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Unformatted text preview: III. Reaction Kinetics Lecture 14: Faradaic Reactions in Concentrated Solutions 1 Reactions in Concentrated Solutions Note: Please see the course notes from 2009 for a detailed stochastic theory and formal derivations of reaction rates. Until now, we have assumed that forward and backward reaction rates are proportional to concentrations, which is appropriate for chemical kinet ics in a dilute solution. From our discussion of thermodynamics, we might expect to simply replace concentrations with activities to describe con centrated solutions in equilibrium, but this not sufficient to describe the dynamics of reactions out of equilibrium, since we also need to include de scribe concentrated-solution effects on the transition pathway. As a starting point, it is useful to introduce the concept of the excess chemical potential of state i defined by i = k B T ln C i + ex i (1) which is related to the activity coefficient i via ex i = k B T ln i (2) where C i is the concentration of state i (equal to the product of component concentrations, if there is more than one chemical species, as before). For concreteness, we could consider a lattice gas, where the chemical potentials are defined per lattice site, but the derivation is more general. From our lattice gas theory, we recognize k B T ln C i as the (entropic) chemical potential ex of a dilute, non-interacting gas . Therefore, contains all interaction free 1 MIT Student Lecture 14: Faradaic reactions in concentrated solutions 10.626 (2011) Bazant energies, between the reactants and each other (for example, contributions from excluded volumes) and the external system (for example, contributions from applied potentials). We conclude that ex ( x ) acts like the energy U ( x ) in a dilute solution, by providing generalized thermodynamic forces on the reactants, including entropic compositional effects....
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- Spring '03