Chemical equilibrium states

As defined in Eq. (2.12), the equilibrium constants for each chemical equilibrium state are given as ... 

There are fundamental aspects of a chemical equilibrium state ... 

Equation (1.38), which is called, in a most strict sense, the law of mass action, is very useful for the consideration of chemical equilibrium. In the chemical equilibrium state AG = 0 in eqn (1.36), we therefore get... 

These rigorous constraints apply to all reactions in closed vessels (those which do not exchange material with the surroundings). When we recognize the special nature of the chemical equilibrium state, it is perhaps not so surprising that if a reaction can be studied under other circumstances, away from these conditions, a much wider range of behaviour becomes possible. 

These have only one true stationary-state solution, ass = pss = 0 (as t - go), corresponding to complete conversion of the initial reactant to the final product C. This stationary or chemical equilibrium state is a stable node as required by thermodynamics, but of course that tells us nothing about how the system evolves in time. If e is sufficiently small, we may hope that the concentrations of the intermediates will follow pseudo-stationary-state histories which we can identify with the results of the previous sections. In particular we may obtain a guide to the kinetics simply by replacing p by p0e et wherever it occurs in the stationary-state and Hopf formulae. Thus at any time t the dimensionless concentrations a and p would be related to the initial precursor concentration by... 

Intuitively, the uniqueness of the chemical equilibrium state of a mixture of reacting gases is more or less obvious. However, it may be of some interest to rigorously prove that the system of equations of the law of mass action (LMA), together with the imposed conditions of conservation of matter for given T and v or T and p, has one and only one real-valued and positive solution. 

Chemical equilibrium state corresponds to the minimum value of the Gibbs free energy. Hence, the chemical equilibrium composition and the reaction direction can be predicted from the dependence of the Gibbs free energy on the reaction extend. For the reaction... 

Consider a simple system 1 consisting of n components and subject to r chemical reaction mechanisms, and having specified values U of energy, V of volume, and values of V, As,. Ay of the amounts of components that are obtained from given values Nla, N2a,Nar. Such a system permits a very large number of states. But the second law requires that among all these states, the chemical equilibrium state is the only stable equilibrium state. In this state, we have... 

Therefore, at equilibrium A, = 0. Equation (8.97) shows that during the time evolution, the surrogate system 2 proceeds through stable equilibrium states, and system 1 proceeds through states Xs. This condition is stated without any reference to microscopic reversibility, and applies for all values of X, which represent both the chemical equilibrium and nonequilibrium states. We can expand each of the r reactions into a Taylor series around the chemical equilibrium state at which X = 0... 

For small values of X (near chemical equilibrium state), the linear term predominates in Eq. (8.40), and the entropy production becomes... 

Therefore, A and. /r must have the same sign. In the chemical equilibrium state, we have A = 0. 

Thermodynamic analyses, in the form of calculations of chemical equilibrium state, have been done for many CVD systems. However, they require data on the enthalpy, entropy and heat capacity for all molecules to be considered, and such data are not always available, especially for the newer CVD precursors. Constraints can be imposed on equilibrium calculations as a way... 

What state is called that of chemical equilibrium and why is it dynamic What factors shift chemical equilibrium State the le Chate-lier principle. 

In this method the chemical equilibrium state is defined by the chemical equilibrium constant [10]. The chemical equilibrium constants can be derived from (6.48) provided that appropriate expressions are introduced for the chemical potential. A change in chemical potential for an isothermal process is related to a change in the fugacity of the species [13] ... 

A mathematical model may be constructed representing a chemical reaction. Solutions of the mathematical model must be compatible with the observed behavior of this chemical reaction. Furthermore if some other solutions would indicate possible behaviors so far unobserved, of the reaction, experiments maybe designed to experimentally observe them, thus to reinforce the validity of the mathematical model. Dynamical systems such as reactions are modelled by differential equations. The chemical equilibrium states are the stable singular solutions of the mathematical model consisting of a set of differential equations. Depending on the format of these equations solutions vary in a number of possible ways. In addition to these stable singular solutions periodic solutions also appear. Although there are various kinds of oscillatory behavior observed in reactions, these periodic solutions correspond to only some of these oscillations. 

The chemical species of the products are all in the chemical equilibrium state as... 

This equation is equivalent to Eq. 13.1-2 and can be used in the prediction of the chemical equilibrium state, provided that we can calculate a value for the equilibrium constant Ka and the species activities Oi. 

In flow reactors there is a continuous exchange of matter due to the inflow and outflow. The species concentrations do not now attain the thermod5mamic chemical equilibrium state— the system now has steady states which constitute a balance between the reaction rates and the flow rates. The steady-state concentrations (and temperature if the reaction is exo/endothermic) depend on the operating conditions through experimental parameters such as the flow rate. A plot of this dependence gives the steady-state locus, see figure A3.14.3. With feedback reactions, this locus may fold back on itself, the fold points corresponding to critical conditions... 

The distinction between chemical kinetics and equilibria can be elearly seen with the evolution of cluster ions. The dissociation processes of cluster ions discussed in Figure 10.5 and Figure 10.6 are typical chemical kinetic problems because the trapped cluster ions can only undergo dissociation of solvated molecules. To reach a chemical equilibrium state, the association of solvent molecules must occurs in the reverse elementary reaction to dissociation. 

These audiences will, during their undergraduate degree, have received a grounding in general thermodynamics and chemical thermodynamics, which all science students are normally taught, and will therefore be familiar with the fundamentals, such as the principles and the basic functions of thermodynamics, and the handling of phase and chemical equilibrium states, essentially in an ideal medium, usually for fluid phases, in the absence of electrical fields and independently of any surface effects. 

By its very nature the essentiai features of a physical or chemical equilibrium state are at a sub-microscopic level beyond our sight. In order to make sense of what we understand is happening at this level it is often necessary to use analogies or thought experiments to create mental pictures of what is occurring in these situations. 

The graph zone represented in Fig. 2.12 shows that the kinetic curve of the source reactant has a characteristic feature in the course of time the concentration becomes time-constant. We met the similar curve behaviour when analyzing reversible reactions however, in this case, stabilization of the concentration with time is not related to establishing the chemical equilibrium state. In the case under consideration, we have a steady-state regime of the process, a state when a reactant loss because of proceeding a reaction is precisely compensated by its gain at the expense of feed of new reactant portions to a reactor. The expression for the steady-state concentration of substance A is easily reduced by equating the derivative in (2.7) to zero... 

The purpose of modeling liquid solutions is to understand the strueture and the properties of the medium, and to help predict certain behaviors by giving expressions for the molar Gibbs energies or activity coefficients. These data can then be used in practical applications such as the establishing of chemical equilibrium states or the plotting of phase diagrams. 

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