Activity-ionic strength relation

It is important to note that the solubility product relation applies with sufficient accuracy for purposes of quantitative analysis only to saturated solutions of slightly soluble electrolytes and with small additions of other salts. In the presence of moderate concentrations of salts, the ionic concentration, and therefore the ionic strength of the solution, will increase. This will, in general, lower the activity coefficients of both ions, and consequently the ionic concentrations (and therefore the solubility) must increase in order to maintain the solubility product constant. This effect, which is most marked when the added electrolyte does not possess an ion in common with the sparingly soluble salt, is termed the salt effect. 

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) ... 

This is an example of a reversible reaction the standard electrode potential of the 2PS/PSSP + 2c couple is zero at pH 7. The oxidation kinetics are simple second-order and the presence of a radical intermediate (presumably PS-) was detected. Reaction occurs in the pH range 5 to 13 with a maximum rate at pH 6.2, and the activation energy above 22 °C is zero. The ionic strength dependence of 2 afforded a value for z Zg of 9 from the Bronsted relation... 

Most measurements include the determination of ions in aqueous solution, but electrodes that employ selective membranes also allow the determination of molecules. The sensitivity is high for certain ions. When specificity causes a problem, more precise complexometric or titri-metric measurements must replace direct potentiometry. According to the Nernst equation, the measured potential difference is a measure of the activity (rather than concentration) of certain ions. Since the concentration is related to the activity through an appropriate activity coefficient, calibration of the electrode with known solution(s) should be carried out under conditions of reasonable agreement of ionic strengths. For quantitation, the standard addition method is used. 

In many drug solutions, it is necessary to use buffer salts in order to maintain the formulation at the optimum pH. These buffer salts can affect the rate of drug degradation in a number of ways. First, a primary salt effect results because of the effect salts have on the activity coefficient of the reactants. At relatively low ionic strengths, the rate constant, k, is related to the ionic strength, p, according to... 

Can the species activity coefficients be calculated accurately An activity coefficient relates each dissolved species concentration to its activity. Most commonly, a modeler uses an extended form of the Debye-Hiickel equation to estimate values for the coefficients. Helgeson (1969) correlated the activity coefficients to this equation for dominantly NaCl solutions having concentrations up to 3 molal. The resulting equations are probably reliable for electrolyte solutions of general composition (i.e., those dominated by salts other than NaCl) where ionic strength is less than about 1 molal (Wolery, 1983 see Chapter 8). Calculated activity coefficients are less reliable in more concentrated solutions. As an alternative to the Debye-Hiickel method, the modeler can use virial equations (the Pitzer equations ) designed to predict activity coefficients for electrolyte brines. These equations have their own limitations, however, as discussed in Chapter 8. 

A second approach is the standard addition method, which is commonly employed when the sample is unknown. The potential of the electrode is measured before and after addition of a small volume of a standard to the known volume of the sample. The small volume is used to minimize the dilution effect. The change in the response is related only to the change in the activity of the primary ion. This method is based on the assumptions that the addition does not alter the ionic strength and the activity coefficient of the analyte. It also assumes that the added standard does not significantly change the junction potential. 

According to Deybe-Huckel limiting law, the activity coefficient/of an ion is related to the ionic strength as... 

It is often more convenient to relate the potentiometer reading directly to concentration by adjusting the ionic strength and hence the activity of both the standards and samples to the same value with a large excess of an electrolyte solution which is inert as far as the electrode in use is concerned. Under these conditions the electrode potential is proportional to the concentration of the test ions. The use of such solutions, which are known as TISABs (total ionic strength adjustment buffers), also allows the control of pH and their composition has to be designed for each particular assay and the proportion of buffer to sample must be constant. 

The effect of solution anionic concentration is probably related to effects on activity coefficients and ion pair formation of more highly charged buffer species. In more concentrated solutions, the activity of the highly charged species is reduced by both ionic strength and ion pair formation. The effect on less charged, acidic species is less. Therefore, as solutions become more concentrated, the activity of basic species is reduced relative to that of acidic species, and at a given fraction... 

To leam that activity a and concentration c are related by the expression a = c X (equation (3.12)) where y is the mean ionic activity coefficient, itself a function of the ionic strength I. 

The activity a and concentration c are related by a = (c/c ) x y (equation (3.12)), where y is the mean ionic activity coefficient, itself a function of the ionic strength /. Approximate values of y can be calculated for solution-phase analytes by using the Debye-Huckel relationships (equations (3.14) and (3.15)). The change of y with ionic strength can be a major cause of error in electroanalytical measurements, so it is advisable to buffer the ionic strength (preferably at a high value), e.g. with a total ionic strength adjustment buffer (TISAB). 

The ionic strength of the solution influences the activity coefficients of the species present and the values of the liquid-junction potentials in the system and thus must be held constant in all related measurements, within a range of about 0.1 to 2m. 

The following text is only intended to provide the reader with a brief outline of the Pitzer method. This approach consists of the development of an explicit function relating the ion interaction coelScient to the ionic strength and the addition of a third virial coefficient to Eq. (6.1). For the solution of a single electrolyte MX, the activity coefficient may be expressed by Eq. (6.29) [15] ... 

So far, we have expressed the number of ions per unit volume by concentration. Physical chemists prefer to use activity to characterize the behavior of solutes in solution. As a solution becomes more concentrated and as the ionic strength increases, ions behave as if there were fewer of them present than would be indicated by their analytical concentrations. The activity of a component is related to its concentration by a proportionality constant known as an activity coefficient . Considerations regarding ionic activity become particularly important, when fluids are quite concentrated. An extension of this treatment is the use of the activity product to... 

A mathematical approach that attempts to explain how the solution behavior of electrolytes depends on their ionic charge and the overall ionic strength of the solution. This treatment allows one to estimate the mean activity coefficients that relate the analytical concentration of an electrolyte to its solution activity. We also can come to understand how the activity coefficient behaves as a function of ionic strength. 

In Eq. 30, Uioo and Fi are the activity in solution and the surface excess of the zth component, respectively. The activity is related to the concentration in solution Cioo and the activity coefficient / by Uioo =fCioo. The activity coefficient is a function of the solution ionic strength I [39]. The surface excess Fi includes the adsorption Fi in the Stern layer and the contribution, f lCiix) - Cioo] dx, from the diffuse part of the electrical double layer. The Boltzmann distribution gives Ci(x) = Cioo exp - Zj0(x), where z, is the ion valence and 0(x) is the dimensionless potential (measured from the Stern layer) obtained by dividing the actual potential, fix), by the thermal potential, k Tje = 25.7 mV at 25 °C). Similarly, the ionic activity in solution and at the Stern layer is inter-related as Uioo = af exp(z0s)> where tps is the scaled surface potential. Given that the sum of /jz, is equal to zero due to the electrical... 

The activity coefficient of a species is related to the ionic strength by the Debye-Hiickel Eq. 

Another important parameter is the acidity of the system. Since the relation between enzyme activity and pH often shows an optimum, buffers are regularly used in enzymatic derivatization to control the pH. Use of buffers, however, can cause increase of the ionic strength of the system, thus changing the tertiary structure of the enzyme and either making it more accessible for the substrate or blocking its active sites. Therefore, optimization of the chromatographic system is recommended for each specific system. 

Just as in aqueous solutions, the activity of solute i (acl) in non-aqueous solutions is related to its (molar) concentration (sj by aCii = yCiiCi, where g is the activity coefficient that is defined unity at infinite dilution. For non-ionic solutes, the activity coefficient remains near unity up to relatively high concentrations ( 1 M). However, for ionic species, it deviates from unity except in very dilute solutions. The deviation can be estimated from the Debye-Hiickel equation, -log yci = Az2 /1/2/ (1+aoBf1 2). Here, I is the ionic strength and / (moll-1), a0 is the ion size parameter... 

The activity 3j of an ion i is related to its concentration q by the relationship d = where 7, is the activity coefficient which depends on the total ionic strength /. This latter term is a measure of the quantity and charge of all ions present in the medium / = 0.5 Cizf- Therefore, for ion i of charge z, equation (18.1) becomes ... 

The ionic atmosphere model leads to the extended Debye-Hiickel equation, relating activity coefficients to ionic strength ... 

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. 

---