The Temperature Dependence of Rate Constants

Seeley J V, Morris R A, Viggiano A A, Wang FI and Flase W L 1997 Temperature dependencies of the rate constants and branching ratios for the reactions of Cr(Fl20)g 3 with CFIjBr and thermal dissociation rates for CI (CFl3Br) J. Am. Chem. Soc. 119 577-84... 

The simplest expression for the temperature dependence of the rate constant k is given by the Arrhenius equation... 

The rate-conttolling step to chlorate is the bimoleculat formation of chlorite, which reacts rapidly with hypochlorite. The temperature dependence of the rate constants is expressed by the equations = 2.1 x 10 g-io3.8/i T 3 2 x 10 g-87.o/i T L/(mol-s) (144). The uncataly2ed decomposition to... 

Fig. 1. Examples of temperature dependence of the rate constant for the reactions in which the low-temperature rate-constant limit has been observed 1. hydrogen transfer in the excited singlet state of the molecule represented by (6.16) 2. molecular reorientation in methane crystal 3. internal rotation of CHj group in radical (6.25) 4. inversion of radical (6.40) 5. hydrogen transfer in halved molecule (6.16) 6. isomerization of molecule (6.17) in excited triplet state 7. tautomerization in the ground state of 7-azoindole dimer (6.1) 8. polymerization of formaldehyde in reaction (6.44) 9. limiting stage (6.45) of (a) chain hydrobromination, (b) chlorination and (c) bromination of ethylene 10. isomerization of radical (6.18) 11. abstraction of H atom by methyl radical from methanol matrix [reaction (6.19)] 12. radical pair isomerization in dimethylglyoxime crystals [Toriyama et al. 1977].

The temperature dependence of the rate constant of rapid hydrogen transfer, measured by Mordzinski and Kuhnle [1986], is given in fig. 1. A similar dependence has been found by Grellmann et al. [1989] for one-proton transfer in half of the above molecule (6.16), which does not include the two rightmost rings. 

The temperature dependence of A predicted by Eq. (5-11) makes a very weak contribution to the temperature dependence of the rate constant, which is dominated by the exponential term. It is, therefore, not feasible to establish, on the basis of temperature studies of the rate constant, whether the predicted dependence of A is observed experimentally. Uncertainties in estimates of A tend to be quite large because this parameter is, in effect, determined by a long extrapolation of the Arrhenius plot to 1/T = 0. 

The numerical values of AG and A5 depend upon the choice of standard states in solution kinetics the molar concentration scale is usually used. Notice (Eq. 5-43) that in transition state theory the temperature dependence of the rate constant is accounted for principally by the temperature dependence of an equilibrium constant. 

Arrhenius acid Species that, upon addition to water, increases [H+], 86 Arrhenius base Species that, upon addition to water, increases [OH-], 86 Arrhenius equation Equation that expresses the temperature dependence of the rate constant In k2/ki = a(l/Ti — 1 IT2)IR, 302-305... 

The temperature dependence of a rate is often described by the temperature dependence of the rate constant, k. This dependence is often represented by the Arrhenius equation, /c = Aexp(- a/i T). For some reactions, the temperature relationship is instead written fc = AT" exp(- a/RT). The A term is the frequency factor for the reaction, which reflects the number of effective collisions producing a reaction. a is known as the activation energy for the reaction, and is a measure of the amount of energy input required to start a reaction (see also Benson, 1960 Moore and Pearson, 1981). 

The temperature dependency of the rate constants on Miike coal was determined between 350 C and 450 C. The result is shown in Table 4. 

Comparison of this equation with the Arrhenius form of the reaction rate constant reveals a slight difference in the temperature dependences of the rate constant, and this fact must be explained if one is to have faith in the consistency of the collision theory. Taking the derivative of the natural logarithm of the rate constant in equation 4.3.7 with respect to temperature, one finds that... 

The concentration of A in the entrance stream is 1.5 lb moles/ft3. The following table provides some information about the temperature dependence of the rate constants and fc j. 

Huie, R.E., Herron, J.T. (1975) Temperature dependence of the rate constants for reaction of ozone with some olefins. Int l. J. Chem. Kinet. SI, 165. 

Witte, F., Urbanik, E., Zetzsch, C. (1986) Temperature dependence of the rate constants for the addition of OH to benzene and to some mono substituted aromatics (aniline, bromobenzene, and nitrobenzene) and the unimolecular decay of the adducts. Kinetics into a quasi-equilibrium. J. Phys. Chem. 90, 3251-3259. 

On the other hand, the low temperature dependance of the rate constants with activation energies around 5 kcal/mole indicates a diffusion limited reaction rate which could refer to diffusion of oxygene into the fibers of the board, i.e. into the fiberwalls. The corresponding negative activation energy for the groundwood based hardboard and the effect of fire retardants there upon are difficult to understand. 

The second method of detecting tunnelling relies on the fact that the primary hydrogen KIE shows an anomalous temperature dependence when significant tunnelling takes place. In the absence of tunnelling, the temperature dependence of the rate constant should follow the Arrhenius equation (42)... 

It is too early to draw any conclusions about the insensitivity of the rate constants to the nature of the dipeptide. Differences among the peptides seem to be revealed more in the temperature dependencies of the rate constants for intramolecular electron transfer than in the magnitude of the rate constant itself. Work is in progress on the synthesis of other di-, tri-, and tetra-peptides separating Co(III) and Ru(II) in order to examine the temperature dependence of the intramolecular rate... 

The temperature dependency of the rate constant k for the first-order... 

In Figure 2.12(b) is shown the temperature dependence of the rate constant for iron removal from N-terminal monoferric transferrin. There is an obvious break between 12 and 20 °C and this is ascribed to a temperature-induced conformational change. The effect becomes less distinct when the ionic strength is increased from 0.13 to 2.0 M,See also Sec. 4.11. 

The third-order rate expression (Equation 9) is applicable over the temperature range 121° to 187°C. The Arrhenius relationship describing the temperature dependence of the rate constant k3 (Figure 7) is... 

A plot of In k against the reciprocal of the absolute temperature (an Arrhenius plot) will produce a straight line having a slope of —EJR. The frequency factor can be obtained from the vertical intercept. In A. The Arrhenius relationship has been demonstrated to be valid in a large number of cases (for example, colchicine-induced GTPase activity of tubulin or the binding of A-acetyl-phenylalanyl-tRNA to ribosomes ). In practice, the Arrhenius equation is only a good approximation of the temperature dependence of the rate constant, a point which will be addressed below. 

The determination of the rate equation is usually a two-step procedure first the concentration dependency is found at fixed temperature and then the temperature dependence of the rate constants is found, yielding the complete rate equation. 

---