Thermodynamic activation parameters

Rate constants and thermodynamic activation parameters. The rate constant for the reaction between C2H4 and HCN catalyzed by a nickel(0) complex was studied over a range of -50 to -10 °C in toluene.31 These authors give the activation parameters A//1 = 36.7kJmor andAS = -145 J mol-1 K I when the reaction rate was expressed using concentrations in the units molL-1 and time in the unit seconds. 

The thermodynamic activation parameters for the enzyme-catalysed reaction are very different from those for the uncatalysed process (Albers et at., 1990). For the isomerization of succinyl-alanyl-leucyl-prolylphenylalanyl-p-nitroanilide catalysed by recombinant human FK binding protein AH = 5.85 kcal mol"1 and AS = -44. e.u. This compares with figures of 18.9 kcal mol 1 and — l.lbe.u. for the uncatalysed reaction of the same substrate. Probably a different step is rate determining in the enzyme-catalysed reaction. 

Similar mixed-ligand complexes of the type (R, R2Dtc)2(MNT)Fe have been synthesized. The complexes were obtained initially as dianions, [(RiR2-Dtc)2(MNT)Fe]J", and were subsequently oxidized either by air or Cu(II) ions in acetonitrile (510). They also exhibit the singlet- triplet equilibrium however, they show a higher population of the triplet state than is found for the TFD analogues. The complexes are stereochemically nonrigid and display the same type of kinetic processes as their TFD counterparts. Thermodynamic activation parameters for inversion of the two complexes (TFD versus MNT) do not differ within experimental error. 

Thermodynamic activation parameters calculated from second-order rate coefficients, unless specifically indicated to the contrary, all refer to the molar scale (standard state 1 mole/1 and unit activity). 

In order to calculate thermodynamic activation parameters, we need to know how to evaluate the translational, rotational, and vibrational parts of the partition functions. This can be accomplished by means of the standard formulas of statistical mechanics (see, for example, Dole, 1954). 

Standard thermodynamic operations (Prigogine and Defay, 1954) on the Gibbs function, AG, yield expressions for related thermodynamic activation parameters. Thus the dependence of k on T can be used to calculate the enthalpy of activation, A, for processes at constant pressure or the thermodynamic energy of activation, A, for processes at constant volume, which in turn lead to the related entropies of activation, ASp and AS respectively. The dependence of k on pressure can be used to calculate the volume of activation, AV which is related to AHp by eqn (5) where a is the thermal... 

The derivation of the various thermodynamic activation parameters is not an end in it itself these quantities organize the information in a way amenable to further analysis. It is assumed in this section that, for a given reaction under a specified set of conditions (T, p, x2), the data have been analysed to obtain the activation parameters AX, where X = G, H, S, U, V, Cp. .. and where AX = X — X [cf. eqn (3) for a first order reaction]. 

Apparent Thermodynamic Activation Parameters for Some Catalase Compound I-Mediated Oxidations ... 

Table 11.1 Thermodynamic activation parameters in cycloadditions at 25°C. (from Lubineau et al. 1994) (reproduced with kind permission from Gauthier-Villars, 1994)...

In kinetic and thermodynamic analyses of chemical processes in solution, there are basically two physical parameters that can be varied experimentally, viz, temperature and pressure. The temperature dependence is used to obtain reaction and activation free energy, enthalpy, and entropy, which are used to construct an energy profile for the reaction under study. The thermodynamic activation parameters reveal information regarding the energetics of the reaction and the nature of the transition state, especially in terms of structural order as obtained from the activation entropy. The pressure dependence is used to obtain reaction and activation volumes that are used to construct a volume profile for the reaction under study (2, 3). 

Table 3 collects activation energies, kinetic nuclear contributions and thermodynamic activation parameters, together with the predicted isomer distributions of TSs. 

The rate-constant is a function of the thermodynamic activation parameters i.e. the Gibbs free energy of activation (AG ) and hence the activation enthalpy (AH ) and the activation entropy (AS ) via the Eyring and Arrhenius equations AG = AH - T AS = -RT(lnk) H- c. (T = temperature, R = gas constant, c = a constant). Two extreme scenarios can be distinguished when reactions take place inside a capsule (a practical situation might be a combination of the two) ... 

ABSTRACT. Molecular inclusion reactions of some azocompounds with a-cyclodextrin were studied in aqueous solution by means of a stopped-flow method. The forward rate constants for the inclusion reactions were found to be in the order of 10-10 mol dm s . The thermodynamic activation parameters were also determined firstly in a-cyclodextrin system. 

The rates and thermodynamic activation parameters for the overall reaction... 

In the process of identifying the quasi-thermodynamic activation parameters in Section 9.9 we assumed that activity could be equated with concentration. While reasonable for the examples discussed in Sections 9.10 and 9.11 it is obviously inappropriate if we wish to consider ionic reactions. From (9.41) the rate constant is related to the ratio wIb/wa b which can no longer be set equal to an equilibrium constant. It is the activities, not the concentrations, which are related to the equilibrium constant... 

Table 1.4. Calculated (MINDO/3) and experimental (in parentheses) values of thermodynamic activation parameters and the kinetic isotopic effect of retroene decompositions at 650 K [59]...

Johnson, I. A. Goldspink, G. (1975). Thermodynamic activation parameters of fish myofibrillar ATPase enzyme and evolutionary adaptations to temperature. Nature (London), 257, 620-2. 

The kinetic polymerizability of monomers belonging to the same class of compounds and studied at similar conditions could be compared using thermodynamic activation parameters. Actually, these parameters are determined from the dependence of the rate constants of elementary reactions (In fep) on 1/T in several instances comparison of fep could be sufficient. Comparison of and A S is more subtle since it provides information on the genuine source of differences in kp and therefore on kinetic polymerizabilities. A good example of such a comparison for CROP of oxetane, 3-methyloxetane, and 3,3-dimethyloxetane is given in a classical work by Saegusa and Kobayashi. ... 

The corresponding ratio of the rate constants fepi/feps may be found from the physical measurements of H /St and It/Sp The dependence on temperature would lead to the thermodynamic activation parameters for both kinds of placements. 

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