Activity coefficient stoichiometric

From the free activity coefficients and values of K obtained in binary solutions it is possible then to calculate total (stoichiometric) activity coefficients in more complex solutions. 

The approach of specific interactions, developed primarily by Pitzer (1973) and Whitfield (1975a,b), considers all salts, from a purely formal point of view, as completely dissociated, and embodies the effects of specific interactions into particular activity coefficients, defined as total activity coefficients or stoichiometric activity coefficients, with symbol y. For instance, for ion /,... 

The activity coefficients of hydrobromic acid in the mixed solvents are lower, as expected, than those in water (20). Hydrobromic acid completely dissociates in the mixed solvents (e = 49.5 at 298.15° K for the 50 mass percent monoglyme) under investigation. Figure 2 clearly indicates that at a particular molality, the stoichiometric activity coefficient of hydrochloric acid is lower than that of hydrobromic acid in the same mixed solvent, and the heat capacity changes (Cp — Cp) also suggest that there are no ion-pair formations. 

Activities in Concentrated Solutions.—For relatively concentrated solutions it is necessary to use the complete Hiickel equation (62) by choosing suitable values for the two adjustable parameters a and it has been found possible to represent the variation of activity coefficients with concentration of several electrolytes from 0.001 to 1 molal, and sometimes up to 3 molal. The values of C seem to lie approximately between 0.05 and 0.15 in aqueous solution. At the higher concentrations it is necessary to make allowance for the difference between the rational and stoichiometric activity coefficients the latter, which is the experimentally determined quantity, is represented by an extension of equation (62) thus (cf. p. 135),... 

In the experimental determination of activity coefficients of strong electrolytes, by the methods described below, the molalities, etc., of the ions are taken as the stoichiometric values, that is, the total possible molality, etc., disregarding incomplete dissociation, For example, in the last problem, the molalities of the sodium and sulfate ions in the 0.5 molal solution of sodium sulfate were taken as exactly 1.0 and 0.5, respectively, without allowing for the possibility that the salt may be only partially dissociated at the specified concentration. The activity coefficients obtained in this manner are called stoichiometric activity coefficients they allow for all variations from the postulated ideal behavior, including that due to incomplete dissociation. If the treatment is based on the actiuil ionic molalities, etc., in the given solution, as in the Debye-Httckel theory (Chapter XVII), there is obtained the true (or actual) activity coefficient. TTie ratio... 

It should be noted that the Debye-Htickel theory yields true, and not stoichiometric, activity coefficients ( 39a), since it is the behavior of the ions only, and not of the whole solute, which is taken into consideration. For strong electrolytes dissociation is virtually complete at all dilutions for which the limiting law may be expected to hold for such solutes, therefore, the distinction between true and stoichiometric activity coefficients may be ignored. 

The activity of each ionic species may be represented as the product of its molality and its (stoichiometric) activity coefficient hence is equal to my. and oci to 2my, where m is the molality of the zinc chloride solution in the cell. By equation (39.9), 7+7I is equal to y , where y is the mean ionic activity coefficient hence equation (45.16) becomes... 

The stoichiometric activity coefficient of bicarbonate ion is less in a 0.7 moVkg solution of NaHCO, than it is in a 0.7 mol/kg solution of NaCl. Why might this be the case ... 

Reardon, E. J. 1975. Dissolution constants of some monovalent sulfate ion pairs at 25°C from stoichiometric activity coefficients. J. Phy.s. Chem. 79 422. 

Values for yA B cannot be determined but T is accessible from the mean stoichiometric activity coefficients in mixed salt solutions via equation (8) thus ... 

ISO] Isono, T., Osmotic coefficients, stoichiometric activity coefficients, and dissociation constants of magnesium and nickel sulfates in aqueous solutions at the freezing-point, Rikagaku Kenkyusho, 65, (1971), 95-99. Cited on pages 181, 183, 188, 189,347. 

So (17.35) gives an estimate of the stoichiometric activity coefficient of a trace component, 7 , which includes the three major non-ideality corrections in a concentrated NaCl solution. In (17.35), Ig is the association-corrected ionic strength including all components of the solution, the parameters Zj and a refer to the trace component (not NaCl), and B is the value for the dominant salt in the solution, NaCl. Because (17.35)... 

Wood, S.A., Crerar, D., Brantley, S.L., and Borcsik, M., 1984, Mean molal stoichiometric activity coefficients of alkali halides and related electrolytes in hydrothermal solutions Amer. Jour. Sci., v. 284, pp. 668-705. 

Mean Molal Stoichiometric Activity Coefficients of H2SO4 in Methanol... 

In 1975. Santos et al. (S41) determined the association constant of NaSOi at 2S°C to be 2.5 . 2 at. 5M ionic strength using a sodium-sdective electrode. That same year, Reardon (S33) presented a value of i =. 82 . 05 (K a. 1514) at 25 C,. 1 molal from stoichiometric activity coefficients. 

Reardon, E.J., "Dissociation constants of some monovalent sulfate ion pairs at 25° from stoichiometric activity coefficients", J. Phys. Chem., v79, 5. pp422-425 (1975)... 

The above analysis shows clearly that a rat exists for functional representation of solubi two-component systems, but may be difficult to experimental or theoretical )cnowledge of activ molar enthalpies. Other phenomena which are r stoichiometric activity coefficients and which include ion pairing, formation of complex ions considerations hold for the variation of solub that the effects are relatively smaller at the investigations of solubility (5). 

In this equation, if we put = and m =I. m, the quantity becomes the stoichiometric activity coefficient and includes within itself the effect of any incompleteness of the dissociation as well as the deviation from ideality, as discussed in 10-9. Adopting this convention we obtain... 

Recall that y is the mean ionic activity coefficient of a strong electrolyte, or the stoichiometric activity coefficient of an electrolyte that does not dissociate completely. 

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