Mass action expressions complexes

Mass action equations. The first step in any calculation is to collate the mass action expressions that define the formation of the species. The way in which the formation constants can be used can be illustrated by considering a metal such as aluminium in an aqueous medium. Aluminium ions can undergo a number of hyrolysis reactions in water to form several hydroxy-metal complexes. The reactions can be written as the overall hydrolysis reactions and their associated equilibrium formation constants are shown below. 

The substitution of the mass action expressions for each species into the MBE for aluminium results in equation (5.42). In this example there is now only one unknown in the equation, Al3+, so the value Al3+ can be calculated for any given value of [Al]x. Once Al3+ has been determined the amounts of the hydroxy complexes can be determined by substitution of Al3+ into the formation equation of the relevant species ... 

By solving for Al3+ and SO4- and back substitution into the mass action expressions, the concentration of each species can be calculated. The proportion of each species as a proportion of the total aluminium is given in Fig. 5.3. The result shows the tendency of SO4 to form complexes in solution with aluminium in the pH range 3-5. 

Complexation of cations and anions is achieved by introducing mass action expressions for the formation of the cation or anion surface complex into the mass balance for the total number of surface complexation sites and, if the new surface species is charged, into the charge balance equation, e.g. metal surface complexes, Cd2+. 

The fact that the stability constants of monodentate ligand complexes of polyion systems are comparable in magnitude with those of the simple molecule resembled, once corrected for the electrostatic effect, is consistent with expectation based on the statistical arguments discussed earlier. The absence of multidentate complex formation is also predictable. Whereas the formation of MA is not affected by the low accessibility of the polyion species, MA and A, their nonideality, and canceling in the mass action expression for the formation of MA (f +/f - = 1), this is not the case for the bidentate species, because f /(f -) = l/f -, the nonideality term for 1/A" remaining uncanceled. The tendency for bidentate complex formation is, on this basis alone, a factor of f - less likely. 

The use of the extended Debye-Hlickel equation with the appropriate equilibrium constants for mass action expressions to solve a complex chemical equilibrium problem is known as the ion-association (lA) method. 

A more complex, and perhaps more realistic, approach is to use a mass action expression for the surface charge. For example, if the surface charge is produced by the loss of protons from the surface, then some of these protons may reabsorb if the pH of the solution is lowered enough. In that case, the surface charge density might be controlled by a surface reaction such as... 

The above-mentioned salts and some other compounds (NH3, pyridine, ethyl-enediamine, butylamine, ethanol, methanol, dioxane, dimethylformamide) were also added to solutions containing 0.04 Ni(CN) and 0.98 M KCN. Relatively small concentrations of all these compounds result in a decrease of absorbance between 375 -500 nm. Since ammonia has nearly the same effect as fluoride ion or dioxane, the authors rejected the possibility of further complex formation (such as Ni(CN)5F ), and explained the observation as a strong decrease of activity coefficients corresponding to the mass action expression ... 

Despite its limitations, the reversible Random Bi-Bi Mechanism Eq. (46) will serve as a proxy for more complex rate equations in the following. In particular, we assume that most rate functions of complex enzyme-kinetic mechanisms can be expressed by a generalized mass-action rate law of the form... 

The kinetic behavior of the reductive dissolution mechanisms given in Figure 2 can be found by applying the Principle of Mass Action to the elementary reaction steps. The rate expression for precursor complex formation via an inner-sphere mechanism is given by ... 

In the absence of an enzyme, the reaction rate v is proportional to the concentration of substance A (top). The constant k is the rate constant of the uncatalyzed reaction. Like all catalysts, the enzyme E (total concentration [E]t) creates a new reaction pathway, initially, A is bound to E (partial reaction 1, left), if this reaction is in chemical equilibrium, then with the help of the law of mass action—and taking into account the fact that [E]t = [E] + [EA]—one can express the concentration [EA] of the enzyme-substrate complex as a function of [A] (left). The Michaelis constant lknow that kcat > k—in other words, enzyme-bound substrate reacts to B much faster than A alone (partial reaction 2, right), kcat. the enzyme s turnover number, corresponds to the number of substrate molecules converted by one enzyme molecule per second. Like the conversion A B, the formation of B from EA is a first-order reaction—i. e., V = k [EA] applies. When this equation is combined with the expression already derived for EA, the result is the Michaelis-Menten equation. 

The expression on the right-hand side of eqns. (112) and (113) is usually written down as a kinetic law for a simple step consisting of two elementary (direct and inverse) reactions satisfying the law of mass action. As a rule, the steady-state rate for a complex reaction does not fit this expression. It appears that this natural type is satisfied by Wj(n Tj) rather than the steady-state rate W. This value is experimentally observed ( W and t, from the steady-state and non-steady-state experiments, respectively). This value must have been given some special term. 

The kinetics of the reductive dissolution mechanisms shown in Fig. 8.1 can be derived using the principle of mass action. The kinetic expression for precursor complex formation by way of an inner-sphere mechanism (Stone, 1986) is... 

THE STABILITY OF COMPLEXES In the previous section hints were made about the differences in stabilities of various complexes. In order to be able to make more quantitative statements and comparisons, a suitable way has to be found to express the stability of complexes. The problem in many ways is similar to that of expressing the relative strength of acids and bases. This was done on the basis of their dissociation constants (cf. Section 1.16), obtained by applying the law of mass action to these dissociation equilibria. A similar principle can be applied for complexes. 

By combining Eqs. (32) and (33), and by relating the quantity of the complexed species in the Donnan phase to their mass-action-based expression, the following equation is obtained ... 

Mechanisms for most chemical processes involve two or more elementary reactions. Our goal is to determine concentrations of reactants, intermediates, and products as a function of time. In order to do this, we must know the rate constants for all pertinent elementary reactions. The principle of mass action is used to write differential equations expressing rates of change for each chemical involved in the process. These differential equations are then integrated with the help of stoichiometric relationships and an appropriate set of boundary conditions (e.g., initial concentrations). For simple cases, analytical solutions are readily obtained. Complex sets of elementary reactions may require numerical solutions. 

These simplifying assumptions allow elimination of some reaction steps, and representation of free radical and short-lived intermediates concentrations in terms of the concentration of the stable measurable components, resulting in complex non-mass action rate expressions. 

Due to practical significance and theoretical interest, much effort has been made to clarify the unique characteristics of metal ion/polyelectrolyte mixture solutions in various disciplines of chemistry. Since a proper equilibrium expression for metal ion binding to polymer molecules is indispensable for the quantification of the physicochemical properties, apparent or macroscopic equilibrium constants have been determined. Unfortunately, however, these overall constants are usually defined arbitrarily, being dependent on the research groups, the experimental techniques, and the systems to be investigated hence they are not comparable with each other nor re-latable to the intrinsic equilibrium constants defined at respective reaction sites. Compared with the situation for the equilibrium analyses of metal complexation with monomer ligands, to which the law of mass action can directly be applied, complete analytical treatment of the metal ion/ polyelectrolyte complexation equilibria has not yet been established even at the present time. There are essential difficulties inherent in the analyses of metal complexation equilibria in polyelectrolyte solutions. 

A basic principle of receptor theory is that when a receptor is activated by a ligand, the effect produced by the ligand is proportional to the concentration of the ligand, e.g., it follows the Law of Mass Action (20). It is now becoming apparent that receptors spontaneously form active complexes as a result of interactions with other proteins. This is especially true when receptor cDNA is expressed in cell systems such that the relative abundance of a receptor is in excess of that normally occur-... 

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