Chemical reaction nearly irreversible systems

For a single, irreversible step in a chemical reaction, i.e., an elementary chemical process, the rate of the reaction is proportional to the concentrations of the reactants involved in the process. The constant of proportionality is called the rate constant, or the unitary rate constant to highlight the fact that it applies to an elementary process. A subtlety that may be introduced into rate expressions is to use chemical activities (see Chap. 10) and not simply concentrations, but activity coefficients in biological systems are generally taken to be near 1. 

Irreversible processes may promote disorder at near equilibrium, and promote order at far from equilibrium known as the nonlinear region. For systems at far from global equilibrium, flows are no longer linear functions of the forces, and there are no general extremum principles to predict the final state. Chemical reactions may reach the nonlinear region easily, since the affinities of such systems are in the range of 10-100 kJ/mol. However, transport processes mainly take place in the linear region of the thermodynamic branch. 

The change of total entropy is dS = dgS + diS. The term deS is the entropy exchange through the boundary, which can be positive, zero, or negative, while the term diS is the rate of entropy production, which is always positive for irreversible processes and zero for reversible ones. The rate of entropy production is diS/dt = JkXk. A near-equilibrium system is stable to fluctuations if the change of entropy production is negative, i.e. Ai5 < 0. For isolated systems, dS/dt > 0 shows the tendency toward disorder as d S/dt = 0 and dS = diS > 0. For nonisolated systems, diS/dt > 0 shows irreversible processes, such as chemical reactions, heat conduction, diffusion, or viscous dissipation. For states near global equilibrium, d S is a bilinear form of flows and forces that are related in linear form. 

In this book we offer a coherent presentation of thermodynamics far from, and near to, equilibrium. We establish a thermodynamics of irreversible processes far from and near to equilibrium, including chemical reactions, transport properties, energy transfer processes and electrochemical systems. The focus is on processes proceeding to, and in non-equilibrium stationary states in systems with multiple stationary states and in issues of relative stability of multiple stationary states. We seek and find state functions, dependent on the irreversible processes, with simple physical interpretations and present methods for their measurements that yield the work available from these processes. The emphasis is on the development of a theory based on variables that can be measured in experiments to test the theory. The state functions of the theory become identical to the well-known state functions of equilibrium thermodynamics when the processes approach the equilibrium state. The range of interest is put in the form of a series of questions at the end of this chapter. 

These processes that bring about averaging of spectral features occur reversibly, whether by acid-catalyzed intermolecular exchange or by unimolecular reorganization. NMR is one of the few methods for examining the effects of reaction rates when a system is at equilibrium. Most other kinetic methods require that one substance be transformed irreversibly into another. The dynamic effects of the averaging of chemical shifts or coupling constants provide a nearly unique window into processes that occur on the order of a few times per second. (The subject is examined further in Section 5-2.)... 

In a chemically reversible redox system the rate of the following reaction(s) is insufficient to perturb the concentration of within the electrochemical reaction layer near the electrode surface. When the following reaction is rapid so that Y is depleted during the experiment, the couple is chemically irreversible. The term quasireversible should not be used in conjunction with chemical reversibility. That terminology is restricted to the electron-transfer step itself. This error is made frequently. Redox systems that are less than totally chemically reversible should be described as having limited chemical reversibility. 

Consider the cyclic voltammetry trace of electrically activated iridium oxide (the so called AIROF) which features reversible reactions (Fig. 3.3). The scan rate is very slow, so the dynamic behavior of the Helmholtz capacitance has a negligible effect on the measured trace. The positive peaks A and B correspond to two distinct oxidation reactions at the surface of the electrode, pertaining to different electrode potentials. The negative peaks C and D correspond to reduction reactions. C matches A and D matches B, as they have similar shape. The reduction potential peak (for example at C, Epc) does not happen at a negative electrode-electrolyte voltage drop, but at a positive one even near to the potential where oxidation potential peak (at A, Epa) is located. If the surface redox reactions are fast and the reaction rate is limited by the diffusion of the reactants in the solution, the difference between the oxidation and reduction peaks is only 59 mV/n for a reaction where n electrons are transferred in the stoichiometry of the reaction. This state is called electrochemical reversibility, which means that the thermodynamic equilibrium in the redox reaction at the surface is established fast at every applied electrode potential. Note that this concept is not the same as the chemical reversibility explained before. A system can be electrochemically irreversible but chemically reversible. As seen in Fig. 3.3, iridium oxide is already electrochemically irreversible even at the very slow potential ramp of 50 mV/s, as the , 4 — is already larger than 59 mV. 

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