Reactions far from equilibrium

Many examples of post-critical organization in the form of dissipative structures have been recognized, but a detailed analysis of transition through a critical point has never been achieved. A theory of chemical reaction far from equilibrium, therefore is a long way off, but some progress has been made towards the understanding of critical phenomena associated with phase transformation. 

TNC. 18. R. Lefever, G. Nicolis and I. Prigogine, On the occurrence of oscillations around the steady state in systems of chemical reactions far from equilibrium, J. Chem. Phys. 47, 1045-1047 (1967). 

A continuation of this application of the second-law analyses is an examination of the various irreversibilities in the reformer process for potential improvements. The chief sources of thermodynamic irreversibilities (with the associated exergy destruction) are (1) frictional losses, (2) heat transfer with a finite temperature difference, (3) chemical reaction far from equilibrium, and (4) diffusion. 

Example 8.9 Chemical reactions far from global equilibrium Consider the following chemical reaction far from equilibrium ... 

As the above equation shows, the network structure relates the relaxation time to capacity C and resistance R, which is similar to what occurs in electrical circuits, and also provides information on any reaction far from equilibrium. 

Experimental. We studied the dissolution of semi-optical grade crystals of Iceland spar (44.5 cm g and 96.5 cm g ) in dilute solutions as a function of pH, PCO2 and temperature. The pH-stat method was used to identify forward reactions far from equilibrium (in the near absence of backward reaction). The "free drift" method was used to study the reaction near equilibrium where both forward and backward rates must be considered. Details of the experimental procedures are given elsewhere ( ). 

As before, the forward rate of the reaction (far from equilibrium) can be expressed in terms of the rate-determining step ... 

Formulation of Eq. 9 is consistent with transition-state theory, where the rate of the reaction far from equilibrium depends solely on the activity of the activated transition-state complex (Wieland et al., 1988). Equations 8 and 9 are equivalent to Eq. 2 for proton attack, where C, is equal to the surface concentration of activated complex. 

The rate of a reaction depends on the concentrations of the reactants. In reactions far from equilibrium, it is often found that the rate of increase of the concentration of a product, or the rate of decrease of the concentration of a reactant, is closely proportional to the product of some integral powers of the concentrations of all or some of the reactants. This product of concentrations can include that of a catalyst. 

Thus, the mechanism of catalytic processes near and far from the equilibrium of the reaction can differ. In general, linear models are valid only within a narrow range of (boundary) conditions near equilibrium. The rate constants, as functions of the concentration of the reactants and temperature, found near the equilibrium may be unsuitable for the description of the reaction far from equilibrium. The coverage of adsorbed species substantially affects the properties of a catalytic surface. The multiplicity of steady states, their stability, the ordering of adsorbed species, and catalyst surface reconstruction under the influence of adsorbed species also depend on the surface coverage. Non-linear phenomena at the atomic-molecular level strongly affect the rate and selectivity of a heterogeneous catalytic reaction. For the two-step sequence (eq.7.87) when step 1 is considered to be reversible and step 2 is in quasi-equilibria, it can be demonstrated for ideal surfaces that... 

Regulation occurs at the three reactions far from equilibrium... 

Remember that at equilibrium the rates of forward and reverse reactions are equal. Therefore, the conversion of, for example, 3-phosphoglycerate to glyceraldehyde-3-phosphate occurs rapidly. In contrast, the reactions far from equilibrium, such as the conversion of phosphoenol pymvate to pymvate, have rates that are greater in the forward than in the reverse direction. Imagine a series of pools in a fountain. If two pools are at the same level, there is no point in putting a dam between them to control the flow of water. On the other hand, the rate of water flow can be controlled effectively at any point where one pool spills into a lower one. Think of the compounds in the free energy... 

Blomberg, C. (1981). Some properties of stochastic equations for coupled chemical reactions far from equilibrium. J. Stat. Phys., 25, 73-109. 

A chemical reaction is normally not described by the linear relation in the third line of eq 14.17. The rate is a non-linear function of hfijT on the macroscopic level, and the law of mass action is used. We explain in subsection 14.3.3 how chemical reactions far from equilibrium also can be included into the scheme of non-equilibrium thermodynamics, cf. also point e of section 14.1.1. 

Consider a simple reaction far from equilibrium where the back reactions of products yielding reactants can be neglected. In many cases this assumption is not too restrictive because the equilibrium is shifted towards the products to such an extent that the back reaction is insignificant even atJbigh conversions. 

According to Eq. (1.2) the rate of a simple reaction far from equilibrium can be written as dcs... 

For a system far from equilibrium, if the reverse reaction follows a distinct mechanism from the forward one, common sense tells us that the ratio of concentrations will be different from that given by the rate laws and the equilibrium constant. The mechanisms of reaction in the forward and reverse directions can only be assumed to be the same close to equilibrium. From the above, it is clear that both the rate laws for the reaction must be obtained experimentally. The relationship between the rate laws for reactions far from equilibrium is only equal to the equilibrium constant for elementary reactions, or for systems where the forward and reverse reactions have the same rate-determining step. 

For the rate of adsorption, we are within the fiamewoik of the dissociative adsorption of Langmuir on identical sites, and the rate is thus given by equation [6.12]. Very frequently, we will use this relationship in reactions far from equilibrium and for the low levels of coverage 6 . The rate then takes the simple form ... 

When we look at the various results obtained for the reactivities in pure modes of adsorption or interface reactions far from equilibrium, we note ... 

If we now consider the case of a reaction scheme in the pseudo-steady state mode but with no rate-determining step, such as a chain reaction far from equilibrium, the quantum yield will be high and the speed will obey a law given by the complex application of Arrhenius law at every stage. 

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