Standard state species activity based

Table 13.1-2 Species Activity Based on Different Choices of Standard-State Activity"... 

As discussed earlier, the observed large difference in the standard state equilibrium constants based on the SIT and Pitzer models must result primarily from the differences in the standard state equilibrium constants for the major aqueous species used in these interpretations. Of course, the activity coefficients for the species involved, in particular that for the Th" ion, are also different in the two models cf. Section VI.3.2). 

The activities in Eq. (4-342) provide the connection between the equilibrium states of interest and the standard states of the constituent species, for which data are presumed available. The standard states are alwavs at the equihbrium temperature. Although the standard state need not be the same for all species, or Sipaliicular species it must be the state represented by both Gf and thej ° upon which the activity dj is based. 

For protonation-dehydration processes, such as trityl cation formation from triphenylcarbinols, equation (24), the water activity has to be included if the formulation of the activity coefficient ratio term is to be the same as that in equation (7), which it should be if linearity in X is to be expected see equation (25). The excess acidity expression in this case becomes equation (26) this is a slightly different formulation from that used previously for these processes,36 the one given here being more rigorous. Molarity-based water activities must be used, or else the standard states for all the species in equation (26) will not be the same, see above. For consistency this means that all values of p/fR listed in the literature will have to have 1.743 added to them, since at present the custom... 

Jnst as free protons do not exist in solution in acid-base reactions, there are no free electrons in redox reactions. However it is possible to define the activity of electrons relative to a specified standard state and thereby treat electrons as discrete species in equilibrinm calcnlations in the same way as ions and molecules. The standard state of electron activity for this pnrpose is by convention defined with respect to the redox conple made by hydrogen ions and hydrogen gas ... 

Equations (16)-(18) contain two terms the first one is a function of the concentrations of the species involved in Eqs. (3"), (4"), and (11), while the second is a function of the activity coefficients of these species. The measurement of the standard free energy changes for these processes involves the determination of both concentration and activity terms. Whenever both terms can be accurately determined, the corresponding pKs are referred to as thermodynamic, that is, based on the standard state defined in Section III,F. 

In Equations 2, 4, and 6, ax represents thermodynamic activities based on molar concentrations Cj of the species indicated, y represents mean ionic activity coefficients, i/ha is the activity coefficient of HA(S) molecules, and the activity of water is chosen to be one in all solvents. Consequently values of K, AG°, and AS° are based on these choices regarding standard states. 

The inclusion of activity coefficients into the simple equations was briefly considered by Purlee (1959) but his discussion fails to draw attention to the distinction between the transfer effect and the activity coefficient (y) which expresses the non-ideal concentration-dependence of the activity of solute species (defined relative to a standard state having the properties of the infinitely dilute solution in a given solvent). This solvent isotope effect on activity coefficients y is a much less important problem than the transfer effect, at least for fairly dilute solutions. For example, we have already mentioned (Section IA) that the nearequality of the dielectric constants of H20 and D20 ensures that mean activity coefficients y of electrolytes are almost the same in the two solvents over the concentration range in which the Debye-Hiickel limiting law applies. For 0-05 m solutions of HC1 the difference is within 0-1% and thus entirely negligible in the present context. Of course, more sizeable differences appear if concentrations are based on the molality scale (Gary et ah, 1964a) (see Section IA). 

Because K, depends on concentrations and the product KyKx is concentration independent, Kx must also depend on concentration. This shows that the simple equilibrium calculations usually carried out in first courses in chemistry are approximations. Actually such calculations are often rather poor approximations when applied to solutions of ionic species, where deviations from ideality are quite large. We shall see that calculations using Eq. (47) can present some computational difficulties. Concentrations are needed in order to obtain activity coefficients, but activity coefficients are needed before an equilibrium constant for calculating concentrations can be obtained. Such problems are usually handled by the method of successive approximations, whereby concentrations are initially calculated assuming ideal behavior and these concentrations are used for a first estimate of activity coefficients, which are then used for a better estimate of concentrations, and so forth. A G is calculated with the standard state used to define the activity. If molality-based activity coefficients are used, the relevant equation is... 

In natural waters, other surface reactions will be occurring simultaneously. These include protonation and deprotonation of the >FeOH site at the inner o-plane and complexation of other cations and anions to either the inner (o) or outer (IS) surface planes. Expressions similar to Equation (5) above can be written for each of these reactions. In most studies, the activity coefficients of surface species are assumed to be equal to unity thus, the activities of the surface sites and surface species are equal to their concentrations. Different standard states for the activities of surface sites and species have been defined either explicitly or implicitly in different studies (Sverjensky, 2003). Sveijensky (2003) notes that the use of a hypothetical 1.0 M standard state or similar convention for the activities of surface sites and surface species leads to surface-complexation constants that are directly dependent on the site density and surface area of the sorbent. He defines a standard state for surfaces sites and species that is based on site occupancy and produces equilibrium constants independent of these properties of the solids. For more details about the properties of the electrical double layer, methods to calculate surface specia-tion and alternative models for activity coefficients for surface sites, the reader should refer to the reference cited above and other works cited therein. 

Relationships analogous to those given above may be derived in an exactb similar manner for the activities referred to mole fractions or molarities. As seen in 37c, the activities for the various standard states, based on the ideal dilute solution, can be related to one another by equation (37.7). The result is, however, applicable to a single molecular species the corresponding relationships between the mean ionic activity coefficients of a strong electrolyte, assumed to be completely ionized, are found to be... 

Table 1.4 Activity of Species Based on Different Standard State Activities of Low and...

Equation 11.8.10 correctly relates ArG° and K only if they are both calculated with the same standard states. For instance, if we base the standard state of a particular solute species on molahty in calculating ArG°, the activity of that species appearing in the expression for K (Eq. 11.8.9) must also be based on molality. 

The activity a/ of each reactant or product species is based on an appropriate standard state. We can replace each activity on the right side of Eq. 12.9.1 by an expression in Table 12.2. 

More recently, Brossia et al. [35] introduced an approach based on new correlations for activity coefficients in concentrated solutions. This proach [101] is based on the Helgeson-Kirkham-Flowers equation for standard-state properties with a nonideal solution model based on the activity coefficient expression developed by Bromley and Pitzer. Using specific software, Brossia et al. were able to predict the dominant ionic species and the salt precipitation in Ni, Fe, Cr, and 308 stainless steels crevice solutions. Fair agreement was observed with the in situ analyses of these crevice solutions by Raman spectroscopy. 

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