Equilibrium position A particular set

Equilibrium position a particular set of equilibrium concentrations of all reactants and products in a chemical system. 

For each reaction system at a given temperature, there is only one value for the equilibrium constant, but there are an infinite number of possible equilibrium positions. An equilibrium position is defined as a particular set of equilibrium concentrations that... 

Whatever the aim of a particular titration, the computation of the position of a chemical equilibrium for a set of initial conditions (e.g. total concentrations) and equilibrium constants, is the crucial part. The complexity ranges from simple 1 1 interactions to the analysis of solution equilibria between several components (usually Lewis acids and bases) to form any number of species (complexes). A titration is nothing but a preparation of a series of solutions with different total concentrations. This chapter covers all the requirements for the modelling of titrations of any complexity. Model-based analysis of titration curves is discussed in the next chapter. The equilibrium computations introduced here are the innermost functions required by the fitting algorithms. 

AG, is directly associated with the direction in which a particular chemical reaction can proceed. If AG < 0 for a given set of conditions of a particular reaction, then the reaction will proceed spontaneously in the indicated direction until equilibrium is reached. Conversely, if AG is positive, then energy will be needed to shift the reaction further from its equilibrium condition. See Helmholtz Energy Endergonic Exergonic Enthalpy Entropy Thermodynamics Biochemical Thermodynamics... 

Each set of equilibrium concentrations is called an equilibrium position. It is essential to distinguish between the equilibrium constant and the equilibrium positions for a given reaction system. There is only one equilibrium constant for a particular system at a particular temperature, but there are an infinite number of equilibrium positions. The specific equilibrium position adopted by a system depends on the initial concentrations, but the equilibrium constant does not. 

Therefore, although the value of AG for a given reaction system tells us whether the products or reactants are favored under a given set of conditions, it does not mean that the system will proceed to pure products (if AG is negative) or remain at pure reactants (if AG is positive). Instead, the system will spontaneously go to the equilibrium position, the lowest possible free energy available to it. In the next section we will see that the value of AG° for a particular reaction tells us exactly where this position will be. 

When equihbrium is established, the concentration of each substance is determined experimentally. In Table 18-1, the symbol [HlJ q represents the concentration of HI at equilibrium. Note that the equilibrium concentrations are not the same in the three trials, yet when each set of equilibrium concentrations is put into the equilihrium constant expression, the value of S gq is the same. Each set of equilibrium concentrations represents an equihbrium position. Although an equilibrium system has only one value for at a particular temperature, it has an unlimited number of equilibrium positions. Equilibrium positions depend upon the initial concentrations of the reactants and products. 

Consider an equilibrium thennodynamic ensemble, say a set of atomic systems characterized by the macroscopic variables T (temperature), Q (volume), andTV (number of particles). Each system in this ensemble contains N atoms whose positions and momenta are assigned according to the distribution function (5.2) subjected to the volume restriction. At some given time each system in this ensemble is in a particular microscopic state that coiTesponds to a point (r, p- ) in phase space. As the system evolves in time such a point moves according to the Newton equations of motion, defining what we call a phase space trajectory (see Section 1.2.2). The ensemble coiTesponds to a set of such trajectories, defined by their starting point and by the Newton equations. Due to the uniqueness of solutions of the Newton s equations, these trajectories do not intersect with themselves or with each other. 

The first factor is associated with the electronic dipole transition probability between the electronic states the second factor is associated between vibrational levels of the lower state v" and the excited state V, and is commonly known as the Franck-Condon factor, the third factor stems from the rotational levels involved in the transition, J" and /, the rotational line-strength factor (often termed the Honl-London factor). In particular, the Franck-Condon information from the spectrum allows one to gain access to the relative equilibrium positions of the molecular energy potentials. Then, with a full set of the spectroscopic constants that are used to approximate the energy-level structure (see Equations (2.1) and (2.2)) and which can be extracted from the spectra, full potential energy curves can be constructed. 

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