Equilibrium constant consecutive reactions

In the above calculations the equilibrium constants of reactions (5.32) and (5.33) were treated as fully adjustable parameters. Although the fitting procedure for the data presented in Fig. 5.67 was successful in the mathematical sense, the physical sense of the best-fit ApK value (cf. Table 5.17) is problematic. The equilibrium constants characterizing consecutive steps of protonation/deprotonation of hydrocomplexes in solution usually differ by over ten orders of magnitude (cf. Section E). Probably the same applies to protonation of surface metal ions, thus, only high ApKa values (> 10) are physically realistic. 

Finally, it should be stressed that the nomenclature used in this section refers to consecutive additions of monomers to the same end. It is assumed implicitly that the equilibrium constants for the reactions kTx+ a total concentration of livings ends, one incorporates this assumption into the calculations. 

The value of the equilibrium constant = iCs[OH ] decreases in the sequence aliphatic aldehydes > ketoacids > ketones. For these compounds, equilibrium is established within one minute. For substituted benzaldehydes the establishment of this equilibrium is slower, the reaction is more complex and consecutive reactions occur. 

The thermodynamics and kinetics of NCS-, CN-,871 Cl-, Br-, NCS- and I- 872 substitutions at [Rh(TPPS)(H2 O)] have been reported the reactions involved are shown in equation (169), and the parameters determined are summarized in Table 60. Spectrophotometric titrations showed two inflection points as OH- is added to [Rh(TPPS)(H20)2]3-, and the consecutive pKx values (7.01 and 9.80 at 20 °C) correspond to the pKk values for fac- and mer-[RhCl3(H20)3], suggesting that the TPPS6- anion and 3 Cl- ligands are comparable electron donors toward the Rh center.872 The trends in the equilibrium constants (Table 60) imply that Rhni is a soft (class B) add in these complexes the NCS- ion is presumed to be sulfur bonded, although no direct evidence is presented to support this assumption. 

KdisR. Ac+ are the dissociation constants of the ion pairs Rf Ac+ and R Ac+. Under suitable conditions, the equilibria (29)—(31) can be followed by spectro-photometric methods [167c, 169], There exist some very important specific reactions of the type shown in eqns. (29) and (30) which are poorly characterized. This concerns, for example, the electron transfer from naphthalene- metal+ (Szwarc initiator) to styrene or other monomers [see Chap. 3, eqn. (46)]. The rapid consecutive reactions of the styrene radical ion make a direct measurement of the equilibrium impossible. Indirect data are not reliable. 

For consecutive reactions in which the desired product is formed in an intermediate step, excess reactant can be used to suppress additional series reactions by keeping the intermediate-species concentration low. A reactive distillation can achieve the same result by removing the desired intermediate from the reaction zone as it is formed. Similarly, if the equilibrium constant of a reversible reaction is small, high conversions of one reactant can be achieved by use of a large excess of the other reactant. Alternatively, by Le Chatelier s principle, the reaction can be driven to completion by removal of one or more of the products as they are formed. Typically, reactants can be kept much closer to stoichiometric proportions in a reactive distillation. 

In these systems, the donor and acceptor diffuse together to give a precursor complex, D A, whose formation is described by the equilibrium constant Kp. Electron transfer, characterized by rate constant eTj occurs within the associated donor-acceptor pair, converting the precursor complex to successor complex D A. Subsequent separation of the oxidized donor (D+) and reduced acceptor (A ) from the successor complex is described by. s- The rate of m/ermolecular electron transfer depends not only on the factors that influence kpj but also on factors affecting the formation of the precursor complex [19]. More quantitatively, as described by Eq. 2, the expression for intermolecular electron transfer has the form of a consecutive reaction mechanism described by an observed rate constant (A obs) consisting of rate constants for diffusion (A ) and the activated electron transfer. 

The kinetic model for the determination of the energies of complex formation was described. Examples of negative-ion mass spectrometry data for the mono-and di-hydrates of 02(—) were given, and typical plots of the equilibrium constants for the 0-1 and 6-7 complexes were presented. Once the equilibrium constants are determined, the equations used to obtain the entropy and energy for the consecutive reactions become the standard. 

The adsorption of CO occurs sequentially with Au CO as an intermediate product. As the carbon monoxide concentration in the trap is constant, all reaction steps are taken to be pseudo-first-order in the simulations. Purely consecutive reaction steps do not fit the experimental data, and it is therefore essential to introduce a final equilibrium (1.2). The fits of the integrated rate equations to the data are represented by the solid lines in Fig. 1.36b and are an excellent match to the experimental results. 

For complexes that contain more than one ligand or central metal ion, there are two ways of writing stability constants. Stepwise formation constants are equilibrium constants for the reactions in which the central metal ion consecutively adds one ligand. An overall formation constant is the equilibrium constant for the reaction in which the central metal ion combines with all of the ligands necessary to form a specific complex. We can illustrate these two types of constants using the formation constants of the chloromercury(II) complexes as an example. For stepwise formation we have... 

Wang and Wu [70] analyzed the extraction equilibrium of the effects of catalyst, solvent, NaOH/organic substrate ratio, and temperature on the consecutive reaction between 2,2,2-trifluoroethanol with hexachlorocyclotriphosphazene in the presence of aqueous NaOH. Wu and Meng [69] reported the reaction between phenol with hexachlorocyclotriphosphazene. They first obtained the intrinsic reaction-rate constant and overall mass transfer coefficient simultaneously, and reported that the mass transfer resistance of QX from the organic to aqueous phase is larger than that of QY from the aqueous to organic phase. The intrinsic reaction-rate constant and overall mass transfer coefficients were obtained in three ways. 

Fig. 6. Normalized ion intensity curves for ions in moist nitrogen. Fno = 2 Torr, PhjO = 1.6 X 10 Torr, 300°K. Successive intensity maxima indicate sequence N2 - N4 H20 -> H (H20)2 > H (H20)3 H (H20)4. Dashed lines represent theoretical curves calculated from integrated rate equations for consecutive reactions including reversible steps using average rate constants of Table II. In experiments where only position of equilibrium is to be studied, higher water concentrations are used so that equilibrium is established in less than 50 /zsec.

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