True activation energy

Just as the surface and apparent kinetics are related through the adsorption isotherm, the surface or true activation energy and the apparent activation energy are related through the heat of adsorption. The apparent rate constant k in these equations contains two temperature-dependent quantities, the true rate constant k and the parameter b. Thus... 

According to Eq. (14.2), the activation energy can be determined from the temperature dependence of the reaction rate constant. Since the overall rate constant of an electrochemical reaction also depends on potential, it must bemeasured at constant values of the electrode s Galvani potential. However, as shown in Section 3.6, the temperature coefficients of Galvani potentials cannot be determined. Hence, the conditions under which such a potential can be kept constant while the temperature is varied are not known, and the true activation energies of electrochemical reactions, and also the true values of factor cannot be measured. 

There might be various reasons that lead to finding an apparent instead of the true activation energy. The use of power-law kinetic expressions can be one of the reasons. An apparent fractional reaction order can vary with the concentration, i.e. with conversion, in one experimental run. Depending upon the range of concentrations or, equivalently, conversions, different reaction orders may be observed. As an example, consider the a simple reaction ... 

Thus, depending on the estimated as, different s and possibly E bs will be obtained. So, the values found will depend on the experimental conditions, i.e. temperature, concentrations, conversions. Experimentally determined E-values may have nothing in common with the true activation energy. 

Analogously to external mass transfer, internal mass transfer can be the rate-limiting step. In that case, it appears that the observed activation energy is related to the true activation energy as follows ... 

Under normal circumstances the true activation energy term in equation 12.3.85 will far exceed the diffusional activation term calculated from either equation 12.3.86 or equation 12.3.87 and, to a good approximation, it may be said that in the limit of low effectiveness factors... 

Under isothermal conditions, we have seen that the apparent activation energy of the reaction is approximately one half the intrinsic value when rj is sufficiently low. When rj exceeds unity, an opposite effect occurs (i.e., the apparent activation energy will exceed the true activation energy). 

For situations where the reaction is very slow relative to diffusion, the effectiveness factor for the poisoned catalyst will be unity, and the apparent activation energy of the reaction will be the true activation energy for the intrinsic chemical reaction. As the temperature increases, however, the reaction rate increases much faster than the diffusion rate and one may enter a regime where hT( 1 — a) is larger than 2, so the apparent activation energy will drop to that given by equation 12.3.85 (approximately half the value for the intrinsic reaction). As the temperature increases further, the Thiele modulus [hT( 1 — a)] continues to increase with a concomitant decrease in the effectiveness with which the catalyst surface area is used and in the depth to which the reactants are capable of... 

Kinetic regime This is the regime of small Thiele modules. The pore system of the catalyst with its interior surface is completely accessible for the educt. rj 1 and krj k, as In k In k0 -EpJRT, that the apparent activation energy is practically identical with the true activation energy. 

For some steps the apparent activation energy is to be used in Eq. (10), and in others, the true activation energy. See text. (2) Where relevant, it is assumed that the symmetry number approximates unity it is also assumed that (Ijs) a 0.5, where s is the number of sites adjacent to a given site in a surface bimolecular reaction. (3) Both Cj, gas concentration in molecules cm", and P, gas pressure in atmospheres are used in this work. For an ideal gas, c, = 7.34 x 1q2i pij< 4 Except where otherwise noted, ft a 1. (5) An adsorption reaction is a Rideal-Eley reaction a surface reaction is a "Langrauir-Hinshelwood reaction. 

The preexponential factor of about 1 ps lies well in the microscopic range. The true activation energy might be somewhat higher because all the evaluation... 

Since all of the above-mentioned interconversion reactions are reversible, any kinetic analysis is difficult. In particular, this holds for the reaction Sg - Sy since the backward reaction Sy -+ Sg is much faster and, therefore, cannot be neglected even in the early stages of the forward reaction. The observation that the equilibrium is reached by first order kinetics (the half-life is independent of the initial Sg concentration) does not necessarily indicate that the single steps Sg Sy and Sg Sg are first order reactions. In fact, no definite conclusions about the reaction order of these elementary steps are possible at the present time. The reaction order of 1.5 of the Sy decomposition supports this view. Furthermore, the measured overall activation energy of 95 kJ/mol, obtained with the assumption of first order kinetics, must be a function of the true activation energies of the forward and backward reactions. The value found should therefore be interpreted with caution. 

These results show that the observed activation energy for reactions influenced by strong pore resistance is approximately one-half the true activation energy. 

Comparison of True Activation Energies in Reactions of Carbon with Oxygen-Containing Gases and the Dissociation Energy of an 0 Atom from the Reactant after Rossberg )... 

Reaction True activation energies, kcal./mole Dissociation reaction and energy, kcal./mole... 

Relation between True Activation Energy and Apparent Activation Energy Found in Zone II. It has been shown 101, 103) that the rate of reaction in the diffusion controlled zone is given by... 

The criteria used for the prediction of gas-carbon reactions entering Zone II, for first order reactions, are presented in Table IV, with the results of Thiele (100) for plane and spherical specimens included. Zone II is entered when (f>n, where is the value of (j> for the start of Zone II and is 2, 4, or 6 for a plane, cylinder, or sphere, respectively. In all cases, the specimens approach uniform internal reaction, that is chemical control, when is [Pg.169]

Also presented in Fig. 18 is the ideal change in reaction rate of the spectroscopic carbon with temperature, assuming a true activation energy of 93 kcal./mole. Zone II should start at a reaction rate of ca. 6 g. of carbon per hour and knowing that t) 0.5 at the start of Zone II, the temperature can be approximated. It is of interest to note that the ideal activation energy in Zone II, 46.5 kcal./mole, is closely approximated by the change in experimental reaction rate with temperature above ca. 1250°. 

True activation energies are obtained when the reaction order is zero and probably also when the rate coefficient, k, and adsorption coefficient, Ka, have been separated by treatment of rate data by means of eqn. (3). In the case of the first-order rate equation, the apparent activation energy, calculated from k values [eqn. (5)] by means of the Arrhenius equation, is the difference between the true activation energy and the adsorption enthalpy of the reactant A... 

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