Calculated activation entropy

The aquation of [IrCl ]3 yields [Ir(Cl)5(H2)]2-, [Ir(Cl)4(H20)2] and [Ir(Cl)3(H20)3].401 The activation entropy associated with this reaction was suggestive of a dissociative mechanism. In the presence of added salts, the calculated activation entropies were attributed to the orienting effect of the cation (e.g. Li+) on the water adjacent to the [IrCl6]3- anion.402 Irradiation of K3[IrCl6] doped into NaCl reportedly yields [IrCl6]4-, based on ESR data.403... 

Powell and Searcy [1288], in a study of CaMg(C03)2 decomposition at 750—900 K by the torsion—effusion and torsion—Langmuir techniques, conclude that dolomite and C02 are in equilibrium with a glassy phase having a free energy of formation of (73 600 — 36.8T)J from 0.5 CaO + 0.5 MgO. The apparent Arrhenius parameters for the decomposition are calculated as E = 194 kJ mole-1 and activation entropy = 93 JK-1 (mole C02)-1. 

The values of the apparent rate constants kj for each temperature and the activation enthalpies calculated using the Eyring equation (ref. 21) are summarized in Table 10. However, these values of activation enthalpies are only approximative ones because of the applied simplification and the great range of experimental errors. Activation entropies were not calculated in the lack of absolute rate constants. Presuming the likely first order with respect to 3-bromoflavanones, as well, approximative activation entropies would be between -24 and -30 e.u. for la -> Ih reaction, between -40 and - 45 e.u. for the Ih la reaction and between -33 and -38 e.u. for the elimination step. These activation parameters are in accordance with the mechanisms proposed above. 

Three possibilities were considered to account for the curved Arrhenius plots and unusual KIEs (a) the 1,2-H shift might feature a variational transition state due to the low activation energy (4.9 kcal/mol60) and quite negative activation entropy (b) MeCCl could react by two or more competing pathways, each with a different activation energy (e.g., 1,2-H shift and azine formation by reaction with the diazirine precursor) (c) QMT could occur.60 The first possibility was discounted because calculations by Storer and Houk indicated that the 1,2-H shift was adequately described by conventional transition state theory.63 Option (b) was excluded because the Arrhenius curvature persisted after correction of the 1,2-H shift rate constants for the formation of minor side products (azine).60... 

Once the activation enthalpies are known, the corresponding activation entropies can be easily obtained from the (simple or modified) Arrhenius plot by combining equations 3.15 or 3.23 with the appropriate TST equation (3.3, 3.5, 3.12). The reaction entropy at temperature T is then calculated with equation 3.9. 

A phase diagram is often considered as something which can only be measured directly. For example, if the solubility limit of a phase needs to be known, some physical method such as microscopy would be used to observe the formation of the second phase. However, it can also be argued that if the thermodynamic properties of a system could be properly measured this would also define the solubility limit of the phase. The previous sections have discussed in detail unary, single-phase systems and the quantities which are inherent in that sjrstem, such as enthalpy, activity, entropy, etc. This section will deal with what happens when there are various equilibria between different phases and includes a preliminary description of phase-diagram calculations. 

Quantum chemical calculations need not be limited to the description of the structures and properties of stable molecules, that is, molecules which can actually be observed and characterized experimentally. They may as easily be applied to molecules which are highly reactive ( reactive intermediates ) and, even more interesting, to molecules which are not minima on the overall potential energy surface, but rather correspond to species which connect energy minima ( transition states or transition structures ). In the latter case, there are (and there can be) no experimental structure data. Transition states do not exist in the sense that they can be observed let alone characterized. However, the energies of transition states, relative to energies of reactants, may be inferred from experimental reaction rates, and qualitative information about transition-state geometries may be inferred from such quantities as activation entropies and activation volumes as well as kinetic isotope effects. 

Stereocontrol of free radical polymerization is influenced by monomer constitution, solventy and temperature. Most polymerizations seem to follow at least a Markov first-order one-way mechanism. Ratios of the four possible rate constants ki/iy ki/8, k8/i, and k8/8 can be calculated from the experimentally accessible concentrations of configurational triads and diads. With increasing temperature, more heterotactic triads are formed at a syndiotactic radical whereas the monomer addition at an isotactic radical favors isotactic and not heterotactic triads. Compensation effects exist for the differences of activation enthalpies and activation entropies for each of the six possible combinations of modes of addition. The compensation temperature is independent of the mode of addition whereas the compensation enthalpies are not. 

In a Markov first-order process, the six possible ratios of rate constants can be calculated according to Equations 7-12 if the three triad fractions Xu, Xi8, and X88 are known. We thus get six differences of activation enthalpies and activation entropies. Only two of them, however, are really independent because by definition ... 

A positive value of (AHf/ — AHf/8) means that the formation of a heterotactic triad is easier with increasing temperature if isotactic diads are formed at syndiotactic ones and not vice-versa. More interesting are the differences of activation enthalpies and activation entropies for the other five ratios of rate constants. Because very few data for the temperature dependency of triad fractions have been reported in literature, the calculation of the corresponding activation enthalpies and en-... 

Much has been said for and aginst the existence of compensation effects [for a recent literature review see Lumry and Rajender (33)]. In low molecular weight chemistry, activation enthalpies and activation entropies are calculated occasionally from rate constants at two different temperatures only. It has been claimed that many reported compensation effects are spurious because the compensation temperature equals... 

A differentiation of the Arrhenius-plot from Fig. 18 by means of spline polynomials gives the second term of the activation enthalpy (31), whereas its first term can be calculated in the way shown in Section 3.1. The results are given in Fig. 20 for three typical degrees of polymerization. The full lines show the temperature-dependence of the activation enthalpy (31), whereas the dashed lines show the corresponding reversible contributions (10a), as predicted by Casper s approximation ( q = 0, v = 1, a = 1) of Eq. (19) of the PDC-calibration curves. The dependence of AH on the degree of polymerization P at two typical column temperatures is shown in Fig. 21 where also the P-dependence of the corresponding activation entropies (33) is plotted for comparison (dashed lines). 

The activation energies corresponding to the y and fi processes, Eay and Eap, are listed in Table 6, together with the activation entropies, A Say and ASap, calculated according to the Starkweather analysis described in Sect. 2.3. The low values of the activation entropy (10-20 J K-1 mol-1) obtained for the y transition means that this transition deals with localised motions. The ft transition, which has a higher activation entropy (50-80 J K-1 mol-1), should correspond to motions with some cooperative character. 

The stereochemistry of GTP of MMA polymerization was measured for Lewis acid as well as for bifluoride catalysis. Lewis acid catalysts gave a ratio of syndiotactic heterotactic triads of 2 1 while bifluoride catalysis gave ratios near 1 1 [9, 41]. The amount of isotactic triads was about 5%. The effect of temperature on triad and diad composition provided data to calculate the difference in activation enthalpy (AAH ) and activation entropy (AAS ) for... 

Activation entropies are useful because they can give information on the structure of a transition state (as stated above, a more confined transition state is signalled by a negative, unfavorable, activation entropy), but the ab initio calculation of rate constants [148] from activation free energies is not as straightforward as... 

The rearrangement of cyclopropylchlorocarbenes (61) and (62) into the corresponding cyclobutenes (63) and (64) was studied.65 The activation energies were 3-4 kcal mol-1 and the activation entropies -20 eu. The authors remarked that these values are close to those observed for the parent cyclopropylchlorocarbene. These observations were taken to suggest that the published differences between observed and calculated activation parameters for the parent system are real and that they may represent an important aspect to the reaction. 

The activation energies, calculated from both thermal and photo-oxidation, were found to be identical. The difference in the rate constant values was attributed to the difference in the activation entropies. A similar study has also been performed in our group for isothermal crystallization of PEO [72]. 

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