Equilibrium constant The value obtained

Equilibrium constant The value obtained when equilibrium concentrations of the chemical species are substituted in the equilibrium expression. 

In the case of cobalt(II) the results obtained by the solubility method could be verified by a spectrophotometric determination of the equilibrium constant. The value obtained in this way is given above, the agreement of the two methods being satisfactory. The advantage of the solubility method lies in its applicability in cases in which the spectrophotometric method cannot be used. 

The numerical solution for the surface potential as a function of pH is compared in Fig. 7, for various NaCI concentrations, with the experimental results provided by Li and Somasundaran [32], The potentials — ]i,s = — ]i(0) and — tyd= — t)t(t/E) are plotted as functions of distance, since the zeta potential determined by electrophoresis is not defined at the surface, but at an unknown location, the plane of slip . The magnitude of <-s is always larger than that of i >d, since the potential decays with the distance. The value dE=4 A, which is provided by the dependence of the surface tension of water on the NaCI concentration at high ionic strengths was employed. For the equilibrium constant, the value K ou= () 10 M, which is consistent with the experimental data for pH values between 3 and 6, was selected. A reasonable agreement with the data (which have a rather large error) was obtained by selecting A=5.0X 1016 sites/m2 and W1 = 0.5kT. 

This form of equation (2.5.79) does not allow us to make any conclusions about the form of the pOw-pO dependence and its slope, since the transformation of this equation into logarithmic values does not result in explicit solutions. Therefore, the calculations of magnitudes were performed for specific values of oxide-ion concentrations, partial pressures of water vapour and equilibrium constants. The dependences obtained in such a manner are presented in Fig. 2.5.11. It should be noted that not all of these plots are strictly linear, and have an appreciable bending toward the abscissa axis. 

A series of related reports have appeared on the equilibria between five- and six-coordinate species and possible adduct formation in Co(iii) corrinoids, on the thermodynamic and kinetic properties for what is termed the base-on/ base-off equilibration of alkyl cobalamins, " and on the kinetics and thermodynamics of parallel equilibria of alkyl-13-epicobalamins. In the first report, the pressure dependence of the UV/visible spectra of the five-coordinate (yellow)/six-coordinate (red) equilibrium for both methylcobalamin and vinylcobinamide was obtained. Water is the ligand that converts the five- to a six-coordinate species. The reaction volumes were obtained from the pressure dependence of the equilibrium constant. The values of AF of —12.5 1.2 and —12.5 l.Ocm moF for the methyl and vinyl complexes are close to the values 13cm moF advocated and accepted for the displacement or... 

Using the average value for the equilibrium constant, the distribution concentration of the different components of a methanol water mixture were calculated for initial methanol concentrations ranging from zero to 100%v/v. The curves they obtained are shown in Figure 28. The molar refractivities of 11.88 is also in accordance with that expected since the molar refractivity s of water and methanol are 3.72 and 8.28 respectively. The refractive index of the associate of 1.3502 is, as would be expected, higher than that of either water or methanol. 

Binding assays for the saxitoxins were conducted with homogenized rabbit brain and saxitoxin exchange-labelled with tritium at C-11 (92, 93). If the various saxitoxins were available with suitably intense radiolabels, then the equilibrium dissociation constant, K, could be measured directly for each. Since only saxitoxin is currently available with the necessary label, the binding experiments instead measure the ability of a compound to compete with radiolabelled saxitoxin for the binding site. The value obtained, Kj, corresponds to the uilibrium dissociation constant, K, that would be observed for the compound if it were measured directly. Affinity is defined for this assay as the reciprocal of Kj. The affinities of several of the saxitoxins (94) are summarized in Figure 11, expressed relative to saxitoxin and plotted on a logarithmic scale. 

Hydration energies of doubly charged anions82 are given in Table 7. The values obtained are also shown in Figure 14 where the -AG°, n are plotted versus n. The data are based on those equilibrium constants Kn x which could be determined at... 

An ion pair is a close association of a cation and an anion in solution, whereas the ion product is the value obtained when the initial concentrations for the dissolved ions involved in the solubility equilibrium are inserted into the equilibrium constant expression. 

However, even using results from various sources in the literature for the surface charge data, we believe that the combined use of t/>o and ao curves leads to more reliable values of the surface equilibrium constants than is obtainable otherwise. 

Equation 2.67 indicates that the standard enthalpy and entropy of reaction 2.64 derived from Kc data may be close to the values obtained with molality equilibrium constants. Because Ar// is calculated from the slope of In AT versus l/T, it will be similar to the value derived with Km data provided that the density of the solution remains approximately constant in the experimental temperature range. On the other hand, the error in ArSj calculated with Kc data can be roughly estimated as R In p (from equations 2.57 and 2.67). In the case of water, this is about zero for most solvents, which have p in the range of 0.7-2 kg dm-3, the corrections are smaller (from —3 to 6 J K-1 mol-1) than the usual experimental uncertainties associated with the statistical analysis of the data. 

The theoretical calculations described have recently been supported by an extraordinary kinetic analysis conducted by Vanrysellberghe and Froment of the HDS of dibenzothiophene (104). That work provides the enthalpies and entropies of adsorption and the equilibrium adsorption constants of H2, H2S, dibenzothiophene, biphenyl, and cyclohexylbenzene under typical HDS conditions for CoMo/A1203 catalysts. This work supports the assumption that there are two different types of catalytic sites, one for direct desulfurization (termed a ) and one for hydrogenation (termed t). Table XIV summarizes the values obtained experimentally for adsorption constants of the various reactants and products, using the Langmuir-Hinshelwood approach. As described in more detail in Section VI, this kinetic model assumes that the reactants compete for adsorption on the active site. This competitive adsorption influences the overall reaction rate in a negative way (inhibition). 

From the values given in the table the equilibrium constants of the hydrogen halogenides can be calculated by use of the equation AF° = —RTlnK. The calculated values are somewhat uncertain because of uncertainty in the estimate of the standard free energy of solution of the dissociated molecules. The values obtained in this way are 2 X 10 for HC1, 5 X 10s for HBr, and 2 X 109 for HI. These acids are accordingly very strong acids. 

Values of the equilibrium constant may be obtained by allowing the reactants to come to equilibrium at a given temperature, analyzing the equilibrium mixture, and then substituting the equilibrium concentrations into Equation 16-2. 

Several alcohols were used as solvent for studying equilibrium (36). It was found that equation (37) predicted quite accurately the variation of the equilibrium constant and the values of s and a yielded, through a comparison with the values obtained in the kinetic analysis of reaction (12), information on the relative degrees of solvation of the products, reactants and transition state. 

It is interesting to note that the value obtained from the direct determination of the equilibrium constant, 33 kcal mol-1, seems to be in better agreement with the well known facile interconversion of these two substances. 

Polarography is valuable not only for studies of reactions which take place in the bulk of the solution, but also for the determination of both equilibrium and rate constants of fast reactions that occur in the vicinity of the electrode. Nevertheless, the study of kinetics is practically restricted to the study of reversible reactions, whereas in bulk reactions irreversible processes can also be followed. The study of fast reactions is in principle a perturbation method the system is displaced from equilibrium by electrolysis and the re-establishment of equilibrium is followed. Methodologically, the approach is also different for rapidly established equilibria the shift of the half-wave potential is followed to obtain approximate information on the value of the equilibrium constant. The rate constants of reactions in the vicinity of the electrode surface can be determined for such reactions in which the re-establishment of the equilibria is fast and comparable with the drop-time (3 s) but not for extremely fast reactions. For the calculation, it is important to measure the value of the limiting current ( ) under conditions when the reestablishment of the equilibrium is not extremely fast, and to measure the diffusion current (id) under conditions when the chemical reaction is extremely fast finally, it is important to have access to a value of the equilibrium constant measured by an independent method. 

As discussed above for the 4,-methoxyflavylium compound, pH jump, temperature jump, and flash photolysis experiments permit the measurement of the rate constants of some of the reactions involved, while steady state titration experiments (using UV-Vis and NMR techniques) enable equilibrium constants to be determined. The values obtained for the most important processes in five flavylium compounds are gathered in Table 1. 

The rate constant kv for both (Px )Fem(H20)2 and (P8 )Fem(OH) was also determined directly by running the reaction in the presence of Rum(EDTA)(H20)-that rapidly removes the liberated NO and makes the dissociation from (P8-)Fem irreversible. The direct measurement yielded kr = 220 s 1 for (P8 )Fem(H20)2 and 11.4 s—1 for (P8 )Fera(OH), both in good agreement with the value obtained from equilibrium kinetics. 

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