Activation free energy equilibrium potential

Having separated the dynamical from equilibrium (or, more accurately, quasi-equilibrium) effects, one can readily discover the origin of the activation free energy and define the concept of the potential of mean force by analysis of the expression for the TST rate constant, k in (A3.8.3). The latter can be written as [7]... 

The important experimentally accessible parameters are reaction rate constants (A et), activation free energies (proportional to RT In(ket)), equilibrium constants of reactions and/or electrochemical potentials of the component couples, and electron transfer absorption (or emission) energies (e.g., /zi abs in Figure 1), fine structure and bandwidths. The perturbations of these parameters by temperature variations, magnetic or electric fields and isotopic substitution can also provide relevant information. The experimental procedures used to evaluate these parameters are not the focus of this chapter. There are many sources dealing with generaF or specific " techniques. 

In principle, reaction and activation free energies required in Equation 3.59 could be obtained from ab initio studies of reaction pathways and mechanisms, such as those performed in Rossmeisl et al. (2005), Jacob (2006), and Roudgar et al. (2010). Values of these energy parameters for the appropriate sequence of steps, evaluated at equilibrium, will determine the effective activation potential and the exchange current density of the ORR. These relations are complicated by adsorbate interaction effects and site-specific dispersion of adsorption energies of oxygen intermediates. Currently, these effects are not accounted for in ab initio studies. 

To proceed fiirther, to evaluate the standard free energy AG , we need infonnation (experimental or theoretical) about the particular reaction. One source of infonnation is the equilibrium constant for a chemical reaction involving gases. Previous sections have shown how the chemical potential for a species in a gaseous mixture or in a dilute solution (and the corresponding activities) can be defined and measured. Thus, if one can detennine (by some kind of analysis)... 

In order to obtain a definite breakthrough of current across an electrode, a potential in excess of its equilibrium potential must be applied any such excess potential is called an overpotential. If it concerns an ideal polarizable electrode, i.e., an electrode whose surface acts as an ideal catalyst in the electrolytic process, then the overpotential can be considered merely as a diffusion overpotential (nD) and yields (cf., Section 3.1) a real diffusion current. Often, however, the electrode surface is not ideal, which means that the purely chemical reaction concerned has a free enthalpy barrier especially at low current density, where the ion diffusion control of the electrolytic conversion becomes less pronounced, the thermal activation energy (AG°) plays an appreciable role, so that, once the activated complex is reached at the maximum of the enthalpy barrier, only a fraction a (the transfer coefficient) of the electrical energy difference nF(E ml - E ) = nFtjt is used for conversion. 

The activation factor in the first case is determined by the free energy of the system in the transitional configuration Fa, whereas in the second case it involves the energy of the reactive oscillator U(q ) = (l/2)fi(oq 2 in the transitional configuration. The contrast due to the fact that in the first case the transition probability is determined by the equilibrium probability of finding the system in the transitional configuration, whereas in the second case the process is essentially a nonequilibrium one, and a Newtonian motion of the reactive oscillator in the field of external random forces in the potential U(q) from the point q = 0 to the point q takes place. The result in Eqs. (171) and (172) corresponds to that obtained from Kramers theory73 in the case of small friction (T 0) but differs from the latter in the initial conditions. 

At equilibrium, all components of a mixture have the same molar free energy, i.e., the same chemical potential, in any phase in which they are present, and they have the same chemical potential as all other components. However it is not always convenient to use the same standard state for all components or even for the same component in all phases. Just as Equation 6 defines fugacity, Equation 7 or 8 defines activity. Furthermore, Equations 6-8 define / and a for all substances, not just gases. However we should keep in mind that we do not use the same standard state for a substance in all the phases, mixtures, or pure states in which it may occur or for all components of a mixture. 

The concept of substance activity was derived by Gilbert N. Lewis in 1907 from the laws of equilibrium thermodynamics and is described in detail in the text entitled Thermodynamics and the Free Energy of Chemical Substances by Lewis and Randell (1923). In a homogeneous mixture, each component has a chemical potential (jjl), which describes how much the free energy changes per mole of substance added to the system. The chemical potential of water (pw) in a solution is given by... 

Application of Activity at cmc. The above consideration suggested us to propose a new treatment for ionic micelle formation. According to thermodynamics, the micelle-monomer equilibrium is achieved when the chemical potential of surfactant in the micelle is equal to that in the bulk solution. The free energy of micelle formation can be represented by the use of the critical micelle activity, cma, which is the activity of surfactant at the cmc, as... 

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