Reactions linearly dependent

The Algebra of Multiple Reactions (Linear Dependence and Linear Independence of Multiple Reactions)... 

In order to obtain more insight into the local environment for the catalysed reaction, we investigated the influence of substituents on the rate of this process in micellar solution and compared this influence to the correspondirg effect in different aqueous and organic solvents. Plots of the logarithms of the rate constants versus the Hammett -value show good linear dependences for all... 

An example of the determination of activation enthalpies is shown in Figs. 11 and 12. A valuable indication for associating the correct minimum with the ionic conductivity is the migration effect of the minimum with the temperature (Fig. 11) and the linear dependence in the cr(T versus 1/T plot (Fig. 12). However, the linearity may be disturbed by phase transitions, crystallization processes, chemical reactions with the electrodes, or the influence of the electronic leads. 

The kinetics of protodeboronation are rather complex, probably due to the occurrence of more than one reaction mechanism depending to some extent on the medium involved. Much of the work has been devoted to showing that a linear log rate versus H0 plot does not mean that the A-l mechanism applies. 

Another simple approach assumes temperature-dependent AH and AS and a nonlinear dependence of log k on T (123, 124, 130). When this dependence is assumed in a particular form, a linear relation between AH and AS can arise for a given temperature interval. This condition is met, for example, when ACp = aT" (124, 213). Further theoretical derivatives of general validity have also been attempted besides the early work (20, 29-32), particularly the treatment of Riietschi (96) in the framework of statistical mechanics and of Thorn (125) in thermodynamics are to be mentioned. All of the too general derivations in their utmost consequences predict isokinetic behavior for any reaction series, and this prediction is clearly at variance with the facts. Only Riietschi s theory makes allowance for nonisokinetic behavior (96), and Thorn first attempted to define the reaction series in terms of monotonicity of AS and AH (125, 209). It follows further from pure thermodynamics that a qualitative compensation effect (not exactly a linear dependence) is to be expected either for constant volume or for constant pressure parameters in all cases, when the free energy changes only slightly (214). The reaction series would thus be defined by small differences in reactivity. However, any more definite prediction, whether the isokinetic relationship will hold or not, seems not to be feasible at present. 

The pH-dependence of the rate is complicated. The rate increases very rapidly between pH values of 8 and 10 and the authors correlate this with the literature value of p bh+ of benzylamine of 9.34. The rate levels off at pH 11-12, but at pH 13-14 a reaction the rate of which is linearly dependent on hydroxyl ion concentration occurs. 

Numerical computations of reacting flows are often difficult owing to the different time-scales involved and the highly non-linear dependence of the reaction rate on concentrations and temperature. The solution of the species concentration equations in combination with the momentum and the enthalpy equation generally requires an iterative procedure such as the one outlined in Section 1.3.4. A rough sketch of the numerical structure of a stationary reacting-flow problem is given as... 

The extraction system which was measured by the HSS method for the first time was the extraction kinetics of Ni(II) and Zn(II) with -alkyl substituted dithizone (HL) [14]. The observed extraction rate constants linearly depended on both concentrations of the metal ion [M j and the dissociated form of the ligand [L j. This seemed to suggest that the rate determining reaction was the aqueous phase complexation which formed a 1 1 complex. However, the observed extraction rate constant k was not decreased with the distribution constant Kj of the ligands as expected from the aqueous phase mechanism. 

The experiment was carried out in a reaction cell shown in Fig. 3.3 with inner walls covered by a zinc oxide film having thickness 10 pm [20]. The surface area of the measuring film on the quartz plate was about 1/445 of the total film area on the wall of the vessel. The results of direct experimental measurements obtained when the adsorbent temperature was -196 C and temperature of pyrolysis filament (emitter of H-atoms) 1000°C and 1100°C, are shown on Fig. 3.4. One can see a satisfactory linear dependence between parameters A r (the change in film conductivity) and APh2 (reduction of hydrogen pressure due to adsorption of H-atoms), i.e. relations... 

These ESR spectra are in good agreement with ESR spectra of ozonized PP published previously (30) The rapid formation of peroxy radicals indicates that ozone reacts with PP without induction period. In the initial stage of reaction the hydroperoxide groups (POOH) concentration increases and the rate of POOH formation is linearly dependent on the ozone concentration (Fig.2). After prolonged ozonization the concentration of POOH remains almost constant. 

We find that the rates of reaction for the various amines examined in (28) are governed by an extremely complex set of equilibria. For example, when R = n-Pr, n-Bu or s-Bu, the rate of reaction exhibit first order dependence on [EtjSiH] at constant amine concentration. However, the rate of reaction exhibits inverse non-linear dependence on [n-PrNH2] and [n-BuNH2], but positive non-linear dependence on [s-BuNH2] at constant [Et-jSiH]. Furthermore, if R t-Bu, then the rate of reaction is almost independent of both [t-BuNH2] and [EtjSiH]. Studies of the rate dependence on catalyst concentration for reaction (28) where R NH2 is n-BuNH2 reveal relative catalyst activities that are inversely dependent on [Ruo(C0) 2]. Similar studies with R NH2 = t-BuNH2 reveal that the rate or reaction is linearly dependent on [Ru3(CO) 2]. Piperidine is unreactive under the reaction conditions studied. 

Calculation of kinetic parameters - In the experiments carried out in the single autoclave the H2 pressure was not maintained and the consumption of H2 controlled the conversion of AcOBu, which could be described by pseudo-first order rate constant. In the activity tests performed in SPR16 the conversion of AcOBu increased linearly up to ca. 50 % with reaction time. Initial reaction rates were calculated from AcOBu conversion vs. reaction time dependence, the initial concentration of substrate and the amount of catalyst or the amount of promoters in 1 g of catalyst. 

In principle, any physical property that varies during the course of the reaction can be used to follow the course of the reaction. In practice one chooses methods that use physical properties that are simple exact functions of the system composition. The most useful relationship is that the property is an additive function of the contributions of the different species and that each of these contributions is a linear function of the concentration of the species involved. This physical situation implies that there will be a linear dependence of the property on the extent of reaction. As examples of physical properties that obey this relationship, one may cite electrical conductivity of dilute solutions, optical density, the total pressure of gaseous systems under nearly ideal conditions, and rotation of polarized light. In sufficiently dilute solutions, other physical properties behave in this manner to a fairly good degree of approximation. More complex relationships than the linear one can be utilized but, in such cases, it is all the more imperative that the experimentalist prepare care-... 

XOD is one of the most complex flavoproteins and is composed of two identical and catalytically independent subunits each subunit contains one molybdenium center, two iron sulfur centers, and flavine adenine dinucleotide. The enzyme activity is due to a complicated interaction of FAD, molybdenium, iron, and labile sulfur moieties at or near the active site [260], It can be used to detect xanthine and hypoxanthine by immobilizing xanthine oxidase on a glassy carbon paste electrode [261], The elements are based on the chronoamperometric monitoring of the current that occurs due to the oxidation of the hydrogen peroxide which liberates during the enzymatic reaction. The biosensor showed linear dependence in the concentration range between 5.0 X 10 7 and 4.0 X 10-5M for xanthine and 2.0 X 10 5 and 8.0 X 10 5M for hypoxanthine, respectively. The detection limit values were estimated as 1.0 X 10 7 M for xanthine and 5.3 X 10-6M for hypoxanthine, respectively. Li used DNA to embed xanthine oxidase and obtained the electrochemical response of FAD and molybdenum center of xanthine oxidase [262], Moreover, the enzyme keeps its native catalytic activity to hypoxanthine in the DNA film. So the biosensor for hypoxanthine can be based on... 

Although this reaction was discussed earlier, it is mentioned here because it is catalyzed by solid acids such as NH4SCN, which provide H+ ions that bond to the pairs of electrons after breaking them loose from the metal. Over a rather wide range of catalyst concentrations, the rate is linearly dependent on the amount of solid acid. Once the NH4+ ion donates a proton, NH3 is lost and the protonated ethyl-enediamine molecule is the acid that remains and continues to catalyze the reaction. While base catalyzed reactions of complexes may be better known, there are many acid catalyzed reactions as well. 

In the meantime temperature-dependent stopped-flow measurements were conducted on the latter complex in order to determine the activation parameters of the N-N cleavage reaction (24). Plots of the absorption intensity at 418 nm vs. time at T — —35 to +15°C indicate biphasic kinetics with two rate constants 0bs(p and obs(2)> in analogy to our measurements of the tungsten complex. This time, however, both rates depended upon the acid concentration. Interestingly much smaller rate constants 0bs(i) and 0bs(2)> were found for all acid concentrations than given by Henderson et al. for his (single) rate constant kobs (up to 1 order of magnitude). Furthermore plots of 0bs(i) and kohs(2) vs. the acid concentration showed no saturation behavior but linear dependencies with slopes k and k and intercepts k und k, respectively (s — acid dependent and i — acid independent), Eq. (2) ... 

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