Equilibrium condition associations/dissociations

The following entry defines the commonly used stability constants (stepwise, overall, conditional, association, dissociation, and pK) and relates the values to a rigorous thermodynamic definition of equilibrium constants. In addition, the article briefly outlines experimental techniques (potentiometric titration, spectroscopic methods involving ultraviolet/visible, infrared, Raman, fluorescence. and nuclear magnetic resonance spectroscopy), together with the numerical methods and computer programs that can be used to derive stability constants from such experimental data. 

We now turn to the dynamic limit where the rates of association/dissociation of ML are infinitely fast. The complex system will maintain a transport situation governed by the coupled diffusion of M and ML. In the case of excess of ligand conditions, equation (57), the full lability condition implies the maintenance of equilibrium on any relevant spatial scale ... 

The equilibrium condition for the distribution of one solute between two liquid phases is conveniently considered in terms of the distribution law. Thus, at equilibrium, the ratio of the concentrations of the solute in the two phases is given by CE/CR = K, where K1 is the distribution constant. This relation will apply accurately only if both solvents are immiscible, and if there is no association or dissociation of the solute. If the solute forms molecules of different molecular weights, then the distribution law holds for each molecular species. Where the concentrations are small, the distribution law usually holds provided no chemical reaction occurs. 

It is possible that similar situations involving rapid association-dissociation equilibria have been encountered in ribosomes, which under appropriate conditions exist in a reversible equilibrium 70S =i50S + 30 S. 

It was pointed out earlier that the natural equilibrium condition for the production and dissociation of ozone resulted in an ozone maximum at some intermediate level in the upper atmosphere. From measurements at different times and by different observers (6, 12, 16, 32, 33, 37, 39, 4I, 4, this maximum has been found to vary in height, thickness, and in general structure, with short and long period fluctuations possibly associated with weather conditions and seasonal variations. On occasion double maxima may appear (41)- Little is yet known, however, about specific relationships between the ozone changes and meteorological conditions except in the instance of seasonal variations (6, 8, 10, 15, 26, 30, 4 ) and certain large air mass movements (9, 56, 59). There is a great need for continuous observations of both the total and the vertical distribution of ozone in order to establish possible relationships between ozone distribution and concentration and solar variation, atmospheric circulation, and weather. 

Theoretically an infinite incubation period would be needed to reach perfect equilibrium in the first step (incubation with H). However, in practice, conditions are chosen so as to shorten this period to reach near-perfect equilibrium. The association and dissociation constants (fca., and /c,) are usually not known, but according to the law of mass action the higher the Ab and H concentrations, the faster Ab-H is formed. The concentration of H, however, should not exceed that of Ab. In the commercial kits (Section 14.3), the concentrations are sometimes so high that the few seconds between... 

Bile salts carry extensive hydrophobic (hydrocarbon) portions in each molecule that attempt to reduce their contact with water (4). This is reflected in rapid, dynamic association-dissociation equilibrium to form self-aggregates or micelles as the total concentration of bile salt solute is increased (the CMC) [2-6]. Experimentally, micelles are undetectable in dilute solutions of the monomers, and are detected in increasing numbers and often size above the CMC [98]. Because bile salt micelles are often small (i.e., dimers) [5], and since self-aggregation continues to proceed in many cases with increasing concentration above the CMC [17,18,20,52,98], the detection of the lowest concentration at which the first aggregates form depends particularly upon the sensitivity of the experimental probes employed [98] and the physical-chemical conditions [3-5]. 

A schematic diagram of the apparatus is shown in Fig. 4 and a photograph of a typical trace in Fig. 5. The top of the initial large spike due to shock arrival is off scale. The observable decay following shock arrival is attributable to the vibrational relaxation process which precedes dissociation and represents the incubation or induction period. The relaxation period is followed by a non-zero minimum or dip which is identified with the end of the induction period and is interpreted as a measure of the initial dissociation rate. It is the magnitude of the dip that is used to calculate the rate coefficient associated with the condition of complete vibrational equilibrium and zero dissociation. Translational and rotational equilibration are much faster processes and are achieved prior to the vibrational relaxation event. 

It is not easy to quantify precisely the supersaturation levels of given species generated in mixed salt systems or in solutions in which ion association occurs. Relationships such as equations 3.67 3.69 cannot be simply applied because of the difficulty of expressing the true reference condition of equilibrium saturation. It is first necessary to identify all the possible single species, ion pairs and solid liquid phase equilibria that can occur in the system. The relevant thermodynamic association/dissociation constants (K values) must be known. The activity coefficients for the various ionic species must be calculated, e.g. by means of Debye-Hiickel type equations (section 3.6.2). Equilibrium concentrations of all the possible species present are then evaluated by iterative procedures. 

The possibility of equilibrium process of chemical bonds association-dissociation should be also exluded, since for this process the value does not exceed 2.03 [58]. After t 48 min in system neither chemical nor physical changes occur, that is reflected by the conditions Q = const and const. The poly condensation reaction realization rate 0 can be obtained from the Eq. (27), differentiating it by time t. This gives the expression [113] ... 

Because binding assays follow mass action kinetics, a finite period of time is required for the reaction to reach equilibrium, the point at which the rate of association of L with R equals the rate of dissociation of the LR complex. To be a useful tool, RRA must always be performed under equilibrium conditions. 

The demonstration of specific hormone receptors in most systems has relied either on direct isolation and characterization of protein-hormone complexes or on analysis of the kinetics of uptake and/or dissociation of labeled hormones by cells or macromolecules. Under equilibrium conditions, uptake at speeifie receptors has been discriminated from nonspecific uptake by displaeement with nonlabeled physiologically active steroids or competitive inhibitors. Such studies have shown that steroids have a high affinity but a relatively slow rate of association with specific receptors, that the reeeptors are saturable at physiological concentrations of hormone, and that binding is competed for by other active steroids... 

The experiments described above have led to the conclusion that the chiral-induced equilibrium shift could be induced in the lanthanide (III) complex by a combination of electrostatic and hydrophobic interactions. Hydrogen bonding effects appear to be less important as suggested by experiments carried out under variable pH, temperature, concentration, solvent type, and solution dielectric constant conditions. By analogy to the associated/dissociated equilibrium shift models of Schipper (1978) in which the source of the equilibrium perturbation is attributed to a free energy of mixing, Brittain (1981) and Wu et al. (1989) attempted to ascertain the complex mechanism responsible for this type of Pfeiffer effect. However, their conclusions were opposite as they concluded that the [Tb(DPA)3] complex interacted with the... 

The effect of tetrahydrofuran on the polymerization of isoprene in hexane has been studied by Morton and co-workers (73, 74). The viscosity method was used to measure the degree of association. This was found to drop from 2 in pure hexane to about 1.3 with a ratio of THF to polyisoprenyllithium of 100 and dissociation of the polymer aggregates was complete at ratios of 500—700. With the reasonable assumption that the only species present in significant amounts were associated polymer molecules and etherates, it was possible to find the concentration of etherate present under all conditions. An equilibrium constant could be evaluated from the overall process... 

A number of recent studies have shown that under certain conditions, FABMS indeed can very accurately measure the balance of ionic species in ongoing chemical reactions in solutions. These studies include the determination of acid dissociation constants (2), equilibrium constants for enzyme catalyzed reactions (1), metal-ligand association constants 03), and measurements of... 

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