Chemical equilibrium general condition

A system that undergoes no net chemical changes over time is said to be in chemical equilibrium. Generally, this condition occurs when the forward and reverse rates of the chemical reactions taking place in a system are equal. Common phenomena, including many phenomena associated with living organisms, can be analyzed in terms of this concept of chemical equilibrium. Several examples are presented below. 

Equation (5.59) is the starting point for deriving the condition for chemical equilibrium. We have written a generalized chemical reaction as... 

In general, the first derivative of the Gibbs energy is sufficient to determine the conditions of equilibrium. To examine the stability of a chemical equilibrium, such as the one described above, higher order derivatives of G are needed. We will see in the following that the Gibbs energy versus the potential variable must be upwards convex for a stable equilibrium. Unstable equilibria, on the other hand, are... 

Let us start by giving a brief introduction into the general method of constructing mixed phases by imposing the Gibbs conditions of equilibrium [23, 18]. From the physical point of view, the Gibbs conditions enforce the mechanical as well as chemical equilibrium between different components of a mixed phase. This is achieved by requiring that the pressure of different components inside the mixed phase are equal, and that the chemical potentials (p and ne) are the same across the whole mixed phase. For example, in relation... 

Figure 20.5 Physical processes at the air-water interface. For calm (smooth) surfaces the horizontal velocities on both sides of the interface decrease toward the boundary. The turbulent eddies become smaller and disappear completely at the interface (boundary layer characteristics). For rough conditions new surfaces are continuously formed by breaking waves, by air bubbles entrapped in the water, and by water droplets ejected into the air. Generally, these surfaces do not last long enough to reach chemical equilibrium between air and water phase.

The oxidation of sulphur dioxide to trioxide is one of the oldest heterogeneous catalytic processes. The classic catalyst based on V2Os has therefore been the subject of numerous investigations which are amply reviewed by Weychert and Urbaneck [346]. These authors conclude that none of the 34 rate equations reported is applicable over a wide range of process conditions. Generally, these equations have the form of a power expression, in which the reverse reaction is taken into account within the limits imposed by chemical equilibrium, viz. 

However, these potentials do not yet express the second law in the form most convenient for chemical applications. Open laboratory vessels exposed to the temperature and pressure of the surroundings are subject neither to constraints of isolation (as required for entropy maximization) nor to adiabatic constant-volume conditions (as required for energy minimization). Hence, we seek alternative thermodynamic potentials that express the criteria for equilibrium under more general conditions. 

The number of independent components, c, in a given system of interest can generally be evaluated as the total number of chemical species minus the number of relationships between concentrations. The latter may consist of initial conditions (defined by conditions of preparation of the system) or by chemical equilibrium conditions (for chemical reactions that are active in the actual system). Sidebar 7.1 provides illustrative examples of how c is determined in representative cases. 

The underlying idea is the restorative tendency of equilibrium, tending to counteract the effects of attempted changes on an original equilibrium system. This restorative tendency is associated with the stability of chemical equilibrium, and we therefore use the rigorous stability condition (8.13) to prove the above statement of Le Chatelier s principle in a general form. 

The stoichiometric coefficients i9, are positive for products and negative for reactants. The Gibbs energy of the system of products and reactants must be minimal at equilibrium. If this condition is combined with the mass balance that is imposed by eq.(2.4-3) we get the general thermodynamic condition for chemical equilibrium ... 

The calculation of the equilibrium conversion of heterogeneous reactions is in most cases much more complicated then in the case of homogeneous reactions, because the calculations involve in general the solution of the conditions for chemical equilibrium and the conditions for phase equilibrium. In the following a relatively simple example is given. 

The general relationships involved for a single chemical reaction in a closed system are shown schematically in Figure 1, where the degree of advancement at point e corresponds to chemical equilibrium. Point t represents a state of the system corresponding to spontaneous chemical reaction. While the invariant condition of the closed system considered is the equilibrium state, e, this generally is not the case for a thermodynamic system open to its environment. For such a system, the time-... 

Since natural waters are generally in a dynamic rather than an equilibrium condition, even the concept of a single oxidation-reduction potential characteristic of the aqueous system cannot be maintained. At best, measurement can reveal an Eh value applicable to a particular system or systems in partial chemical equilibrium and then only if the systems are electrochemically reversible at the electrode surface at a rate that is rapid compared with the electron drain or supply by way of the measuring electrode. Electrochemical reversibility can be characterized... 

This is the general condition of the equilibrium partitioning process. As we show later, it applies to both electrically neutral and electrically charged species. The chemical potential of species X in a phase (gas, solid, or solution) is (c.f. (A. 16), (A. 19), and (A.25))... 

Because dc may be brought outside the summation sign and is not zero, this gives as the general condition for chemical equilibrium ... 

From these considerations, it follows that in the case of formation of the layer of a chemical compound under conditions of simultaneous dissolution of a solid in a liquid, the shape of the layer thickness-time dependence is rather complicated. An evolution of this dependence in the course of interaction of initial substances from the moment of their contact to the establishment of equilibrium in the A-B system will now be analysed in its most general features. It should be noted that the time of wetting the solid surface by the liquid phase will not be taken into account, i.e. this process is assumed to be instantaneous. 

The phase rule of Josiah Willard Gibbs (1839-1903) gives the general conditions for chemical equilibrium between phases in a system. At equilibrium, AG = 0, there is no further change with time in any of the system s macroscopic properties. It is assumed that surface, magnetic, and electrical forces may be neglected. In this case, the phase rule can be written as... 

Near-equilibrium flow conditions generally yield the maximum thrust for rocket propulsion, because partial recombination of the dissociated atoms, as the temperature falls, releases additional kinetic energy. On the other hand, when the rocket engine is considered for high temperature chemical processing, it is invariably desirable to freeze the composition attained in the combustion chamber. From both theoretical and practical standpoints, it is not always possible to predetermine the flow conditions in the De Laval nozzle as the foregoing discussion indicates,... 

In Section A.l, the general laws of thermodynamics are stated. The results of statistical mechanics of ideal gases are summarized in Section A.2. Chemical equilibrium conditions for phase transitions and for reactions in gases (real and ideal) and in condensed phases (real and ideal) are derived in Section A.3, where methods for computing equilibrium compositions are indicated. In Section A.4 heats of reaction are defined, methods for obtaining heats of reaction are outlined, and adiabatic flame-temperature calculations are discussed. In the final section (Section A.5), which is concerned with condensed phases, the phase rule is derived, dependences of the vapor pressure and of the boiling point on composition in binary mixtures are analyzed, and properties related to osmotic pressure are discussed. 

Although conventional derivations of the conditions for chemical equilibrium sometimes are restricted to isothermal, isobaric processes (possibly because often dT = 0 and dp = 0 in experimental equilibrium determinations), the general equilibrium conditions do not depend on these assumptions, as will be seen from the following development. By substituting equation (1) into equation (2) and using equation (3) to eliminate dU from the resulting expression, we find that... 

In this section, we discuss the general problem of chemical equilibrium under the assumption that the system considered is guaranteed to exist in a one-phase (homogeneous) condition at all possible compositions. We initially follow the logical approach discussed in Chapter 3 of Astarita (1989a), and we are therefore very concise in the first subsection, referring the reader to that work for details. 

There remains one problem, that of applying the conditions of equilibrium just found to the phenomena ot equilibrium treated in the first section especially in the more complex cases last dealt with, that three or four substances take part in the equilibrium. Since the treatment for the case of three substances is contained in the lectures on the formation and dissociation of double salts, which have been published separately b we will here discuss only the case of chemical equilibrium between four substances, in connexion with the former example of two salts which sufier double decomposition. We may then generalize the results of the particular case in Lowenherz s... 

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