The departure of the Perrin equation from linearity may be considered more generally. A curvature convex to the T/rj axis may result from the complete kinetic dissociation of rigid units or from increased rotational freedom within the polypeptide chain 26, 32, 65, 66, 68). A curvature concave to the T/rj axis may occur whenever more than one rotational relaxation time is present and may be detected when the two rotational relaxation times differ by more than fivefold 65). The initial slope, for small values of T/tj, depends upon the harmonic mean of the relaxation times involved and is determined practically by the shorter one. Such curvature has been reported in studies with DNS-labeled polyvinylamine and poly-p-amino-styrene 22, 33, 64). By applying a theory which deals with the case of an emitting group which has only one degree of rotational freedom, Gottlieb and Wahl 33) concluded that the rotations activated by temperature in... [Pg.203]

The initial goal of the kinetic analysis is to express k as a function of [H ], pH-independent rate constants, and appropriate acid-base dissociation constants. Then numerical estimates of these constants are obtained. The theoretical pH-rate profile can now be calculated and compared with the experimental curve. A quantitative agreement indicates that the proposed rate equation is consistent with experiment. It is advisable to use other information (such as independently measured dissociation constants) to support the kinetic analysis. [Pg.273]

The dissociation constant is most accurately estimated from kinetic data when all of the data points are used in the evaluation. There are several ways to do this. The Henderson-Hasselbalch equation... [Pg.281]

When estimates of k°, k, k", Ky, and K2 have been obtained, a calculated pH-rate curve is developed with Eq. (6-80). If the experimental points follow closely the calculated curve, it may be concluded that the data are consistent with the assumed rate equation. The constants may be considered adjustable parameters that are modified to achieve the best possible fit, and one approach is to use these initial parameter estimates in an iterative nonlinear regression program. The dissociation constants K and K2 derived from kinetic data should be in reasonable agreement with the dissociation constants obtained (under the same experimental conditions) by other means. [Pg.290]

The dissociation constants are thermodynamic constants, independent of ionic strength. Equation (8-33), which was derived from (8-30), is, therefore, identical in its form, and its salt effect, with Eq. (8-31). Therefore, salt effects cannot be used to distinguish between Eqs. (8-30) and (8-31). Another way to express this is that if kinetically equivalent forms can be written, it is not possible to determine, on the... [Pg.411]

The first equation was derived by assuming that the rate-controlling step is the reaction of one molecule of adsorbed C02 with two molecules of dissociated adsorbed hydrogen. The second equation, which correlates almost as well, is based on the assumption that the rate-determining step is the reaction of one molecule of adsorbed C02 with two molecules of adsorbed hydrogen. This indicates that, in this particular case, it was not possible to prove reaction mechanisms by the study of kinetic data. [Pg.22]

Gas, cells, 464, 477, 511 characteristic equation, 131, 239 constant, 133, 134 density, 133 entropy, 149 equilibrium, 324, 353, 355, 497 free energy, 151 ideal, 135, 139, 145 inert, 326 kinetic theory 515 mixtures, 263, 325 molecular weight, 157 potential, 151 temperature, 140 velocity of sound in, 146 Generalised co-ordinates, 107 Gibbs s adsorption formula, 436 criteria of equilibrium and stability, 93, 101 dissociation formula, 340, 499 Helmholtz equation, 456, 460, 476 Kono-walow rule, 384, 416 model, 240 paradox, 274 phase rule, 169, 388 theorem, 220. Graetz vapour-pressure equation, 191... [Pg.541]

Activation energy values for the recombination of the products of carbonate decompositions are generally low and so it is expected that values of E will be close to the dissociation enthalpy. Such correlations are not always readily discerned, however, since there is ambiguity in what is to be regarded as a mole of activated complex . If the reaction is shown experimentally to be readily reversible, the assumption may be made that Et = ntAH and the value of nt may be an indication of the number of reactant molecules participating in activated complex formation. Kinetic parameters for dissociation reactions of a number of carbonates have been shown to be consistent with the predictions of the Polanyi—Wigner equation [eqn. (19)]. [Pg.169]

Baechler and coworkers204, have also studied the kinetics of the thermal isomerization of allylic sulfoxides and suggested a dissociative free radical mechanism. This process, depicted in equation 58, would account for the positive activation entropy, dramatic rate acceleration upon substitution at the a-allylic position, and relative insensitivity to changes in solvent polarity. Such a homolytic dissociative recombination process is also compatible with a similar study by Kwart and Benko204b employing heavy-atom kinetic isotope effects. [Pg.745]

The initial kinetic energy of 0 ions produced by dissociative attachment in 02 at an electron energy of 6.9 e.v. may be determined from Equation 4 to be 1.64 e.v. using values of 1.465 e.v. (1) for A(0) and 5.09 e.v. (7) for D(O—O). The residence time for 0 ions calculated from Equation 1 is 6.0 X 10 7 sec. at 10 volts repeller potential. Rate constants for Reaction 6 determined from data at varying Vr are shown in Table I and are seen to increase sharply with increasing repeller potential, as expected for an endothermic process. [Pg.41]

In this chapter, the voltammetric study of local anesthetics (procaine and related compounds) [14—16], antihistamines (doxylamine and related compounds) [17,22], and uncouplers (2,4-dinitrophenol and related compounds) [18] at nitrobenzene (NB]Uwater (W) and 1,2-dichloroethane (DCE)-water (W) interfaces is discussed. Potential step voltammetry (chronoamperometry) or normal pulse voltammetry (NPV) and potential sweep voltammetry or cyclic voltammetry (CV) have been employed. Theoretical equations of the half-wave potential vs. pH diagram are derived and applied to interpret the midpoint potential or half-wave potential vs. pH plots to evaluate physicochemical properties, including the partition coefficients and dissociation constants of the drugs. Voltammetric study of the kinetics of protonation of base (procaine) in aqueous solution is also discussed. Finally, application to structure-activity relationship and mode of action study will be discussed briefly. [Pg.682]

The catalysts used in hydroformylation are typically organometallic complexes. Cobalt-based catalysts dominated hydroformylation until 1970s thereafter rhodium-based catalysts were commerciahzed. Synthesized aldehydes are typical intermediates for chemical industry [5]. A typical hydroformylation catalyst is modified with a ligand, e.g., tiiphenylphoshine. In recent years, a lot of effort has been put on the ligand chemistry in order to find new ligands for tailored processes [7-9]. In the present study, phosphine-based rhodium catalysts were used for hydroformylation of 1-butene. Despite intensive research on hydroformylation in the last 50 years, both the reaction mechanisms and kinetics are not in the most cases clear. Both associative and dissociative mechanisms have been proposed [5-6]. The discrepancies in mechanistic speculations have also led to a variety of rate equations for hydroformylation processes. [Pg.253]

Equations (2.10) and (2.12) are identical except for the substitution of the equilibrium dissociation constant Ks in Equation (2.10) by the kinetic constant Ku in Equation (2.12). This substitution is necessary because in the steady state treatment, rapid equilibrium assumptions no longer holds. A detailed description of the meaning of Ku, in terms of specific rate constants can be found in the texts by Copeland (2000) and Fersht (1999) and elsewhere. For our purposes it suffices to say that while Ku is not a true equilibrium constant, it can nevertheless be viewed as a measure of the relative affinity of the ES encounter complex under steady state conditions. Thus in all of the equations presented in this chapter we must substitute Ku for Ks when dealing with steady state measurements of enzyme reactions. [Pg.37]

As we described in Chapter 3, the binding of reversible inhibitors to enzymes is an equilibrium process that can be defined in terms of the common thermodynamic parameters of dissociation constant and free energy of binding. As with any binding reaction, the dissociation constant can only be measured accurately after equilibrium has been established fully measurements made prior to the full establishment of equilibrium will not reflect the true affinity of the complex. In Appendix 1 we review the basic principles and equations of biochemical kinetics. For reversible binding equilibrium the amount of complex formed over time is given by the equation... [Pg.99]

Both the onset of binding, when the radioligand is first applied, and offset, when dissociation is promoted, can be studied directly. The relevant kinetic equations relating to the simple bimolecular interaction of ligand with receptor are presented in Chapter 1, Section 1.3. [Pg.160]

Equations 16 and 17 imply that 02 adsorption is not dissociative, which is coherent with the kinetic data. However, 02 should be dissociated in further steps of the surface reaction. On ceria, new sites for 02 activation are created at the metal/support interface or in the vicinity of metal particles. As CO and 02 do not compete with the same sites, the rate equation becomes ... [Pg.244]

Hydrogenation catalysts from non-platinum group have been also reported. For example, some organolanthanides of formula [ (r/5-C5Me5)2MH)2] are active catalyst for alkene hydrogenation.384 It has been proposed on the basis of kinetic studies that first the dimer dissociates according to (Equation (18)),... [Pg.127]

A semi-classical treatment171-175 of the model depicted in Fig. 15, based on the Morse curve theory of thermal dissociative electron transfer described earlier, allows the prediction of the quantum yield as a function of the electronic matrix coupling element, H.54 The various states to be considered in the region where the zero-order potential energy curves cross each other are shown in the insert of Fig. 15. The treatment of the whole kinetics leads to the expression of the complete quenching fragmentation quantum yield,

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