Energy of activation, Arrhenius

Usually, only the Arrhenius energy of activation, E, is given in these papers it differs from the heat of activation,JH, by RT (about 0.6 kcal at ordinary temperatures). Only a few entropies of activa-tion, JS, were calculated the frequency factor, whose logarithm is tabulated, is proportional to this reaction parameter. It is clear that the rate, E, and JS determined for an 8jfAr2 reaction are for the overall, two-stage process. Both stages will contribute to the overall results when their free energies of activation are similar. 

Approximately the same as E, the Arrhenius energy of activation, the difference at ordinary temperatures being about one-half kcal per mole. 

The calculated Arrhenius energies of activation, using equation 6, are reasonably close to the experimental values for reactions 1,... 

Table V. Comparison of Calculated versus Experimental Arrhenius Energies of Activation for Reactions 1-4 (in kcal/mole)...

Any energy change (from the ground state to the transition state in a chemical reaction) that accounts (a) for the presence of a reaction barrier and (b) for the temperature dependence of a rate constant. This quantity is symbolized by and may also be referred to as the Arrhenius energy of activation and activation energy. 

We have determined the rate of formation of dimethylethylpyridine, and trimethylbenzene in a batch reactor in the presence of cpCo(cod), which acts as the catalyst precursor. The reaction was found to be of order 1.7 with respect to alkyne and of zero order in nitrile concentration. The Arrhenius energy of activation for the formation of both pyridine and benzene derivatives was calculated to 22.8 kcal/mol (80MI3). 

A comparison of a series of [YCo(cod)] catalysts in the test reaction (Scheme 5) under identical conditions in the continuous-flow apparatus (Fig. 1) has revealed that the reaction temperature required for 65% pro-pyne conversion depends on the nature of the controlling ligand Y. Further, an inspection of Table VIII reveals that both the Arrhenius energy of activation Ea for the reaction and the selectivity of the catalyst are strongly controlled by the ligand Y [85AG264, 85AG(E)248]. 

If one plots the 8rei ( Co) values against the Arrhenius energies of activation determined for the [RcpCo(cod)] and [(R-indenyl)Co(cod)] catalysts, then an almost linear correlation is found (Fig. 6). The linear relationship between the Arrhenius energy of activation and 8rei( Co) can also be expressed by the regressional Eq.(48),... 

Fig. 6. Correlation between Arrhenius energies of activation (Ea) and Co-NMR chemical shifts for Rep Co (cod) catalysts.

An Arrhenius energy of activation, E, and Eyring enthalpy of activation, AH, were obtained by plotting In k and In (ko/T) vs. 1/T. The values were 32.0 kcal./mole for the Arrhenius activation energy and 31.0 kcal./mole for the Eyring activation enthalpy (Table III and Figures 9 and 10). 

The initial rate of chain-length degradation AS/At, with S = 1/DP (Table II), increased, of course, with degradation temperature, both in the thermal and the thermohydrolytic treatments of the linters, but the Arrhenius energy of activation was much lower in thermohydrolysis. The difference in the rate between both kinds of treatment decreased significantly after a decrystallizing pretreatment of the linters with liquid... 

Usually, only the Arrhenius energy of activation, E, is given in these papers it differs from the heat of activation, JH, by RT (about... 

Owing to the rapid decomposition of the intermediate precursor of the unstable cycloalkyne, such as 26 or 27, kinetic investigations to confirm the intermediacy of cyclic acetylenes could not be performed. However, l-Iithio-2-bromocyclopentene (48) was found to be fairly stable at room temperature. The kinetic measurements indicate that 48 loses lithium bromide in a first-order reaction (k = 2 x lO" s at 20 °C in ether), and the Arrhenius energy of activation for this reaction was estimated... 

The rate constant for the reverse of Reaction 1 is 1.8 X 107 liter/mole sec. (5). This value is somewhat less than would be expected for a diffusion controlled reaction. If the pre-exponential factor is near the 1010 liter/mole sec. considered normal for an activation-controlled reaction of an ion with a neutral molecule, the Arrhenius energy of activation would be about 3.8 kcal./mole in reasonable agreement with the value of 4.5 kcal./mole based on the AHr entry in Table II. Since the transition state for Reaction 1 almost certainly has negative charge more dispersed than in the neighborhood of an hydroxide ion, the pre-exponential term for the reverse reaction may even be somewhat more positive than the normal 1010 liter/mole sec., and the enthalpy of activation would then be larger also. Even if the correct enthalpy of activation is less than the value quoted in Table II, the difference could hardly be more than 2 kcal./mole. 

AS can be readily obtained from Eqs. (2-58) and (2-70). Alternatively, if the Arrhenius energy of activation is of interest, it may be obtained in the usual manner from a plot of In/ versus 1/T, and can be related to the transition-state thermodynamic parameters through Eqs. (2-58), (2-70), (2-81), and (2-82). In carrying out these calculations, the role of the choice of standard state in relation to the numerical values of AS and AG should be firmly kept in mind. Since AH° and A are independent of the standard state for ideal systems, the standard state is automatically determined by the units used for the rate constant [Eq. (2-72)] (unless a conversion factor such as that for going from to Kp is used). For nonideal systems, no additional... 

The apparent energy of activation of a chemical reaction, or Arrhenius energy of activation, is defined by the equation... 

Usually, only the Arrhenius energy of activation, isgivenin these... 

At the present time, it is not possible in general to obtain the free energy of activation from numerical data tabulated in the literature. The enthalpy of activation is obtained experimentally by measuring the reaction rate as a function of temperature (by a plot of Log k/T as a function of (1/T)), and Arrhenius energy of activation by a plot of log k as a function of (1/T). The two plots should be linear with slopes equal to... 

---