Basic equations for the analysis of chemical relaxations

The forcing functions used to initiate chemical relaxations are temperature, pressure and electric held. Equilibrium perturbations can be achieved by the application of a step change or, in the case of the last two parameters, of a periodic change. Stopped-flow techniques (see section 5.1) and the photochemical release of caged compounds (see section 8.4) can also be used to introduce small concentration jumps, which can be interpreted with the linear equations discussed in this chapter. The amplitudes of perturbations and, consequently of the observed relaxations, are determined by thermodynamic relations. The following three equations dehne the dependence of equilibrium constants on temperature, pressure and electric held respectively, in terms of partial differential equations and the difference equations, which are convenient approximations for small perturbations  

The number of intermediates which can be detected in a system will depend not only on the relation between the relaxation times, but also on the sensitivity of steps to different forcing functions. This can be illustrated with a model of a two step ligand binding reaction (three states of the receptor R)  

Let us assume that k 2 + k2 ) k2i + k 2) and that the first step is pressure independent, but temperature dependent, while the second step is pressure dependent but relatively temperature independent. If the observed concentration variable is [AR], pressure perturbation will result in two observed relaxations, while temperature perturbation will allow only the 

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 

Note t These are hybrid constants involving the -NH and the -SH groups. 

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