Stoichiometry equilibria involving complex

In conventional reversed phase HPLC, differences in the physicochemical interactions of the eluate with the mobile phase and the stationary phase determine their partition coefficients and, hence, their capacity factor, k. In reversed-phase systems containing cyclodextrins in the mobile phase, eluates may form complexes based not only on hydrophobicity but on size as well, making these systems more complex. If 1 1 stoichiometry is involved, the primary association equilibrium, generally recognized to be of considerable importance in micellar chromatography, can be applied (11-13). The formation constant, Kf, of the inclusion complex is defined as the ratio of the entrance and exit rate constants between the solute and the cyclodextrin. Addition of organic modifiers, such as methanol, into the cyclodextrin aqueous mobile phase should alter the kinetic and thermodynamic characteristics of the system. This would alter the Kf values by modifying the entrance and exit rate constants which determine the quality of the separation. 

Matty of the equilibiiiun problems we encounter involve equilibrium constants, such as K, and Ksp, that are very small. Often, this enables us to neglect the unknown x in the denominator of the equilibrium expression, which simplifies the math necessary to solve the problem [ Section 16.5], The solution of an equilibrium problem involving complex ion formation is complicated both by the magnitude of and by the stoichiometry of the reaction. Consider the combination of aqueous copper(II) ions and ammonia to form the complex ion Cu(NH3)4 ... 

Complexes formed by tetradentate siderophores involve stepwise complex formation and therefore, have somewhat different equilibria from their hexadentate analogs. Initial chelation will occur with a tetracoordinate FeL complex forming. A subsequent equilibrium then occurs, where the FeL complexes will react in a 2 1 stoichiometry with free ligands in solution to form a single Fe2L3 complex (coordinated water and charges not shown for clarity). 

The photophysical properties (extinction coefficient, shifts in absorption and emission spectra, quantum yield, and lifetime) of a variety of probes are modified by pH changes, complexation by metal ions, or redox reactions. The resulting changes in photophysical parameters can be used to determine concentration of H+ and metal cations with suitably designed fluorophores. Most of these resulting sensors involve an equilibrium between the analyte, A, and the free probe (unprotonated or noncom-plexed by metal ion), Pf. If the stoichiometry of this reaction is 1 1, the reaction may be represented by... 

It Is postulated that mixed-valence species or complex salts (12) formed as a result of this field Induced redox reaction control the semiconducting behavior of these films and these complex salts exist In a solid-state equilibrium with the simple 1 1 salt. Since non-integral oxidation states are common In solids, It Is difficult to predict exact stoichiometry In the equilibrium equation, but a likely equation for switching In Cu-TCNQ, for example, may Involve... 

The three Salem samples show increased leaching rates as a function of increased acidity, but not the rate values predicted by simple chemical stoichiometry. A pH decrease from 5.6 to 4.0 is a 39.8x increase in acidity, while a change from 4.0 to 3.0 is a 10x acidity increase. The observed changes were factors of 2.88x and 1.58x, respectively. These discrepancies can be attributed to the complex equilibrium interactions involved in the solubilities of the metal carbonates. These two solubility equilibria are further complicated by the two acid equilibria for the carbonic acid/bicarbon-ate/carbonate system in addition to the equilibrium solubility of congas in water. The solution of these simultaneous equilibria processes to determine the relationship between carbonate solubility and acid concentration is a non-trivial one (sixth degree in concentration). This solubility problem has been approached from several different viewpoints (31-35), the most convenient being a graphical solution of the solubility as a function of initial solution and final solution pH. From this method, it can be theoreti-... 

Whilst the synthesis of new transition metal-olefin and -acetylene complexes continues unabated, only a relatively small amount of data has accumulated on the thermodynamic stability of these complexes and these are restricted almost exclusively to complexes of the unsatured species acting as monodentate ligands. Metals able to coordinate strongly with unsaturated ligands are restricted to those in a small triangle around the centre of the periodic table, and designated class (b) acceptors by Ahrland et al., 0>. Class (b) acceptors include Cu(I), Rh(II), Ag(I), Pt(II) and Hg(II). However the majority of such metals form inert complexes which are either very readily oxidised or involve solubility problems. If thermodynamic stability constants are to be measured reliably, the equilibrium should be reached reasonably quickly, the reaction should be clean and the stoichiometry should be known or easily deduced. Furthermore, the equilibrium must be followed by means of suitable electrodes or changes in some physical property of the reaction mixture. The solvent is therefore important. 

Here the rate equations are written as if they were for elementary steps (reaction order corresponds to stoichiometry) except for the more complex steps involved in 4 and 5 where first-order is assumed. The equilibrium constants for 2, 6, and 8 can be obtained from tabulated data thus... 

Several techniques have been employed to examine the thermodynamics of Pb(Il)-ligand interactions and determine consistent values of log ATpbL. By far, the most common method used to date is a direct determination by potentio-metry in aqueous solution. However, in cases where the reagents or the complex are insoluble, other techniques have been employed (303). Generally, one can use any method that can measure the concentration of at least one of the species involved in the formation of a metal complex at equilibrium (301), provided that the concentration of the species and the stoichiometry of the reaction provide enough information to account for all of the species present in solution. 

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