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** First-order reactions reaction **

If experimental conditions are carefully selected so that all individual steps are either first-order or pseudo-first-order processes, then, under transient or pre-steady-state conditions, the reaction time courses will take the form of a sum of exponentials (i.e., a linear combination of the individual rate equations for each relaxation), such that the observable, time-dependent changes in absorbance, AZ, are given by the relationship [Pg.174]

Since P and M have strongly different absorption spectra (10), the kinetics of reaction 1 could be followed spectrophoto-metrically in the stopped-flow spectrophotometer. Under pseudo first order conditions the relaxation time is given by [Pg.178]

The latter is invariably used in the relaxation or photochemical approach to rate measurement (Sec. 1.8), rmd is the time taken for A to fall to 1/e (1/2.718) of its initial value. Half-lives or relaxation times are eonstants over the complete reaction for first-order or pseudo first-order reactions. The loss of reactant A with time may be described by a single exponential but yet may hide two or more concurrent first-order and/or pseudo first-order reactions. [Pg.8]

If ordinary pseudo first-order kinetics were obeyed, log [M] vs. t should be linear here, however, the result is just opposite [M] vs. log t is almost linear over more than 4 decades of time. The first half-time is about 20 h and the next one 300 h. Physically, this would mean that the monomer molecules are distributed among traps and that the molecules from the shallowest traps escape and diffuse to a reactive radical site more quickly than the other ones. Further reaction will deepen the traps of the remaining molecules, so that the relaxation time of the system increases continuously. [Pg.48]

Solution of the coupled mass-transport and reaction problem for arbitrary chemical kinetic rate laws is possible only by numerical methods. The problem is greatly simplified by decoupling the time dependence of mass-transport from that of chemical kinetics the mass-transport solutions rapidly relax to a pseudo steady state in view of the small dimensions of the system (19). The gas-phase diffusion problem may be solved parametrically in terms of the net flux into the drop. In the case of first-order or pseudo-first-order chemical kinetics an analytical solution to the problem of coupled aqueous-phase diffusion and reaction is available (19). These solutions, together with the interfacial boundary condition, specify the concentration profile of the reagent gas. In turn the extent of departure of the reaction rate from that corresponding to saturation may be determined. Finally criteria have been developed (17,19) by which it may be ascertained whether or not there is appreciable (e.g., 10%) limitation to the rate of reaction as a consequence of the finite rate of mass transport. These criteria are listed in Table 1. [Pg.103]

For reactions between ions of like charge, the term in /cre(l + kR) should be multiplied by a number 0.6—0.9, whereas for unlike charges, this number is 0.3—0.6 depending on R. Certainly, eqn. (58) is not the appropriate correction term. In eqn. (57), the ionic relaxation time for univalent ions is = l/(47rlrc Dn), where n is the electrolyte concentration. This is also the characteristic time for reaction (pseudo first-order decay time) of a univalent species reacting with one or other ion of the [Pg.58]

A somewhat different approach to hot atom reactions has been taken by Keizra, who examined the evolution with time of the probability distribution of hot-atom energies. If the reaction rate is much smaller than the collision frequenqy the probability distribution relaxes to a steady state, which can be used to d ne hot-atom rate constants. The characterization of the hot-atom distribution in terms of a time-dependent hot-atom temperature was explored, and it was shown that under conditions where the hot-atom distribution becomes steady the pseudo-first-order rate constant differs from the equilibrium rate constant only by the appearance of the steady-state temperature. [Pg.105]

** First-order reactions reaction **

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