Actual ionic strength

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. 

If the ionic strength is lowered, mobility increases (Fig. 15), but there is a limit to this favorable effect, as fractionation becomes less sharp and some proteins may even lose their solubility. The practical range of u for electrophoretic work on proteins is about 0.05-0.075. It is easy to calculate x for a given buffer, but there is no means for determining the actual ionic strength of the buffer inside the strip and consequently no means of measuring absolute mobilities. One reason is that... 

Activity coefficients for each species can be calculated from the Debye-Hiickel theory. The actual ionic strength must be calculated from the experimental conditions, and this generally involves successive approximations (see Worked Problem 8.22). ... 

Since there are no equilibria involved in either electrode compartment the actual ionic strength is found direcdy from the concentrations, and the mean activity coefficients for each of the electrode compartment solutions can be calculated from the Debye-Hiickel equation. 

Since the ionic strength for the solution in the right hand electrode compartment can be found from the quoted concentration - there are no equilibria involved here and the stoichiometric ionic strength is the same as the actual ionic strength - flcr(aq) can be replaced by [Cr]y (Kci). 

Experimental activity coefficients are always quoted as stoichiometric values, ]/j, based on stoichiometric concentrations and ionic strengths. This is still the case for associated electrolytes. However, when association occurs the actual ionic strength will be less than the stoichiometric ionic strength, and it then becomes vital to distinguish between based on the actual concentration and the actual ionic strength, and based on the stoichiometric concentration and the stoichiometric ionic strength. 

Once the possibility of ion association is postulated it becomes absolutely vital that stoichiometric and actual concentrations, and stoichiometric and actual ionic strengths are clearly... 

If association occurs then the actual concentration of free ions will be less than the stoichiometric concentration. Likewise, the actual ionic strength is less than the stoichiometric value. 

These activity coefficients must refer to activity coefficients calculated in terms of the actual ionic strength not the stoichiometric ionic strength, since they relate to the free ions only, and thus to a Their calculation will thus involve a series of successive approximations. 

The potential of the ion-selective electrode actually responds to the activity of picrate in solution. By adjusting the NaOH solution to a high ionic strength, we maintain a constant ionic strength in all standards and samples. Because the relationship between activity and concentration is a function of ionic strength (see Chapter 6), the use of a constant ionic strength allows us to treat the potential as though it were a function of the concentration of picrate. 

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. 

In many situations, the actual molar amount of the enzyme is not known. However, its amount can be expressed in terms of the activity observed. The International Commission on Enzymes defines One International Unit of enzyme as the amount that catalyzes the formation of one micromole of product in one minute. (Because enzymes are very sensitive to factors such as pH, temperature, and ionic strength, the conditions of assay must be specified.) Another definition for units of enzyme activity is the katal. One katal is that amount of enzyme catalyzing the conversion of one mole of substrate to product in one second. Thus, one katal equals 6X10 international units. 

Standard potentials Ee are evaluated with full regard to activity effects and with all ions present in simple form they are really limiting or ideal values and are rarely observed in a potentiometric measurement. In practice, the solutions may be quite concentrated and frequently contain other electrolytes under these conditions the activities of the pertinent species are much smaller than the concentrations, and consequently the use of the latter may lead to unreliable conclusions. Also, the actual active species present (see example below) may differ from those to which the ideal standard potentials apply. For these reasons formal potentials have been proposed to supplement standard potentials. The formal potential is the potential observed experimentally in a solution containing one mole each of the oxidised and reduced substances together with other specified substances at specified concentrations. It is found that formal potentials vary appreciably, for example, with the nature and concentration of the acid that is present. The formal potential incorporates in one value the effects resulting from variation of activity coefficients with ionic strength, acid-base dissociation, complexation, liquid-junction potentials, etc., and thus has a real practical value. Formal potentials do not have the theoretical significance of standard potentials, but they are observed values in actual potentiometric measurements. In dilute solutions they usually obey the Nernst equation fairly closely in the form ... 

The nature of the Debye-Hiickel equation is that the activity coefficient of a salt depends only on the charges and the ionic strength. The effects, at least in the limit of low ionic strengths, are independent of the chemical identities of the constituents. Thus, one could use N(CH3)4C1, FeS04, or any strong electrolyte for this purpose. Actually, the best choices are those that will be inert chemically and least likely to engage in ionic associations. Therefore, monovalent ions are preferred. Anions like CFjSO, CIO, /7-CIC6H4SO3 are usually chosen, accompanied by alkali metal or similar cations. 

The actual characteristics of REV produced depend on a number of factors such as choice of lipids (% cholesterol and charged lipids), lipid concentration used in the organic solvent, rate of evaporation, and ionic strength of the aqueous phase (Szoka and Papahadjopoulos, 1980). Modifications of this REV technique were proposed by several groups. The SPLV (stable plurilamellar vesicles) method consists of bath-sonicating an emulsion of the aqueous phase in an ether solution of lipid while evaporating the ether (Griiner et al., 1985). 

No evidence has yet been obtained in support of such a mechanism in the present context, and it is unlikely that it has general applicability. NMR measurements for example provide no support for a conformational change of PCu(I) on association with Cr(III) complexes (13). Moreover it has in one case been demonstrated that ket in (4) is not dependent on ionic strength, consistant with an intramolecular as opposed to intermolecular process (11). Although caution is required, particularly as isolated examples of (7) - (8) may exist, the invoking of such a mechanism seems to be a case of looking for greater complexity than may actually exist. A reasonable stance, and one which we have adopted, is that discussion should proceed in terms of (5) -(6) until evidence in support of (7) - (8) is obtained. 

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). 

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