Activation energies from Arrhenius equation

Despite all teachers using activation energy at a qualitative level according to the Arrhenius definition (as a barrier of energy), only one teacher clearly showed a comprehensive understanding of both the Arrhenius equation itself and how to obtain the activation energy from this equation. 

This equation results from the assumption that the actual reaction step in themial reaction systems can happen only in molecules (or collision pairs) with an energy exceeding some tlireshold energy Eq which is close, in general, to the Arrhenius activation energy defined by equation (A3.13.3). Radiative energization is at the basis of classical photochemistry (see e.g. [4, 3 and 7] and chapter B2.5) and historically has had an interesting sideline in the radiation... 

A = rate constant (pre-exponential factor from Arrhenius equation k = A exp (-E /RT), sec (i.e., for a first order reaction) B = reduced activation energy, K C = liquid heat capacity of the product (J/kg K)... 

Calculation of Activation Energy from the JMAK Model and the Arrhenius Equation... 

Still another form of the Arrhenius equation can be derived that allows us to estimate the activation energy from rate constants at just two temperatures. At temperature Tv... 

The pre-exponential factor Df (or rf) is the diffusion constant (or correlation time) of a freely rotating methyl group and is given by an equation analogous to Eq. 21. A rigorous approach to this problem is to calculate activation energies from variable-temperature relaxation measurements, using an Arrhenius-type plot of D, (or tc i ) versus 1/T(K).67... 

Temperature Effect Determination of Activation Energy. From the transition state theory of chemical reactions, an expression for the variation of the rate constant, k, with temperature known as the Arrhenius equation can be written... 

Equation (5) was used to correct the heating times in Table VII, and new reaction rate constants were then calculated. Thereafter, a new activation energy was obtained by a second Arrhenius fit of the corrected data. This procedure was repeated until the difference in the calculated activation energy from two successive iterations was less than the standard deviation of the error of the fit of the data. The final activation energy value obtained was 22,182 612 cal/mol K, and the correlation coefficient was then 0.996. 

The experimental activation energy, from the Arrhenius expression, depends on the reaction kinetics according to the equation,... 

Hudson38 measured the temperature coefficient for the interconversions of a- and /3-lactose, and Lowry and Smith57 calculated activation energies from Hudson s data by means of the integrated Arrhenius equation ... 

Also consider what happens if we vary the temperature and tr> to determine the reaction s activation energy. Let the temperature dependence of the diffusMty, Pa, be represented also in Arrhenius form, with faiff the activation energy of the diffusion coefficient. Let rxn be the intrinsic activation energy of the reaction. The observed activation energy from Equation 7.69 is... 

After the average rate constant is obtained at each temperature, fit the rate constants to the Arrhenius equation and determine the activation energy from the slope. 

To determine whether or not the reaction displays Arrhenius behavior, we will need to compare the data to the model represented by the Arrhenius equation. Ib do this we plot In k versus 1/T. If the plotted data form a straight line, the slope of the line is -EJR. So, we can determine the activation energy from that slope. 

Finally, from Arrhenius Equation and Eyring Equation plots (Fig. 3), activation parameters, e.g. energy ( .4), enthalpy (AH ) and entropy (zl5 ) of activatiOTi, were calculated. Values of these parameters are gathered in Table 2 ... 

There are a few cases where the rate of one reaction relative to another is needed, but the absolute rate is not required. One such example is predicting the regioselectivity of reactions. Relative rates can be predicted from a ratio of Arrhenius equations if the relative activation energies are known. Reasonably accurate relative activation energies can often be computed with HF wave functions using moderate-size basis sets. 

The activation energies for the decomposition (subscript d) reaction of several different initiators in various solvents are shown in Table 6.2. Also listed are values of k for these systems at the temperature shown. The Arrhenius equation can be used in the form ln(k j/k j) (E /R)(l/Ti - I/T2) to evaluate k j values for these systems at temperatures different from those given in Table 6.2. 

Some workers in this field have used Eyring s equation, relating first-order reaction rates to the activation energy d(7, whereas others have used the Arrhenius parameter E. The re.sults obtained are quite consistent with each other (ef. ref. 33) in all the substituted compounds listed above, AG is about 14 keal/mole (for the 4,7-dibromo compound an E value of 6 + 2 keal/mole has been reported, but this appears to be erroneous ). A correlation of E values with size of substituents in the 4- and 7-positions has been suggested. A/S values (derived from the Arrhenius preexponential factor) are... 

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