Half-time irreversible system

There are well-defined criteria for this "reversible" system in terms of peak separation, wave shape, etc. and the maximum current scales inversely with the square root of the scan rate. The half-wave potential of a "reversible" redox process may readily be obtained from the voltammogram. If, however, the electron transfer produces a species that is chemically reactive on the experimental time scale, then the return wave is missing and the peak potential shifts as a function of the kinetics of the follow-up processes. The peak is not as well defined, and without a proper return wave it is now not straightforward to obtain thermodynamic half-wave potentials from the trace of such an irreversible system. Furthermore, if a disk electrode is used of micrometer-dimensions, then hemispherical diffusion now takes place and a sigmoidal current-potential curve is obtained [Fig. 4(b)]. 

One would obtain the pseudo-stationary state concentrations for each of the intermediate chemical species from the thermodynamics of irreversible processes if it were supposed that the relaxation time for the production or destruction of each of these species is very small compared to the half-time for the overall chemical reaction of the fuel to go to the product molecules. In the pseudo-stationary states approximation, the net rate of formation, Kp of each of the intermediate chemical species by chemical reactions is set equal to zero. This provides exactly the right number of simultaneous algebraic equations to express the concentration of each of the chemical intermediates in terms of powers of the concentrations of the fuel and product molecules. For example, in the hypothetical chain system given by Eqs. (130), (131), and (132), the pseudo-stationary mole fraction of B (which we shall designate as x ) is the solution of the equation ... 

It is generally accepted that the time required for desorption of adsorbed polymer is very long, and this process seems to appear to be irreversible(ljO. Accordingly, it is expected that the high adsorption values which appeared near the LCST may be held for a long time under different temperature conditions. In Table 3, experimental results for irreversibility of adsorption in the HPC-latex systems are shown. After the HPC samples and the latex particles were mixed for 2 hrs at 1+8 °C under the same condition as in the case of the adsorption process, one portion of one of the samples was separated immediately by centrifugation at 1+8 °C. The other half portion of the HPC-coated latex suspension was kept at room temperature for 1+8 hrs and then centrifuged at 6 °C. As... 

Polarography is valuable not only for studies of reactions which take place in the bulk of the solution, but also for the determination of both equilibrium and rate constants of fast reactions that occur in the vicinity of the electrode. Nevertheless, the study of kinetics is practically restricted to the study of reversible reactions, whereas in bulk reactions irreversible processes can also be followed. The study of fast reactions is in principle a perturbation method the system is displaced from equilibrium by electrolysis and the re-establishment of equilibrium is followed. Methodologically, the approach is also different for rapidly established equilibria the shift of the half-wave potential is followed to obtain approximate information on the value of the equilibrium constant. The rate constants of reactions in the vicinity of the electrode surface can be determined for such reactions in which the re-establishment of the equilibria is fast and comparable with the drop-time (3 s) but not for extremely fast reactions. For the calculation, it is important to measure the value of the limiting current ( ) under conditions when the reestablishment of the equilibrium is not extremely fast, and to measure the diffusion current (id) under conditions when the chemical reaction is extremely fast finally, it is important to have access to a value of the equilibrium constant measured by an independent method. 

Whereas radioactive decay is never a reversible reaction, many first-order chemical reactions are reversible. In this case the characteristic life time is determined by the sum of the forward and reverse reaction rate constants (Table 9.5). The reason for this maybe understood by a simple thought experiment. Consider two reactions that have the same rate constant driving them to the right, but one is irreversible and one is reversible (e.g. k in first-order equation (a) of Table 9.5 and ki in first-order reversible equation (b) of the same table). The characteristic time to steady state tvill be shorter for the reversible reaction because the difference between the initial and final concentrations of the reactant has to be less if the reaction goes both ways. In the irreversible case all reactant will be consumed in the irreversible case the system tvill come to an equilibrium in which the reactant will be of some greater value. The difference in the characteristic life time between the two examples is determined by the magnitude of the reverse reaction rate constant, k. If k were zero the characteristic life times for the reversible and irreversible reactions would be the same. If k = k+ then the characteristic time for the reversible reaction is half that of the irreversible rate. 

Radioactive decay Irreversible decline in the activity of a radionuclide Important attenuation mechanism when file half-life for decay is < residence time in flow system results in by-products... 

In contrast to the relaxation technique, the flow methods can be used for reactions with large equilibrium constants (irreversible reactions) as well as with small ones (reversible reactions). The shortest half life that can be measured in flow systems depends on the mixing time. In shopped flow arrangements, the stopping time sets a barrier at 5.10 s. In a continuous flow system, only the mixing process is limiting. 

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