Stoichiometric calculations complex ions

These fundamental steps of the catalytic cycle have been confirmed by stoichiometric reactions starting from isolated stable complexes, and by DFT calculations [11], Although many aspects of the Heck olefination can be rationalized by this textbook mechanism , it provides no explanation of the pronounced influence that counter-ions of Pd(II) pre-catalysts or added salts have on catalytic activity [12], This led Amatore and Jutand to propose a slightly different reaction mechanism [13]. They revealed that the preformation of the catalytically active species from Pd(II) salts does not lead to neutral Pd(0)L2 species a instead, three-coordinate anionic Pd(0)-complexes g are formed (Scheme 3, top). They also observed that on the addition of aryl iodides la to such an intermediate g, a new species forms quantitatively within seconds and the solution remains free of iodide and acetate anions. It may then take several minutes before the expected stable, four-... 

This global can be calculated by differentiating the logarithm of Equation 10.6 with respect to (1/T). The weighted averaged AH° was tentatively calculated only on the basis of a stoichiometric approach and under the additional assumption that ion-pair complex formation in the mobile phase is the dominant process [19]. The conclusions, however, are dubious. 

Once the stoichiometry of the complex has been established, the stability constant(s) can be calculated, provided the data yields a curve showing some dissociation in the neighborhood of the stoichiometric point (curve B in Figure 22-12). Briefly, for any data point in the region of curvature, complex formation did not proceed to completion, as evidenced from the difference between the measured curve and the "theoretical" one. Here there is obviously an equilibrium between metal ion, ligand and complex, and from each data point a value of the stability constant can be calculated. 

The technique is generally unaffected by the state (ionic, imdissociated, sometimes complexed) of the analyte to be titrated. For example, the direct potentiometric determination of pH in a solution of a weak acid reports only the hydrogen ion concentration. Since the major portion of the acid is present in the undissociated form, direct potentiometry can not provide data yielding the total acid concentration. Potentiometric titration involves titrating the acid solution with a standard base, determining the equivalence point volume of standard base solution used, and calculating the total weak acid concentration from the stoichiometric data. 

Thermodynamic activities of ionic species in aqueous solutions with ionic strength (I) < 0.01 molal (m) commonly are calculated using the ion-pair model (3), which is valid also for solutions with I < 0.1 m. In dominantly NaCl solutions, the ion-pair model can be used for I < 3 m with appropriate adjustments to the activity coefficients (4). The specific ion interaction model ( may be more appropriate for solutions of high ionic strengths. The effect of pressure on the thermodynamic activities of single ions in this model can be estimated from the stoichiometric partial molal volume and compressibility data (]) However, a complete data set for all the ion-interaction parameters is not yet available for this model to be used in complex geochemical solutions. 

Besides, the water composition, as previously noted, may be analytical and real. In this connection, ionic strength may be stoichiometric and real. Stoichiometric ionic strength is the value calculated based on the analytical composition, i.e., on the content of totally dissociated ions. True ionic strength is characterized by a value, calculated taking into accoimt the process of complex-formation, i.e., for the real composition of the solution. Ionic strength of different salinity natural waters is represented in Figiue 1.6. 

B was redefined by Helgeson (1969) by replacing the stoichiometric ionic strength I with the trae ionic strength I which includes a correction for ion-pairing and complexing. Various methods of calculating 7 are described... 

Goldich-Jackson s weathering series and solubility calculations indicate that mobilities of Ca " and Na" during chemical weathering are relatively large, but those of A1 and Fe are small, and those of Mg, Mn, and Si are intermediate. In the natural environment stoichiometric relation is not established because many solid phases are present and the assumption, mNa+ = mHcOs"- is not established. In fact, ion pairs and complexes in aqueous solution have to be taken into account in addition to free cations and anions. Therefore, the solubility of silicates in the system consisting of multi-components and multi-phases has to be considered. 

In support of this hypothesis, Putnam and Neurath (117) were able to demonstrate that the binding of tingle detergent ions with individual protein groups took place stoichiometrically. Electrophoretic analysis indicated that the two serum albumin-SDS complexes at pH 6.8 had the same constant composition as the complexes that precipitate at pH 4.5. Similar calculations (81, 117) indicated that the number of moles of alkylbenzene sulfonate strongly bound in neutral solution by egg... 

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