Activity coefficient Kielland values

Kielland assigned to each ion an empirical value of a parameter a and used (2-19) to calculate its activity coefficient. A selection of Kielland s values is listed in... 

Kielland has estimated values of x for numerous ions from a variety of experimental data. His best values for effective diameters are given in Table 10-2. Also presented are activity coefficients calculated from Equation iO-5 using these values for the size parameter. 

Kielland (53) examined critically varied data for unassociated electrolytes and recommended values of a for a series of single cations and anions. This convenient procedure has found wide use. Tam-amushi (54) has calculated activity coefficients for single ionic species by identifying in Equation 8 with the distance parameter in the Debye-Htfckel-Onsager equations for electrolytic conductance. Neff (55) prefers to express ionic activity coefficients as a function of the sums of the activities of all species rather than the ionic strength. 

Normal serum calcium level in man is 4.5-5.5 x IO m. About 40 % of this is bound to protein (nondialyzable) and is not in rapid equilibrium with the solution. Thus, we use about 3 x 10 m for the available calcium(II). Similarly, there is about 1 x 10 available phosphates, mainly H2PO4 and HPO (see a diagrams). This is higher in children during bone-forming years. First, we might ask whether these levels are near or above saturation for the solids listed above. To find the appropriate phosphate ion concentration, we need only multiply the total available phosphates by the a value for blood serum pH, 7.40. We use the Kielland table (Appendix A-1) values of activity coefficients to adjust the K values to / = 0.1 M. The / values are for Ca ", 0.405 for P04 , 0.095 for HPO , 0.37 for OH , 0.755. This produces new conditional K values for the set(ll-5a)-(ll-5e) ... 

Tables 2.1-2.4 relative to sodiiun, lithium, potassium, rubidium, and cesium salts, also show that, in general, the values of a obtained by fitting experimental data of activity coefficients are larger than the sum of ionic radii in solutions (or crystal-lattice spacing) and the interatomic distances, d. Also they are close to the values obtained from Kielland sdata and toab initio values calculated by using two models model I and model II, considering the absence and the presence of five water molecules between anion and cation, optimized in the gas phase, respectively), and also to those obtained fi om MM studies, where no water molecules are consid-...

Table 3.1 summarizes a values of 20 acids in aqueous solution, determined from different experimental techniques and/or theoretical approaches, informing us that one estimation of this parameter, at least, was done for every system. Table 3.1 also shows that, in general, the values of a obtained by fitting experimental data of diffusion and activity coefficients are similar but smaller than those obtained from Kielland sdata. This fact could be interpreted on the basis that some effects such as ion-ion and ion-solvent... 

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