Stoichiometric ionic strength

Since AG° can be calculated from the values of the chemical potentials of A, B, C, D, in the standard reference state (given in tables), the stoichiometric equilibrium constant Kc can be calculated. (More accurately we ought to use activities instead of concentrations to take into account the ionic strength of the solution this can be done introducing the corresponding correction factors, but in dilute solutions this correction is normally not necessary - the activities are practically equal to the concentrations and Kc is then a true thermodynamic constant). 

The exceptional reactivity of DNA for protonated N-hydroxy arylamines can be rationalized by at least two mechanisms. First, intercalation of the electrophilic intermediate between DNA bases could sterically assist in desolvation and in directing the electrophilic center of the carcinogen over the nucleophilic region of the DNA base. This seems unlikely, however, as pretreatment of DNA with cis-Pt, which decreased the DNA contour length by 50%, failed to reduce the reactivity of N-hydroxy-1-naphthylamine for the DNA (137). A second possibility involves an electrostatic attraction between the electrophile and the phosphate backbone of the DNA (77). This seems more probable since eithe j +high ionic strength or stoichiometric (to DNA-P) amounts of Mg strongly inhibit DNA adduct formation (77,137). In addition, evidence has been presented that N-hydroxy arylamine-DNA/RNA phosphotriesters may be formed which induce strand breaks (137,138) and could serve as a catalyst for desolvation and subsequent adduct formation. 

The ideality of the solvent in aqueous electrolyte solutions is commonly tabulated in terms of the osmotic coefficient 0 (e.g., Pitzer and Brewer, 1961, p. 321 Denbigh, 1971, p. 288), which assumes a value of unity in an ideal dilute solution under standard conditions. By analogy to a solution of a single salt, the water activity can be determined from the osmotic coefficient and the stoichiometric ionic strength Is according to,... 

Fig. 8.5. Water activity aw versus stoichiometric ionic strength 7s of NaCl solutions at 25 °C and 300 °C, according to the activity model of Helgeson (1969). Dashed line shows 3 molal limit to the model parameterization values to right of this line are extrapolations of the original data.

A comparison of experimental results with those calculated from the Fuoss (2) theory is presented in Table I. The theory 1s only valid approximately so that the order of magnitude agreement is fairly good, except in the cases of MgC03° and CaC03 . Stoichiometric association constants K are then obtained from the activity coefficients, expressions for K, and from equations for the conservation of mass. The latter express the total concentration of a given ion as the sum of the concentrations of the free ion and of the ion-pairs. Values of K and of the activity coefficients of free ions in ionic media depend only upon the effective ionic strength as is shown later. 

The statistical thermodynamic approach of Pitzer (14), involving specific interaction terms on the basis of the kinetic core effect, has provided coefficients which are a function of the ionic strength. The coefficients, as the stoichiometric association constants in our ion-pairing model, are obtained empirically in simple solutions and are then used to predict the activity coefficients in complex solutions. The Pitzer approach uses, however, a first term akin to the Debye-Huckel one to represent nonspecific effects at all concentrations. This weakens somewhat its theoretical foundation. 

Originally, the stoichiometric stability constants 6 for the lead and the cadmium complexes with chloride had been determined in NaCl-NaC104 solutions and it had been assumed that the NaCl was completely dissociated. The nominal ionic strength was one molal. The constants were later corrected by replacing the actual free chlorides for the total chlorides in the calculation of... 

This assumes H2O = 1, which is nearly true, even in seawater. For example, H2O = 0.98 at 35%o, 25°C, and 1 atm. As with other equilibrium expressions, and can be rewritten as stoichiometric constants that are specific for a particular temperature, pressure, and ionic strength. 

Reaction 72 was found to proceed in one-electron steps (228), so that it does not regenerate Craq002 +. The scavenging of Cra+ by Craq002 + in Eq. (73) (58) is a rapid reaction (k7S = 8 x 108 M-1 s-1 at 1 M ionic strength) that generates some, but less than stoichiometric amounts of Craq02 +, and will therefore deplete the catalyst in Scheme 15. 

Selective electrodes have a variable specificity. Precision can be increased when they are used as indicating electrodes in potentiometric measurements. The concentration of ions present in solution and the ionic strength will undergo small variations during measurement relative to the concentration of the ion being measured. When two ionic species undergo stoichiometric reaction, this property can be used for their determination. The end point in the measurement is characterised either by the total disappearance of one of the species or by the appearance of an excess of one of the species. The appearance or disappearance of a secondary species can also be used to determine the end point. 

If S0 = [M]m[L] is the stoichiometric solubility product for the species MmL at a given ionic strength, precipitation will not take place unless this ion product is exceeded. However if M or L undergoes side reactions, the analytical concentrations of the free ions left in solution will be reduced such that [M ] < [M] and [L ] < [L] and the effective or conditional solubility product, S o, is now given by... 

Determining solubility constants in aqueous solutions generally involves analytical work to determine concentrations [ ] or potentiometric measurements to obtain activities. The ratio of activity and concentration—i.e., the activity coefficient and its change with concentration— depends on the choice of the standard state. If pure water is chosen as a standard state, the activity coefficients approach unity only in dilute solutions. It is therefore necessary to express the so-called thermodynamic constants TK (48) in terms of activities. If, on the other hand, one chooses as reference an aqueous solution of comparatively high and constant ionic strength, the activity coefficients remain close to unity even at rather high concentrations of the reacting species. In this case, we may use stoichiometric constants K (48), expressed in molarities, M, and related to a particular ionic medium. 

Many others confirmed later the existence of two different species, stoichiometrically equivalent to H atoms, but different in reactivity. An unequivocal proof, however, that the neutral form is e aq, has been obtained by Czapski and Schwarz (12). They showed that the ionic strength effect on reactions of e aq was indeed as expected with unit negatively charged species. This result was verified by other workers (11). 

Ion association and other associative phenomena are not discussed. It is vital that such effects are considered, especially at higher ionic strengths, where significant association occurs. In kinetic studies, allowances for ion pairing are made by distinguishing between the stoichiometric ionic concentrations and the actual ones. 

Kinetic results which apparently do not fit the above treatment of the primary salt effect do so when the observed rates are correlated with the actual ionic strengths rather than the stoichiometric values. The actual concentrations in the reaction solution are calculated using the known value of the equilibrium constant describing the ion pair. This is discussed in Problem 7.5. 

The same distinction can be made between the actual ionic strength, calculated from the actual concentrations, and the stoichiometric ionic strength. 

Problem 7.5 is particularly important as it illustrates conclusively that linearity of a plot of log10 k0bs versus Z7/( 1 + Zf) should not be taken to be the final word on the reaction. There are many reactions where a linear graph is obtained when the stoichiometric ionic strength is used. However, a further scrutiny of the results will reveal, as in the example quoted in Problem 7.5, that there are discrepancies which need to be explained. If this is done, considerable insight into the details of the reaction can be made. It will be of interest to compare this problem with Problem 8.3, where a similar hydrolysis is studied, but where the ion pair is found to be as reactive as OH-. 

The extent of speciation in solution depends on the stoichiometric coefficients of the components of a species the polyvalent nature and protonation behaviour of anionic complexing ligands the type and relative ability of different cations and anions to form complexes pH ionic strength, and the ratio of the total concentrations of the reactants in solution (the total cation anion ratio). 

The rate of hydrolysis depends markedly on pH and on the cobalt to ADP stoichiometric ratio it depends also on the nature of any pre-equilibration procedures. Variations in the ionic strength (NaClO ) have a minor effect. 

The influence of pressure on the apparent or stoichiometric constants can be determined by using equations 1.43, 1.44, and 1.45 with the data in Table 1.10. It should be noted that the currently available information for V and K is restricted to S=35. A reasonable approximation of pressure effects at other salinities, however, can be made assuming a linear variation of V and K between pure water and S=35 seawater as a function of the square root of ionic strength. The variations of pK values with pressure at 0 and 25°C for S=35 seawater are presented in Figure 1.6. 

As noted, the retention of a polypeptide or protein with HP-IEX sorbents primarily arises from electrostatic interactions between the ionized surface of the polypeptide or protein and the charged surface of the HPLC sorbent. Various theoretical models based on empirical relationships or thermodynamic considerations have been used to describe polypeptide and protein retention, and the involvement of the different ions, in HP-IEC under isocratic and gradient elution conditions (cf. Refs.6,19 33 40,78-90). Over a limited range of ionic strength conditions, the following empirical dependencies derived from the stoichiometric retention model can be used to describe the isocratic and gradient elution relationships between the capacity factor In and the corresponding salt concentration [C,] or the median capacity factor In k ex, and the median salt concentration [C,] of a polypeptide or protein solute, namely,... 

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. 

It must be emphasized that such stoichiometric stability constants are dependent, inter alia, upon the ionic strength of the solution, and, in reporting experimental results, the ionic strength of the experimental solutions should always be specified. Further, the numerical value of a stoichiometric constant will depend upon the units used, viz. mole fractions, molar, molal, millimole, and so on, and which is used should always be made clear. 

Since AmG is sensitive to both the composition and concentration of electrolytes A and B, its calculation would be simplified considerably if the initial solutions and the final mixture were at the same stoichiometric ionic strength based on 1 kg of solvent in the final mixture. This suggests that for a given mixture of electrolytes in solution sufficient sets of common ion mixtures at the same I should be found which in sum describe the total solution, allowing the excess free energy of the mixture to be found using a series of calculations shown by equation 9. Basically, this is the approach used to calculate AmG in this study. 

Equation (47) was suggested for the first time by Bredig and Ripley [202]. In order to establish it unambiguously, it is necessary to carry out experiments at a constant ionic strength since feH and kHX are influenced by salt effects. Studies in the presence of halides at a constant ionic strength have never been done. Other approaches have been used instead. Albery and Bell [200] measured hydrolysis rates of ethyl diazoacetate in moderately concentrated perchloric acid and hydrochloric acid solutions. Rates in hydrochloric acid were faster than those in perchloric acid at the same stoichiometric concentration. In order to verify the dependence on the chloride ion concentration, it was assumed that rates of the reaction without participation of chloride (first term in eqn. (47)) are the same in perchloric acid and hydrochloric acid if the H0 values are equal. Activity coefficients were introduced in eqn. (47) as follows ... 

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