Equilibrium constant of association

To leam how equilibrium constants of association, K, may be obtained polarographically by analysing shifts in the half-wave potential 1/2 as a function of complex concentration. 

To influence the equilibrium constant of association reactions between analytes and additives (e.g., for the adjustment of the degree of com-plexation an important example is the separation of chiral compounds by the use of cy-clodextrins). 

As part of their molecular-based investigation of solvation at supercritical conditions, Chialvo et al. [230] performed molecular dynamics simulations of supercritical electrolyte solutions with three different ion-water models toward the determination of the association constant for the ion pair Na lCF and the equilibrium constant of association between the solvent-separated and the contact... 

Figure 5 Dependence of the observed propagation rate constant, Ap, on the effective initiator concentration and the equilibrium constants of association, /(a, in the anionic poiymerization of MMA using methyl alpha-...

Determinations by Electrospray of Equilibrium Constants of Association Reactions in Solution and Possible Sources of Error Due to the ESI Process... 

The complex has been separated by ion exchange and characterised by direct analysis . The complex has a distinctive absorption spectrum (Fig. 11), quite unlike that of Np(V) and Cr(III). The rate coefficient for the first-order decomposition of the complex is 2.32 x 10 sec at 25 °C in 1.0 M HCIO. Sullivan has obtained a value for the equilibrium constant of the complex, K = [Np(V) Cr(III)]/[Np(V)][Cr(III)], of 2.62 + 0.48 at 25 °C by spectrophotometric experiments. The associated thermodynamic functions are AH = —3.3 kcal. mole" and AS = —9.0 cal.deg . mole . The rates of decay and aquation of the complex, measured at 992 m/t, were investigated in detail. The same complex is formed when Np(VI) is reduced by Cr(II), and it is concluded that the latter reaction proceeds through both inner- and outer-sphere paths. It is noteworthy that the substitution-inert Rh(lII), like Cr(III), forms a complex with Np(V) °. This bright-yellow Np(V) Rh(III) dimer has been separated by ion-exchange... 

We have given defect-equations for edl nine types of defects, and the Equilibrium Constants thereby associated. However, calculation of these equilibria would require values in terms of energy at each site, values which are difficult to determine. A better method is to convert these EC equations to those involving numbers of each Qrpe of intrinsic defect, as a ratio to an intrinsic cation or einion. This would allow us to calculate the actual number of intrinsic defects present in the crystal, at a specified temperature. 

Figure 12 [115] shows a series of complex formation titration curves, each of which represents a metal ion-ligand reaction that has an overall equilibrium constant of 1020. Curve A is associated with a reaction in which Mz+ with a coordination number of 4 reacts with a tetradentate ligand to form an ML type complex. Curve B relates to a reaction in which Mz+ reacts with bidentate ligands in two steps, first to give ML complexes, and finally close to 100% ML2 complexes in the final stages of the titration. The formation constant for the first step is 1012, and for the second 108. Curve C refers to a unidentate ligand that forms a series of complexes, ML, ML2. .. as the titration proceeds, until ultimately virtually 100% of Mz+ is in the ML4 complex form. The successive formation constants are 108 for ML, 106 for ML2, 104 for ML3, and 102 for ML4 complexes. 

In a typical SPR experiment real-time kinetic study, solution flows over the surface, so desorption of the guest immobilized on the surface due to this flow must be avoided.72 In the first stage of a typical experiment the mobile reactant is introduced at a constant concentration ([H]0) into the buffer flowing above the surface-bound reactant. This favors complex association, and the progress of complex formation at the surface is monitored. The initial phase is then followed by a dissociation phase where the reactant is removed from the solution flowing above the surface, and only buffer is passed over the surface to favor dissociation of the complex.72 74 The obtained binding curves (sensograms) contain information on the equilibrium constant of the interaction and the association and dissociation rate constants for complex formation (Fig. 9). 

The apparent rate constant increased with the concentration of DNA and values for the association (ka) and dissociation (kd) rate constants were determined from the linear relationship of k° s with the sum of the association process (fJDNA]) and dissociation process (ka), equivalent to Equation (3) (Table 5). Note that the parameters k and kd will be employed when these values were determined from overall apparent rate constants to differentiate them from rate constants (k+ and k ) determined for an elementary process. The most important conclusion from this work is that despite similar equilibrium constants the association and dissociation rate... 

Surface plasmon resonance studies were employed to measure the equilibrium constants and association and dissociation rate constants of bisnaphthalimide derivatives (20, 21) with hairpin DNA immobilized on the metal surface.123 The equilibrium constants were higher and the dynamics slower for compounds 20 and 21 when compared to the equilibrium constants and dynamics of the model monomer (19). The values for ka and kd were determined from the change in the surface plasmon resonance signal when, respectively, the ligand solution was flowed over the... 

Table 14 Equilibrium constants and association and dissociation rate constants for the ground-state and triplet excited state of xanthone (35) with CDs...

The equilibrium constant expression associated with systems of slightly soluble salts is the solubility product constant, Ksp. It is the product of the ionic concentrations, each one raised to the power of the coefficient in the balanced chemical equation. It contains no denominator since the concentration of a solid is, by convention, 1, and for this reason it does not appear in the equilibrium constant expression. The Ksp expression for the PbS04 system is ... 

The equilibrium concentration of the ions A- and B- participating in the equlibrium can be directly observed by mass spectrometry. Thus, the free-energy change can be derived from the equilibrium constant, since the concentrations of the neutral species are known in advance. Similarly, by measuring the temperature dependence of the equilibrium constants, the associated enthalpy and entropy can be obtained from van t Hoff plots. By measuring a series of interconnecting equlibria, an appropriate scale can be established. The primary standard in such work has frequently been SO2 whose electron affinity is well established by electron photodetachment36. 

D. Measurement of Equilibrium Constants for Association Processes In Solution... 

The equilibrium constants of the diastereomeric association complexes formed between the enantiomers (R and S) and the auxiliary compound (R ) are different, e.g., for binary... 

In hydrocarbon solvents it is known that most of the growing chains are associated and it is necessary to enquire what effect this has on the copolymerization mechanism. The reactivity ratios measured from copolymer composition are unaffected because they refer to a common ion-pair. The equilibrium constants for association cancel and the reactivity ratios measured give a true measure of the relative propagation constants of the two monomers. No assessment can be made of the real reactivity of two types of active chain with the same monomer, however. In this case the observed rates are a function of the relative reactivities of the free ion-pairs and also of the relative extents of association. For example in hydrocarbon solvents polystyryllithium reacts with butadiene much more rapidly than does polybutadienyllithium. Until we know the two equilibrium constants for self-association we cannot find out if the increased rate is due to greater intrinsic reactivity or to a higher concentration of free polystyryllithium. In polar solvents or in hydrocarbon solvents in the presence of small amounts of ethers, these difficulties do not arise as self-association is no longer important. 

This table is a supplement to Table I. It gives equations for the electron-transfer steps, and for (he chemical reactions associated with them, that are involved in the half-reactions undergone by the compounds listed in Table I, and it also gives values of the rate and equilibrium constants of these processes. 

The concentrated solution viscosity measurement yields the weight-average degree of association of active chain ends rather than the more conventional number-average (mole fraction) value. However, the calculation of the equilibrium constant for association, K, can be accomplished if Mw and the heterogeneity index of the polymer sample are known. The latter parameter can be determined via postpolymerization characterization. 

Schwager F, Marand E, Davis RM. 1996. Determination of self-association equilibrium constant of ethanol by FTIR spectroscopy. J Phys Chem 100 19268-19272. 

Another alternative to occupancy theory is rate theory. Rate theory was developed by Paton through examination of receptors that bind stimulants.30 Paton proposed that a response is caused by the act of binding, not the state of being bound or free (Scheme 5.8). This seemingly subtle difference shifts the theory away from KD and toward kon and fcoff, the rate constants of association and dissociation. Interestingly, at equilibrium, KD is equal to koa/kon (Equations 5.19-5.21). For this reason, occupancy and rate theory are closely related. 

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