First-order rate constant, temperature dependence

The effect of temperature on the photoinduced electron transfer from [Ru(bpy)3]2+ to methyl viologen solubilized in cellophane has been investigated 98 K The first-order rate constant which depends exponentially on the distance between the reactants shows a non-Arrhenius type of behavior in the temperature interval from 77 to 294 K. This phenomenon, previously found to be of great importance in biological systems, is quantitatively interpreted in terms of a nonadiabatic multiphonon non-radiative process. 

Since a first-order rate constant does not depend on [A]o, one need not know either the initial concentration or the exact instant at which the reaction began. This characteristic should not be used to rationalize experimentation on impure materials. These features do allow, however, a procedure in which measurements of slower reactions are not taken until the sample has reached temperature equilibrium with the thermostating bath. The first sample is simply designated as t = 0. Likewise, for rapidly decaying reaction transients, knowing the true zero time is immaterial. 

Composite temperature dependence. Show that a plot of the apparent first-order rate constant of Eq. (7-34) as ln(/tapp/r) versus lIT will always be curved downward, corresponding to an apparent AW that decreases with increasing temperature. What will the shape of the plot be if by chance AW = AHif ... 

The experimentally observed pseudo-first order rate constant k is increased in the presence of DNA (18,19). This enhanced reactivity is a result of the formation of physical BaPDE-DNA complexes the dependence of k on DNA concentration coincides with the binding isotherm for the formation of site I physical intercalative complexes (20). Typically, over 90% of the BaPDE molecules are converted to tetraols, while only a minor fraction bind covalently to the DNA bases (18,21-23). The dependence of k on temperature (21,24), pH (21,23-25), salt concentration (16,20,21,25), and concentration of different buffers (23) has been investigated. In 5 mM sodium cacodylate buffer solutions the formation of tetraols and covalent adducts appear to be parallel pseudo-first order reactions characterized by the same rate constant k, but different ratios of products (21,24). Similar results are obtained with other buffers (23). The formation of carbonium ions by specific and general acid catalysis has been assumed to be the rate-determining step for both tetraol and covalent adduct formation (21,24). 

Fig. 6. Temperature dependence of first-order rate constant for hexane cracking (HZSM-5,150 torr hexane).

In this reaction, the rate depends only on the concentration of S. This is called a first-order reaction. The factor A is a proportionality constant that reflects the probability of reaction under a given set of conditions (pH, temperature, and so forth). Here, A is a first-order rate constant and has units of reciprocal time, such as s "1. If a first-order reaction has a rate constant k of 0.03 s-1,... 

Kinetic measurements of the binding of NO to the porphyrin species were carried out in excess [NO] 3> [porphyrin], as a function of varying [NO], pH, temperature, and pressure. The first-order rate constants showed a linear dependence on [NO], allowing the determination of the kon and k,)tl values at pH 3 of 9.6 x 10 dm3/(mol s) and 51 s 1, respectively, in good agreement with values determined from earlier flash photolysis studies.327 Kinetics measurements over a range of pH permitted the... 

Autoxidation of DMS DMS is autoxidized by 02 very slowly in solution at ordinary temperatures but the reaction is catalyzed by metal ions. In a saline solution of pH 8, Brimblecombe and Shooter (University of East Anglia, unpublished data) obtained a first order rate constant of 2.2 x 10-8 s-1 at 20 C and an activation energy of 78 kJ. The rate was also found to decrease with pH (but not linearly dependent on the H+ ion concentration). In the presence of Cu(II) ions (10-4 M) at pH 5.6 and temperatures at 20° C, a tenfold increase in first order rate constant was observed (ka = 2 x 10-7 s-1). Reactions in NaG solutions were found to be nearly an order of magnitude slower than in seawater and at least an order of magnitude faster than in distilled water. 

The hydrolysis of (i-C IIyO POF was studied at different acidities. The apparent first-order rate constant, k, at a particular temperature was found to depend on pH but not on the nature or concentration of the buffer used to regulate the pH. The value of k was fairly constant from pH 4 to pH 7, but rose from this constant value with decreasing pH below 4 or with increasing pH above 7. What is the nature of the cause of this behavior ... 

The electron transfer reaction from copper to heme within the ternary protein complex was also studied in solution by stopped-flow spectroscopy. Analysis by Marcus theory of the temperature dependence of the limiting first-order rate constant for the redox reaction (Davidson and Jones, 1996) yielded values for the of 1.1 eV and H b of 0.3 cm , and predicted an electron transfer distance between redox centers which was consistent with the distance seen in the crystal structure. Thus, the electron transfer event is rate-limiting for this redox reaction. Experiments are in progress to determine the validity of the predicted pathways for electron transfer shown in Figure 7. 

To those beginning work in this field, the study reported by Zhou and Notari on the kinetics of ceftazidime degradation in aqueous solutions may be used as a study design template. First-order rate constants were determined for the hydrolysis of this compound at several pH values and at several temperatures. The kinetics were separated into buffer-independent and buffer-dependent contributions, and the temperature dependence in these was used to calculate the activation energy of the degradation via the Arrhenius equation. Ceftazidime hydrolysis rate constants were calculated as a function of pH, temperature, and buffer by combining the pH-rate expression with the buffer contributions calculated from the buffer catalytic constants and the temperature dependencies. These equations and their parameter values were able to calculate over 90% of the 104 experimentally determined rate constants with errors less than 10%. 

As indicated above, intraparticle diffusion lowers the apparent activation energy. The apparent activation energy is even further lowered under external mass-transfer control. Figure 7-9 illustrates how the rate-controlling step changes with temperature, and as a result the dependence of the apparent first-order rate constant on temperature also changes, from a very strong dependence under kinetic control to virtual independence under external mass-transfer control. 

As defined, the Debye relaxation time is the reciprocal of a first-order rate constant. Thus, it is expected to depend on temperature according to the usual Arrhenius relationship... 

The temperature dependence of a first order rate constant is given by the well-known Arrhenius equation ... 

Figure 4 [CH3/] and temperature dependence of the pseudo-first-order rate constant for the iodomethane oxidative addition to (a) trans-[i /iC/(CO) As(p-7 o/)3 2] and (b) trans-[/ C/(CO) P p-Tol) 2] in acetone...

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