Variable-time kinetics

E.W. Chlapowski, H.A. Mottola, Some comparative studies on data handling in variable-time kinetic determinations. Modification of manganese(II) catalysis with 1,10-phenanthroline and some analogs, Anal. Chim. Acta 76 (1975) 319. 

These reasons led Pardue and Fields to consider that this type of titration is actually another variable-time kinetic method insofar as it is based on the measurement of a time increment, At, between two preselected reference points located at the same height from the baseline in the rising and falling portions of an FIA peak yielded by a physico-chemical process which has attained neither physical equilibrium —there is some mass flow between the sample plug and the regent solution— nor chemical equilibrium —the reaction is still incomplete. 

Noncnzymc-Catalyzcd Reactions The variable-time method has also been used to determine the concentration of nonenzymatic catalysts. Because a trace amount of catalyst can substantially enhance a reaction s rate, a kinetic determination of a catalyst s concentration is capable of providing an excellent detection limit. One of the most commonly used reactions is the reduction of H2O2 by reducing agents, such as thiosulfate, iodide, and hydroquinone. These reactions are catalyzed by trace levels of selected metal ions. Eor example the reduction of H2O2 by U... 

Time is a variable in kinetics but not in thermodynamics rates dealt with in the latter are with respect to temperature, pressure, etc., but not with respect to time equilibrium is a time-independent state. 

Time is an important variable in kinetics, and its measurement, whether direct or indirect, is a primary consideration. Several time quantities can be defined. 

TTie classification of kinetic methods proposed by Pardue [18] is adopted in the software philosophy. TTie defined objective of measurement in the system is to obtain the best regression fit to a minimum of 10 data points, taken over either a fixed time (i.e. the maximum time for slow reactions) or variable time (for reactions complete in less than 34 min, which is the maximum practical observation time). In an analytical system generating information at the rate of SO datum points per second, with reactions being monitored for up to 2040 s, effective data-reduction is of prime importance. To reduce this large quantity of analytical data to more manageable proportions, an algorithm was devised to optimize the time-base of the measurements for each individual specimen. 

Pseudo-first-order rate constants for carbonylation of [MeIr(CO)2l3]" were obtained from the exponential decay of its high frequency y(CO) band. In PhCl, the reaction rate was found to be independent of CO pressure above a threshold of ca. 3.5 bar. Variable temperature kinetic data (80-122 °C) gave activation parameters AH 152 (+6) kj mol and AS 82 (+17) J mol K The acceleration on addition of methanol is dramatic (e. g. by an estimated factor of 10 at 33 °C for 1% MeOH) and the activation parameters (AH 33 ( 2) kJ mol" and AS -197 (+8) J mol" K at 25% MeOH) are very different. Added iodide salts cause substantial inhibition and the results are interpreted in terms of the mechanism shown in Scheme 3.6 where the alcohol aids dissociation of iodide from [MeIr(CO)2l3] . This enables coordination of CO to give the tricarbonyl, [MeIr(CO)3l2] which undergoes more facile methyl migration (see below). The behavior of the model reaction closely resembles the kinetics of the catalytic carbonylation system. Similar promotion by methanol has also been observed by HP IR for carbonylation of [MeIr(CO)2Cl3] [99]. In the same study it was reported that [MeIr(CO)2Cl3]" reductively eliminates MeCl ca. 30 times slower than elimination of Mel from [MeIr(CO)2l3] (at 93-132 °C in PhCl). 

To extend the above kinetic model to this more general case in which degenerate levels occur, one uses the number of molecules in each level (Nf and Nf for the two levels in the above example) as the time dependent variables. The kinetic equations then governing their time evolution can be obtained by summing the state-to-state equations over all states in each level... 

TRPES has been recently reviewed and details of the experimental method and its interpretation can be found elsewhere [5], Trans-azobenzene was introduced via a helium supersonic molecular beam into the interaction region of a magnetic bottle photoelectron spectrometer. The molecules were photoexcited by a tunable femtosecond laser pulse (pump pulse) with a wavelength of 280-350nm. After a variable time delay, the excited molecules were ionized by a second femtosecond laser pulse (probe pulse) with a wavelength of 200 or 207nm. The emitted photoelectrons were collected as a function of pump-probe time delay and electron kinetic energy. 

CV has become a standard technique in all fields of chemistry as a means of studying redox states. The method enables a wide potential range to be rapidly scanned for reducible or oxidizable species. This capability, together with its variable time scale and good sensitivity, makes CV the most versatile electroanalytical technique thus far developed. It must, however, be emphasized that its merits are largely in the realm of qualitative or diagnostic experiments. Quantitative measurements (of rates or concentrations) are best obtained via other means (e.g., step, pulse, or hydrodynamic techniques). Because of the kinetic control of many CV experiments, some caution is advisable when evaluating the results in terms of thermodynamic parameters (e.g., measurement of E° for irreversible couples). 

The kinetics of the addition of aniline (PI1NH2) to ethyl propiolate (HC CCChEt) in DMSO as solvent has been studied by spectrophotometry at 399 nm using the variable time method. The initial rate method was employed to determine the order of the reaction with respect to the reactants, and a pseudo-first-order method was used to calculate the rate constant. The Arrhenius equation log k = 6.07 - (12.96/2.303RT) was obtained the activation parameters, Ea, AH, AG, and Aat 300 K were found to be 12.96, 13.55, 23.31 kcalmol-1 and -32.76 cal mol-1 K-1, respectively. The results revealed a first-order reaction with respect to both aniline and ethyl propiolate. In addition, combination of the experimental results and calculations using density functional theory (DFT) at the B3LYP/6-31G level, a mechanism for this reaction was proposed.181... 

The time dependence of desorption remains a little-explored but potentially useful approach for mechanistic studies. Cotter (33) has monitored secondary ion kinetic energies in a laser desorption (LD) time-of-flight instrument. Laser pulses 40 ns wide were used to desorb K+ ions from solid KC1, and the ions were sampled at variable times after the laser pulse. Emission persists for several microseconds after excitation, and secondary ion kinetic energies were found to decrease when examined at longer times after excitation. This result supports a thermal model for... 

Kinetics of the addition of PI13P to p-naphthoquinone in 1,2-dichloromethane, using the initial rate method, revealed the order of reaction with respect to the reactants the rate constant was obtained from pseudo-first-order kinetic studies. A variable time method using UV-visible spectrophotometry (at 400 nm) was employed to monitor this addition, for which the following Arrhenius equation was obtained log k = 9.14- (13.63/2.303RT). The resulting activation parameters a, AH, AG, and Aat 300 K were 13.63, 14.42 and 18.75 kcalmol-1 and —14.54 calmol 1K 1,... 

To model the karst fracture the keyword TRANSPORT is used and 30 elements are defined by the sub key word -cells. For the fracture being 300 m long the length of the cells is 10 m each. The number of 30 shifts is required to exchange the water volume one time completely. According to the assumed flow velocity the variable -time step is set to 360 seconds (= 0.1 hours). With -punch 1-30 all 30 cells are printed in the output, with -punch frequency 30 only the result after 30 shifts is considered for all of those 30 cells. The adjustment of the equilibrium during transport can be done using EQUILIBRIUM PHASES. It is important to add 1-30 behind the key words SOLUTION, EQUILIBRIUM PHASES and KINETICS in order to consider all 30 cells. 

Figure 4.4 Plot of enzyme complex concentration as a function of time for the Michaelis-Menten mechanism of Equations (4.22). The concentration of ES predicted from a kinetic simulation of Equations (4.22) is plotted as a solid line. The parameter values used are k+ = 1000M-1 sec-1,k i = 1.0sec-1,k+2 = 0.1 sec-1, and E0 = 0.1 mM. The left plot illustrates the fast-time kinetics. The fast-time variable n(r) predicted by Equation (4.29) is plotted as a dashed line.

A different experimental approach to NRMS is embodied in the tandem quadrupole acceleration-deceleration instrument that uses quadrupole mass filters for mass selection and analysis of low-energy (70-80 eV) ions whereas collisional electron transfer is carried out after ion acceleration to 4-8 keV kinetic energies (Fig. 5) [10, 50]. The reionized products are decelerated back to 70-80 eV for mass analysis. The quadrupole instrument achieves unit mass resolution of NR products and it is versatile enough to allow variable-time and photoexcitation experiments described briefly below. Coupling with soft ionization methods... 

The only pieces of hardware needed for photo-CIDNP are a light source and an unmodified NMR spectrometer. Pulsed lasers are most convenient for illumination, as they allow both time-resolved experiments (when the laser flash is followed by an acquisition pulse after a variable time delay) and steady-state ones (when the laser is triggered with a high repetition rate, thus providing quasi-continuous excitation). All the examples of this work draw on the second variant. Nevertheless, they yield kinetic information about much faster processes than would be observable by direct... 

Catalytic reactions— Nonenzymatic Kinetic analysis through the use of catalyzed reactions is normally performed by the variable-time technique. This technique is appropriate because measured and constant quantities of A -H B in (21-23) can be used in a reaction. Typically, the time for completion of the reaction is measured and then related to the concentration of the catalyst. 

Basic pharmacologic principles apply as much to drug interactions as to drug actions. Each kinetic property—absorption, distribution, metabolism (biotransformation), and excretion—is potentially affected by the presence of coadministered medications. Drug interactions follow a variable time-course pattern, from immediate to delayed. Consequently, it is important to remember that several weeks may elapse before the effects of an interactive combination are evident. 

The simulation uses a variable-time step method in order to simulate the kinetics over different Pd and PdAu surfaces [85]. The temporal behavior of all intermediates is explicitly tracked throughout the simulation. All atop, bridge, and 3-and 4-fold hollow sites are specifically followed as a function of time. The simulation follows all lateral and through-space interactions between coadsorbed intermediates within a cut off of two nearest-nearest neighbors. 

The numerical procedures used to deal with experimental data are illustrated with results from an experiment in chemical kinetics recorded in table C.l. The reaction is first order but that will be ignored in the analysis of the data. Note that the data points have been obtained for equal increments in the independent variable time. It turns out that numerical techniques are especially easy to apply when this is the case. The second feature of this data set is that the precision of the time data is much higher than that of the concentration data. 

Therefore, the trial model function will in general be a nonlinear function of the independent variable, time. Various mathematical procedures are available for iterative x2 minimization of nonlinear functions. The widely used Marquardt procedure is robust and efficient. Not all the parameters in the model function need to be determined by iteration. Any kinetic model function such as Equation 3.9 consists of a mixture of linear parameters, the amplitudes of the absorbance changes, A and nonlinear parameters, the rate constants, kb For a given set of kb the linear parameters, A, can be determined without iteration (as in any linear regression) and they can, therefore, be eliminated from the parameter space in the nonlinear least-squares search. This increases reliability in determining the global minimum and reduces the required computing time considerably. 

The temperature along a reaction path may be constant or variable. In non-kinetic mode, it may be treated as a function of the reaction progress variable. In kinetic mode, it may be treated as a function of time. Therefore, EQ6 can also be used to compute the consequences, such as pH shift and mineral precipitation, of heating or cooling an aqueous fluid (1,26). 

Equation 18.12 is the basis for the derivative approach to rate-based analysis, which involves directly measuring the reaction rate at a specific time or times and relating this to [A]fl. Equation 18.11 is the basis for the two different integral approaches to kinetic analysis. In one case, the amount of A reacted during a fixed time is measured and is directly proportional to [A]o ( fixed-time method) in the other case, the time required for a fixed amount of A to react is measured and is also proportional to [A]o variable-time method). Details of these methods will be discussed in Section... 

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