. The ratio of the pseudo-equilibrium constant at a certain ionic strength to that at zero ionic strength has been termed the "ionic characterization factor". However, ionic strength alone is insufficient to determine the ionic characterization factors. As well the ionic characterization factors are sometimes not a simple linear function of ionic strength. 

These equilibrium constants vary with molarity of the HF solution. Measured values corrected for zero ionic strength at 25 °C are = 6.71 x 10 4 mol 1, K2=3.86 1 mol-1, and K3=2.71mor1 [BrlO, Iul, Wall], implying a dissociation of only a few percent. This unusual behavior is still controversial and has been attributed to the greater strength of the H-F bond compared to the other hydrogen halides [Pal], to the presence of the dimer (HF)2 [Wal], or to polymers that may... 

We confine our attention to the limit of zero ionic strength (i.e., an extremely dilute solution of reactants) and make comparison with experimental data extrapolated to zero ionic strength (10, 11). Furthermore, a very simple primitive... 

Calculated Rate Constants and Activation Parameters. Calculated results based on the three different models (TST, SCT, and QMT) are displayed in Table II and compared with experimental results (30) extrapolated to zero ionic strength (Tl). 

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