Equilibrium constant pressure jump perturbations

A pressure perturbation results in the shifting of the equilibrium the return of the system to the original equilibrium state (i.e., the relaxation) is related to the rates of all elementary reaction steps. The relaxation time constant associated with the relaxation can be used to evaluate the mechanism of the reaction. During the shift in equilibrium (due to pressure-jump and relaxation) the composition of the solution changes and this change can be monitored, for example by conductivity. A description of the pressure-jump apparatus with conductivity detection and the method of data evaluation is given by Hayes and Leckie (1986). 

Other perturbations have been demonstrated. The pressure,, jump, similar to the T-jump in principle, is attractive for organic reactions where Joule heating may be impractical both because of the solvent being used and because concentrations might have to be measured by conductivity. Large (104—105 kPa) pressures are needed to perturb equilibrium constants. One approach involves pressurizing a liquid solution until a membrane ruptures and drops the pressure to ambient. Electric field perturbations affect some reactions and have also been used (2), but infrequendy. 

Perturbation approaches such as temperature jump, pressure jump, etc., are based on a simple principle. For a system initially at equilibrium the forward and reverse rates of reaction are equal. In a temperature-jump experiment the system is heated so rapidly that the temperature increases faster than the concentrations can respond. The initial reaction rate is determined by the rate constants at the new temperature T and concentrations are set by the equilibrium at the original temperature Tq the initial reaction rate is then... 

Show that T (temperature) jump is a useful kinetic probe only if AHrxni O. Show that P (pressure) jump requires A Vrxn 0. (Consider the effect of the perturbation on the equilibrium constant.)... 

The time resolution of rapid-flow methods is limited by the rate at which two reactants are mixed, which is restricted to about 1 ms. To measure faster reactions, alternative methods are required. A generally applicable method is the measurement of system adjustment following a relatively small perturbation. A system at equilibrium is perturbed by a sudden temperature or pressure jump, applied as a single rapid change or as a periodic oscillation. Changes in the concentration of reactants and products are subsequently monitored. From the patterns observed, individual rate constants can be obtained. 

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 ... 

There are various direct measurements of micellar solutions giving access to the dynamics rate constants - mainly based on disturbance of the equilibrium state by imposing various types of perturbations, such as stop flow, ultrasound, temperature and pressure jump [14,15[. This aspect is also not further elaborated here we focus instead on the impact of micellar kinetics on interfacial properties, to demonstrate that tensiometry and dilational rheology are suitable methods to probe the impact of micellar dynamics. The first work on this subject was published by Lucassen already in 1975 [16[ and he showed that the presence of micelles in the bulk have a measurable impact on the adsorption kinetics, and hence on the dilational elasticity, when measured by a longitudinal wave damping technique. Subsequent work demonstrated the effect of micellar dynamics on non-equilibrium interfacial properties [17-29]. The physical idea of the impact of micellar dynamics on the dynamic properties of interfacial layers can be easily understood from the scheme given in Figure 13.1. 

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