Chemical equilibrium A dynamic reaction system in which the

Chemical equilibrium A dynamic reaction system in which the concentrations of all reactants and products remain constant as a function of time. 

Chemical change the change of substances into other substances through a reorganization of the atoms a chemical reaction. (1.9) Chemical equation a representation of a chemical reaction showing the relative numbers of reactant and product molecules. (3.8) Chemical equilibrium a dynamic reaction system in which the concentrations of all reactants and products remain constant as a function of time. (13)... 

Chemical equilibrium A dynamic state in which the rates of forward and reverse reactions are identical a system in equilibrium will not spontaneously depart from this condition. Chemiluminescence The emission of energy as electromagnetic radiation during a chemical reaction. 

In the reactive case, r is not equal to zero. Then, Eq. (3) represents a nonhmoge-neous system of first-order quasilinear partial differential equations and the theory is becoming more involved. However, the chemical reactions are often rather fast, so that chemical equilibrium in addition to phase equilibrium can be assumed. The chemical equilibrium conditions represent Nr algebraic constraints which reduce the dynamic degrees of freedom of the system in Eq. (3) to N - Nr. In the limit of reaction equilibrium the kinetic rate expressions for the reaction rates become indeterminate and must be eliminated from the balance equations (Eq. (3)). Since the model Eqs. (3) are linear in the reaction rates, this is always possible. Following the ideas in Ref. [41], this is achieved by choosing the first Nr equations of Eq. (3) as reference. The reference equations are solved for the unknown reaction rates and afterwards substituted into the remaining N - Nr equations. 

We have mentioned salts in solution (i.e., dissolved in water), reversible reactions and equilibrium in solution, and ions in solution. Most chemical reactions occur in solution. It was apparent to Van t Hoff at an early stage that to understand the dynamics and thermodynamics of chemical reactions, he needed to understand the nature of solutions in general. And it was equally clear when he began his work that very little was known about the nature of solutions. Solutions always involve specific chemicals, the solvent (often water) and the dissolved substance or solute (often a salt, e.g., sodium chloride). But although they are always chemical systems, they can also be considered as physical systems, to which the principles of thermodynamics can be applied. 

We frequently also encounter so-called steady states in which the macroscopic concentrations of species are not changing with time, even though the system is not at equilibrium. Steady states are maintained not by a dynamic balance between forward and reverse processes but rather by the competition between a process that supplies the species to the system and a process that removes the species from the system. Many chemical reactions occur in living systems in steady states and do not represent an equilibrium between reactants and products. You must be certain that a reaction is at equilibrium and not in steady state before applying the methods of this chapter to explain the relative concentrations of reactants and products. 

Theoretical and experimental studies of reacting systems on the molecular level show that reactions among the participating species continue even after equilibrium is achieved. The constant concentration ratio of reactants and products results from the equality in the rates of the forward and reverse reactions. In other words, chemical equilibrium is a dynamic state in which the rates of the forward and reverse reactions are identical. 

When no net change occurs in the amount of reactants and products, a system is said to be in equilibrium. In most situations, chemical reactions exist in equilibrium when products and reactants form at the same rate. Such a system, in which opposite actions are taking place at the same rate, is said to be in dynamic equilibrium. 

In the case of the fast binary reaction we could eliminate the reaction term from the reaction-diffusion-advection equation. But in general this is not possible. In this chapter we consider another class of chemical and biological activity for which some explicit analysis is still feasible. We consider the case in which the local-reaction dynamics has a unique stable steady state at every point in space. If this steady state concentration was the same everywhere, then it would be a trivial spatially uniform solution of the full reaction-diffusion-advection problem. However, when the local chemical equilibrium is not uniform in space, due to an imposed external inhomogeneity, the competition between the chemical and transport dynamics may lead to a complex spatial structure of the concentration field. As we will see in this chapter, for this class of chemical or biological systems the dominant processes that determine the main characteristics of the solutions are the advection and the reaction dynamics, while diffusion does not play a major role in the large Peclet number limit considered here. Thus diffusion can be neglected in a first approximation. 

The dynamic viewpoint of chemical kinetics focuses on variations in chemical composition with either time in a batch reactor or position in a continuous flow reactor. This situation may be contrasted with the essentially static perspective of thermodynamics. A kinetic system is a system in which there is unidirectional movement toward thermodynamic equilibrium. The chemical composition of a closed system in which a reaction is occurring evolves as time elapses. A system that is in thermodynamic equilibrium, on the other hand, undergoes no net change with time. The thermodynamicist is interested only in the initial and final states of the system and is not concerned with the time required for the transition or the molecular processes involved therein the chemical kineticist is concerned primarily with these issues. 

However, dielectric solvation models do suffer from a too simple description of the solute-solvent interactions, and also from a static vision of the solvated system, which is supposed to be at thermodynamic equilibrium. A step forward was done after the publication in 1990 of a paper by Field et al. [19] on the QM/MM model, which was an extension of the seminal work reported by Warshel and Levitt in 1976 [20] (the acronym QM/MM stands for Quanmm Mechanics/Molecular Mechanics). The QM/MM model was initially developed to carry out Molecular Dynamics (MD) simulations of large molecules such as proteins using a semi-empirical description of the active site. But extension to first-principles studies of ions and molecules in solution [21-23] was reported soon after Karplus work and algorithms to simulate chemical reaction trajectories and analyze non-equilibrium effects in solution based on a rare event sampling approach were developed [24, 25]. 

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