Significance of the Arrhenius parameters

Before discussing such theories, it is appropriate to refer to features of the reaction rate coefficient, k. As pointed out in Sect. 3, this may be a compound term containing contributions from both nucleation and growth processes. Furthermore, alternative definitions may be possible, illustrated, for example, by reference to the power law a1/n = kt or a = k tn so that k = A exp(-E/RT) or k = n nAn exp(—nE/RT). Measured magnitudes of A and E will depend, therefore, on the form of rate expression used to find k. However, provided k values are expressed in the same units, the magnitude of the measured value of E is relatively insensitive to the particular rate expression used to determine those rate coefficients. In the integral forms of equations listed in Table 5, units are all (time) 1. Alternative definitions of the type 

The slope of the Arrhenius plot has units (temperature) 1 but activation energies are usually expressed as an energy (kJ mol 1), since the measured slope is divided by the gas constant. There is a difficulty, however, in assigning a meaning to the term mole in solid state reactions. In certain reversible reactions, the enthalpy (AH) = E, since E for the reverse reaction is small or approaching zero. Therefore, if an independently measured AH value is available (from DSC or DTA data), and is referred to a mole of reactant, an estimation of the mole of activated complex can be made. 

Redfem [510] has suggested that the activation energy is the average 

Differential, integral, and non-isothermal forms of kinetic expressions 

Equation derived from equation number Differential form da dt Integral form kt = Exponents in 7= kam (1 -a)n dr x (—ln(l — a))p Rising temperature expression 

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We are now ready to build a model of how chemical reactions take place at the molecular level. Specifically, our model must account for the temperature dependence of rate constants, as expressed by the Arrhenius equation it should also reveal the significance of the Arrhenius parameters A and Ea. Reactions in the gas phase are conceptually simpler than those in solution, and so we begin with them. 

Accounts for rate constants and the exponential form of the Arrhenius equation Reveals the significance of the Arrhenius parameters A and E ... 

If reversibihty is ignored, the significance of reported Arrhenius parameters is diminished because of a possible compensation effect dependent on reaction conditions [93,168], Assessment of the reUability of measured Arrhenius parameters, particularly when using non-isothermal methods, requires demonstration that they are not dependent upon experimental variables, other than temperature, such as sample mass, etc. Evidence that a reaction is (or is not) reversible... 

This appendix includes a summary of the available MNR relative rate coeflBcients (Table VIII) and Arrhenius parameters (Table IX). In light of the recent demonstration (6) that CgFe F unimolecular complications accompany thermal Reaction 3 at 1.0 kTorr, the quantitative significance of these Arrhenius parameters is uncertain. They are thus only provisionally endorsed pending the availability of new measurements carried out at increased (P/Z). In the present study Table IX has provided the basis for small (kaV s ) adjustments in the neighborhood of 300 K. 

Innumerable experimental rate measurements of many kinds have been shown to obey the Arrhenius equation (18) or the modified form [k = A T exp (—E/RT)] and, irrespective of any physical significance of the parameters A and E, the approach is an important, established method of reporting and comparing kinetic data. There are, however, grounds for a critical reconsideration for both the methods of application and the theoretical interpretations of observed obedience of experimental data for the reactions of solids to eqn. (18). 

The isotopic ratios of the Arrhenius pre-exponential parameters for these reactions (Table 43) are significantly different. The ratio is smallest (0.602) for the reaction of [22] then increases significantly to 0.821 for the reaction of [23] and to 0.898 for the reaction of [24]. However, all of the isotopic ratios are less than unity. Therefore, this second criterion for tunnelling indicates there is a sizable tunnelling contribution in all three reactions. 

In fused sodium hydroxide, the rate of decomposition is much higher (e.g. > 10 ) than in fused sodium nitrate systems . The rate shows a significant, though much less than proportional, dependence on sodium hydroxide concentration in mixed nitrate-hydroxide melts, and the Arrhenius parameters differ... 

The magnitudes of the parameters of the Arrhenius and the Fulcher equations for the studied concentrated apple and grape juices are given in Tables 2-6 and 2-7, respectively. The physical interpretation of the three constants in the Fulcher equation is ambiguous, but by translating them in terms of the WLF parameters their significance can be clarified and it is functionally equivalent to the WLF equation (Ferry, 1980 Soesanto and Williams, 1981) ... 

The rate constants obtained by the above method for uncatalyzed polyesterification of adipic acid with different glycols are shown in Table 5.2. The Arrhenius parameters A and E of the equation k — Aexp —E/RT) are also presented in Table 5.2 for those reactions that have been studied kinetically at more than one temperature. Note that the concentration units of the rate constants are in terms of moles per kilogram, which is a more convenient measure of concentration than the usual moles per liter because the volume of the system decreases significantly due to reaction. 

Complete characterization of the kinetic parameters for the HKR of epichlorohy-drin was then obtained by evaluation of the reaction dependence on temperature. A standard experiment at 25 °C (Fig. 19) was numerically fitted, which allowed the expression of the kinetic constants in term of an Arrhenius law relationship (Eq. 21). From this relationship, the activation energy (E ) and pre-exponential frequency parameter (ki) were derived for each component of the reaction (Tab. 8). Of significant practical importance is the impact an increase in reaction temperature has by decreasing the selectivity of the HKR and increasing the level of impurity production. For this experiment, a maximum yield of only 44% (to reach ee>99%) was possible compared with 48% when the reaction was performed at... 

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