Pseudo first order reaction perturbations

Early studies of ET dynamics at externally biased interfaces were based on conventional cyclic voltammetry employing four-electrode potentiostats [62,67 70,79]. The formal pseudo-first-order electron-transfer rate constants [ket(cms )] were measured on the basis of the Nicholson method [99] and convolution potential sweep voltammetry [79,100] in the presence of an excess of one of the reactant species. The constant composition approximation allows expression of the ET rate constant with the same units as in heterogeneous reaction on solid electrodes. However, any comparison with the expression described in Section II.B requires the transformation to bimolecular units, i.e., M cms . Values of of the order of 1-2 x lO cms (0.05 to O.IM cms ) were reported for Fe(CN)g in the aqueous phase and the redox species Lu(PC)2, Sn(PC)2, TCNQ, and RuTPP(Py)2 in DCE [62,70]. Despite the fact that large potential perturbations across the interface introduce interferences in kinetic analysis [101], these early estimations allowed some preliminary comparisons to established ET models in heterogeneous media. 

For reactions other than first (or pseudo-first) order, the equations become more complicated, but one major simplification is available. If an existing equilibrium is slightly perturbed by sudden dilution, laser pulse, change of temperature or pressure, and so on, and if the displacement of the system from equilibrium is minor (<10%), then the establishment of the new equilibrium will follow first-order kinetics, regardless of the rate law that would be applicable if the entire course of the reaction were monitored. 

Mu addition to double bonds places the muon two bonds away from the radical center. Mu is thus not normally directly involved in reactions of the radical, and any kinetic isotope effects are secondary and thus small. This makes the muon a non-perturbing radical kinetics probe. Its advantage is the extraordinary sensitivity of the technique which requires only a single muon in the sample at a given time. This eliminates any radical termination reactions. With on the order of 10 muons needed for an experiment the concentration of the reaction partner does not change, and kinetics is of ideal pseudo-first order. This eliminates a munber of sources for serious errors which often affect the accuracy of conventional radical kinetics. 

If we use a pH jiunp, as an example for the consequence of a temperature perturbation of an equilibrium, one can easily derive from the above that, in a solution in Tris buffer (pAT= 8 and AH=45.6 kJ mole ), an increase of 5 degrees will reduce the pATby 0.12. The corresponding shift of a solution at pH 8 would be to pH 7.88. The effect of a temperature jump, or of any other perturbation of the equilibrium constant, is maximal when the ratio of the reactants is unity. In a simple first order isomerization one has little control over this, but most of the reactions under discussion are, at least distantly, linked to a pseudo first order process with equilibrium positions dependent on reactant concentrations. Unfortunately the choice of experimental conditions (concentrations) is often limited by solubilities and the optical properties used for monitoring the reactants, a problem also encountered in... 

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