Concentration jump experiments

Time/s Hypothetical experiment with [Ph3C ]o = 0 Concentration-jump experiment ... 

The entries were reconstructed for Eq. (3-30) from the rate constant values of kI = 0.406 s l and k 1 = 383 L mol"1 1 from Ref. 2. One calculation is for the reaction starting with A alone, and the other for a concentration-jump experiment with a two-fold dilution of a solution made up to have an original concentration of A of 2.84 X... 

Opposing reactions. Derive a kinetic equation for the system A P + Q that expresses the time dependence of 8, the shift in a concentration-jump experiment. Could 8 also be regarded as the difference between the timed value of [A] and the equilibrium value of [A] If so, what are the limitations on the ways in which A, P, and Q might be mixed ... 

RELAXATION AMPLITUDES IN CONCENTRATION JUMP EXPERIMENTS. APPLICATION TO ANTHOCYANINS. 

Figure B2.5.2. Schematic relaxation kinetics in a J-jump experiment, c measures the progress of the reaction, for example the concentration of a reaction product as a fiinction of time t (abscissa with a logaritlnnic time scale). The reaction starts at (q. (a) Simple relaxation kinetics with a single relaxation time, (b) Complex reaction mechanism with several relaxation times x.. The different relaxation times x. are given by the turning points of e as a fiinction of ln((). Adapted from [110].

The lines show data for the triphenyl methyl system, Eq. (3-30). The data represent the results of a relaxation experiment consisting of a concentration jump (i.e., a dilution) on a pre-equilibrated solution. The solid line shows the least-squares fit of the second data set in Table 3-2 according to Eq. (3-36). Panel A shows 5, itself, and panel B the quantity ln[S,/(a - 4K-- 5,)], as in Eq. (3-35). 

Opposing reactions. Use the data on the right side of Table 3-2, concerning the triphenyl methyl radical, to calculate ki. This experiment refers to the concentration-jump method in which the parent solution was diluted with solvent to twice its initial volume. 

A schematic representation of temperature and concentration profiles in a temperature-jump experiment. All scales are arbitrary, and the matter to be emphasized is that the temperature jump occurs rapidly compared with the re-equilibration reaction. 

Competition reactions ad eosdem, 106 ad eundem, 105 (See also Reactions, trapping) Competitive inhibitor, 92 Complexation equilibria, 145-148 Composite rate constants, 161-164 Concentration-jump method, 52-55 Concurrent reactions, 58-64 Consecutive reactions, 70, 130 Continuous-flow method, 254—255 Control factor, 85 Crossover experiment, 112... 

The effect of the DNA sequence dependence on the binding dynamics of 5 and 6 with ct-DNA (42% GC content) and ml-DNA (72% GC content) was investigated using laser temperature jump experiments.118 Only one relaxation process was observed for both guests, but the presence of the leveling off effect at high DNA concentration was dependent on the guest and the type of DNA. No values for the rate constants were reported in this study. 

Compounds 30-32 formed 2 1 complexes with CDs (Scheme 13). The formation of the 1 1 complex was fast and for this reason only one relaxation process was observed. In the cases where the 2 2 complex was present its formation was also fast and only one relaxation process for the 2 1 complex was observed in the temperature jump experiments. Since the equilibria are coupled the expression for the observed rate constant includes Kt, (and K22 when the 2 2 complex is present), k21, k2, and the concentrations of guest, 1 1 complex and CD.180 182 The values for the association and dissociation rate constants and equilibrium constants were obtained from the non-linear fit of the dependence of kobs on the total concentration of CD (Table 9). 

In recent years, evidence has been found that both mechanisms of proton transfer can occur for certain intramolecularly hydrogen-bonded acids. Also, new kinetic behaviour has been obtained which allows a much more detailed examination of the reaction steps in (22). Kinetic data for the second ionization of substituted phenylazoresorcinols in the presence of hydroxide ions (25) were some of the first to be obtained for an intramolecularly hydrogen-bonded acid. The reciprocal relaxation time (t ) for the approach to equilibrium in a temperature-jump experiment was measured at different hydroxide-ion concentrations. A linear dependence of x on [OH] was obtained of the form of (26) (Eigen and Kruse, 1963 Inskeep et al., 1968 Rose and Stuehr, 1971). However, careful measurements at lower hydroxide-ion concentrations (Perlmutter-Hayman and Shinar, 1975 Perl-mutter-Hayman et al., 1976 Yoshida and Fujimoto, 1977) revealed that the... 

The function describing the change in equilibrium concentration of a given species following a sudden rise in temperature (in a so-called temperature jump experiment), has two parts, corresponding to times before and after the temperature jump (Figure 2.9). 

Ikeda et al. (1984b) plotted Eq. (4.42) by determining the equilibrium concentrations from adsorption isotherms for S(H), S(NH4), and NH4, and using the pH value to determine [H+]. This plot shows good linearity (Fig. 4.11), which confirms that the mechanism hypothesized in Eq. (4.40) is operational. The kv and k- values for Eq. (4.42) can then be calculated from the slope and intercept of Fig. 4.11, and the kinetic Keq can be determined from the ratio kjk x (Table 4.2). It is important to notice that the values calculated kinetically and statically (equilibrium method) are similar, which indicates that the rate constants one calculates from p-jump experiments are chemical kinetics rate constants. These data also verify... 

Obviously, to find a specific set of conditions for the onset of a concentration jump between stable states, or for the occurrence of oscillations, for that matter, would require the testing of a huge number of reaction mixtures under conditions maintained far from equilibrium. Since such an experiment is not easily accomplished in ordinary glassware, we conducted our studies of oscillatory reactions in continuous flow reactors patterned after those used at the Paul Pascal Research Center in Bordeaux, France35). 

CN is formally as stable as Laasonen, and more accurate, with errors of 0(STA, Ha). However, it has one serious drawback. If the initial conditions are a sharp change in concentration (as in potential jump experiments), CN responds with errors oscillating about zero and for large A values these oscillations can persist over much of the simulation period. This has meant that simulators have tended to use other methods instead. The stability, and the reason for the oscillatory response, of CN are explained in Chap. 14, but here, a method of damping the oscillations will be described. 

Although motional averaging might occur in ways other than that envisioned by Cates, temperature-jump experiments have yielded values of Tbr that indicate Tbr < in the region where the relaxation is nearly monoexponential, in agreement with Cates theory. In addition, Cates theory offers distinctive predictions for the concentration-dependencies of the viscoelastic behavior these allow the theory to be tested rather stringently. To obtain these predictions, we note that in the semi-dilute regime, the mean-field reptation time is L 4>, where 0 is the volume fraction of surfactant. Hence, from Eqs. (12-31) and... 

Recovery evaluation using surrogates or spikes implies the assumption that the extraction of spike is equivalent of the native analyte. In practice, it is often difficult to demonstrate that equivalence, and the only solution left is to accept the above assumption (extraction of spike is equivalent to that of native compound). A special form of this method is the standard addition method, where spiking at different levels is performed. Depending on the number of levels (i.e., two, three, or more) and/or the concentration jump chosen for the spiking experiment, a different recovery evaluation can be obtained. 

Figure 3. Oscilloscope trace of a temperature-jump experiment on Octopus hemocyanin reacting with oxygen. Potassium phosphate buffer, 0.2M, pH 7, and 20 C (before the jump). Discharge 30 kv yielding a temperature increase of 4 to 5 C. Protein concentration = 4.5 X 10 binding equivalent L fractional saturation with oxygen = 0.53 free oxygen concentration = 3.4 X lOr M. Sweep time = 100 fxsec per large screen division observation wavelength = 348 nm (24).

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