Arrhenius’ law

Mathematically, multiplicities become evident when heat and material balances are combined. Both are functions of temperature, the latter through the rate equation which depends on temperature by way of the Arrhenius law. The curves representing these b ances may intersect in several points. For first order in a CSTR, the material balance in terms of the fraction converted can be written... 

It is found that a force F will inject a given weight of a thermosetting polymer into an intricate mould in 30 s at 177°C and in 81.5 s at 157°C. If the viscosity of the polymer follows an Arrhenius Law, with a rate of process proportional to calculate how long the process will take at 227°C. 

Estimate the time that it would take for recrystallisation to be completed at an annealing temperature of 700°C. Because the new strain-free grains grow by diffusion, you may assume that the rate of recrystallisation follows Arrhenius law, i.e. the time for recrystal-lisation, f is given by f, =... 

Fig. 19.8. The variation of gloss viscosity with temperature. It follows an Arrhenius law (p exp Q/RT]] at high temperature.

The rate constant k varies with the absolute temperature T of the system according to the Arrhenius law k = k e . ... 

A gas decomposition reaction with stoichiometry 2A —> 2B -i- C follows a second order rate law rj(mol / m s) = kC, where C is the reactant concentration in mol/m. The rate constant k varies with the reaction temperature according to the Arrhenius law ... 

The same experiment is performed at several other temperatures at a single initial pressure of 1.0 atm. The results are shown in Table 3-20. Determine the Arrhenius law parameters (kg and E) for the reaction. 

The reactions were shown, in a representative number of cases, to follow second-order kinetics and to obey the Arrhenius law. The kinetic parameters are, of course, for the entire two-stage process. 

Several points are worth noting about these formulae. Firstly, the concentrations follow an Arrhenius law except for the constitutional def t, however in no case is the activation energy a single point defect formation energy. Secondly, in a quantitative calculation the activation energy should include a temperature dependence of the formation energies and their formation entropies. The latter will appear as a preexponential factor, for example, the first equation becomes... 

Integr ation may lead to a relation for rate constant with temperature dependency in the form of Arrhenius law ... 

The graphical presentation of the equation shows a straight line with a negative slope for kA. As the death rate constant follows Arrhenius law,1 the death rate constant is temperature dependent. The value of kA is about 0.02 min 1 at 100 °C, the death rate constant increases by 10-fold at 110 °C and 100-fold at 120 °C.2... 

A ten to hundredfold decrease in the velocity of the reaction, seen as a break down of the Arrhenius plot, is observed at a temperature which, for any given pressure, is always higher than that thermodynamically foreseen for the beginning of the a-/3 transition (this discrepancy is smallest at 265 mm Hg pressure). The marked decrease of the rate of reaction is characteristic of the appearance of the /3-hydride phase. The kinetics of reaction on the hydride follows the Arrhenius law but with different values of its parameters than in the case of the a-phase. 

The most general representation of the isokinetic relationship is the plot of logk against the reciprocal temperature. If the Arrhenius law is followed, each... 

Of course, Sqo Sq if the difference is significant, the hypothesis of a common point of intersection is to be rejected. Quite rigourously, the F test must not be used to judge this significance, but a semiquantitative comparison may be sufficient when the estimated experimental error 6 is taken into consideration. We can then decide whether the Arrhenius law holds within experimental error by comparing Soo/(mi-21) with 6 and whether the isokinetic relationship holds by comparing So/(ml — i— 2) with 5. ... 

The idea that /3 continuously shifts with the temperature employed and thus remains experimentally inaccessible would be plausible and could remove many theoretical problems. However, there are few reaction series where the reversal of reactivity has been observed directly. Unambiguous examples are known, particularly in heterogeneous catalysis (4, 5, 189), as in Figure 5, and also from solution kinetics, even when in restricted reaction series (187, 190). There is the principal difficulty that reactions in solution cannot be followed in a sufficiently broad range of temperature, of course. It also seems that near the isokinetic temperature, even the Arrhenius law is fulfilled less accurately, making the determination of difficult. Nevertheless, we probably have to accept that reversal of reactivity is a possible, even though rare, phenomenon. The mechanism of such reaction series may be more complex than anticipated and a straightforward discussion in terms of, say, substituent effects may not be admissible. 

A special case of the isokinetic temperature is still to be mentioned, confined to a single reaction only, not strictly obeying the Arrhenius law (53). Temperature itself thus represents the variable factor, and the relation of AH and AS may be written... 

In the standard ZFK flame model [6], the chemical reaction rate, Q, is governed by a first-order irreversible one-step Arrhenius law... 

The kinetic parameters are listed in Table 1. The linearity of lnAr l/r plot is revealed by the correlation coefficient. For all reactions but the deactivation, the rate constants follow the Arrhenius law satisfactorily, implying catalyst deactivation may involve more than one elementary steps. 

The viscosity of a cement affects the pumping properties. The viscosity must be kept low enough to ensure pumpability of the slurry during the entire operation period. In deep wells, because of the increased temperature, the viscosity becomes increasingly lower, which leads to undesirable flow characteristics of the slurry. This effect can be serious, because the viscosity follows the Arrhenius law. Some of the additives used for viscosity control also... 

SRPAC spectra of Fig. 9.33a with a model that allows random, single-activated jumps of the EFG on a cone (Fig. 9.33b) was possible over the entire temperature range. This random jump cone model follows an Arrhenius law with activation energy a = (20.1 0.8) kJ moP and frequency factor A = (5.5 1.6) 10 s and it yields a cone opening angle of about 47° above 380 K [81]. 

A different situation arises with a preliminary reduced surface. In this case the measured value of y is within lO - 10 2, and as the temperature increases, the y grows by the Arrhenius Law (Equation) with the activation energy of 5.2 kcal/mole. In addition, there is dependence of y upon the triplet oxygen pressure in the set-up, though the experiment conditions allow us to neglect a priori the impact of homogeneous processes on the spatial distribution of 02( A ) molecules. Prolonged... 

In real systems, a distribution in the characteristic time may lead to a stretched exponential decay. In the thermally activated regime where the relaxation of the magnetization is due to the Orbach mechanism, the temperature dependence of the relaxation time may be described by an Arrhenius law of the form ... 

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