Reacting Systems

Figure A2.1.9. Chemically reacting systems, (a) The entropy. S as a fiinction of the degree of advancement of the reaction at constant U and V. (b) The affinity Aas a fiinction of for the same reacting system. Equilibrium is reached at 0.623 where tiis a maxuniim and A= 0.

The Onsager regression hypothesis, stated mathematically for the chemically reacting system just described, is given in the classical limit by... 

A 3.13.7 SUMMARIZING OVERVIEW ON ENERGY REDISTRIBUTION IN REACTING SYSTEMS... 

McCullough J P and Scott D W (eds) 1968 Experimental Thermodynamics Calorimetry of Non-Reacting Systems vol I (London Butterworths)... 

Almost all aspects of the field of chemistry involve tire flow of energy eitlier witliin or between molecules. Indeed, tire occurrence of a chemical reaction between two species implies tire availability of some minimum amount of energy in tire reacting system. The study of energy transfer processes is tluis a topic of fundamental importance in chemistry. Energy transfer in gases is of particular interest partly because very sophisticated methods have been developed to study such events and partly because gas phase processes lend tliemselves to very complete and detailed tlieoretical analysis. 

Most chemically reacting systems tliat we encounter are not tliennodynamically controlled since reactions are often carried out under non-equilibrium conditions where flows of matter or energy prevent tire system from relaxing to equilibrium. Almost all biochemical reactions in living systems are of tliis type as are industrial processes carried out in open chemical reactors. In addition, tire transient dynamics of closed systems may occur on long time scales and resemble tire sustained behaviour of systems in non-equilibrium conditions. A reacting system may behave in unusual ways tliere may be more tlian one stable steady state, tire system may oscillate, sometimes witli a complicated pattern of oscillations, or even show chaotic variations of chemical concentrations. 

In spite of these limitations it is hoped that this chapter will provide an introduction to the unusual phenomena that chemically reacting systems exlribit when driven far from equilibrium and an indication of how these phenomena may be analysed. Although such systems were often regarded as curiosities in the past, it is now clear that they are the mle rather than the exception in nature and deserve our full attention. 

It appears that a loose interpretation of this type may be the origin of a discrenancy found by Otanl and Smith [59] in attempting to apply effective diffusivities from Wakao and Smith s [32] isobaric diffusion data to measurements on a chemically reacting system. This was pointed out by Steisel and Butt [60], and further pursued to the point of detailed computer modeling of a particular pore network by Wakao and Nardse [61]. 

From the third law of thermodynamics, the entiopy 5 = 0 at 0 K makes it possible to calculate S at any temperature from statistical thermodynamics within the hamionic oscillator approximation (Maczek, 1998). From this, A5 of formation can be found, leading to A/G and the equilibrium constant of any reaction at 298 K for which the algebraic sum of AyG for all of the constituents is known. A detailed knowledge of A5, which we already have, leads to /Gq at any temperature. Variation in pressure on a reacting system can also be handled by classical thermodynamic methods. 

In a Lewis-acid catalysed Diels-Alder reaction, the first step is coordination of the catalyst to a Lewis-basic site of the reactant. In a typical catalysed Diels-Alder reaction, the carbonyl oxygen of the dienophile coordinates to the Lewis acid. The most common solvents for these processes are inert apolar liquids such as dichloromethane or benzene. Protic solvents, and water in particular, are avoided because of their strong interactions wifti the catalyst and the reacting system. Interestingly, for other catalysed reactions such as hydroformylations the same solvents do not give problems. This paradox is a result of the difference in hardness of the reactants and the catalyst involved... 

The most effective Lewis-acid catalysts for the Diels-Alder reaction are hard cations. Not surprisingly, they coordinate to hard nuclei on the reacting system, typically oxygen atoms. Consequently, hard solvents are likely to affect these interactions significantly. Table 1.4 shows a selection of some solvents ranked according to their softness. Note that water is one of the hardest... 

A combination of the promoting effects of Lewis acids and water is a logical next step. However, to say the least, water has not been a very popular medium for Lewis-acid catalysed Diels-Alder reactions, which is not surprising since water molecules interact strongly with Lewis-acidic and the Lewis-basic atoms of the reacting system. In 1994, when the research described in this thesis was initiated, only one example of Lewis-acid catalysis of a Diels-Alder reaction in water was published Lubineau and co-workers employed lanthanide triflates as a catalyst for the Diels-Alder reaction of glyoxylate to a relatively unreactive diene . No comparison was made between the process in water and in organic solvents. 

The fact that good correlations are observed with d" rather than with a, is indicative of a strong infiuence of the substituent through a direct resonance interaction with a positive charge in the reacting system. The p-values are positive, which is expected for substituted dienophiles in a normal electron demand Diels-Alder reaction. Furthermore, the p-values do not exceed unity and are not significantly different from literature values reported for the uncatalysed reaction. It is tempting to... 

The observation that in the activated complex the reaction centre has lost its hydrophobic character, can have important consequences. The retro Diels-Alder reaction, for instance, will also benefit from the breakdown of the hydrophobic hydration shell during the activation process. The initial state of this reaction has a nonpolar character. Due to the principle of microscopic reversibility, the activated complex of the retro Diels-Alder reaction is identical to that of the bimoleciilar Diels-Alder reaction which means this complex has a negligible nonpolar character near the reaction centre. O nsequently, also in the activation process of the retro Diels-Alder reaction a significant breakdown of hydrophobic hydration takes placed Note that for this process the volume of activation is small, which implies that the number of water molecules involved in hydration of the reacting system does not change significantly in the activation process. 

The reaction quotient may be measured, at least in principle, for the reacting system at any time. If Z is observed not to change, the system is at equiUbrium, or trapped in a metastable state that serves as a local equiUbrium. In informal work, a time-independent Z is identified directiy with the equiUbrium constant... 

Heat transfer and mass transfer occur simultaneously whenever a transfer operation involves a change in phase or a chemical reaction. Of these two situations, only the first is considered herein because in reacting systems the complications of chemical reaction mechanisms and pathways are usually primary (see HeaT-EXCHANGETECHNOLOGy). Even in processes involving phase changes, design is frequendy based on the heat-transfer process alone mass transfer is presumed to add no compHcations. But in fact mass transfer effects do influence and can even limit the process rate. 

System instabilities involve interactions between flows in different parts of a reacting system. Although these instabilities can cause turbulence, they caimot be analy2ed on their own and the whole system should be considered as a unit (11,25). 

Any property of a reacting system that changes regularly as the reaction proceeds can be formulated as a rate equation which should be convertible to the fundamental form in terms of concentration, Eq. (7-4). Examples are the rates of change of electrical conductivity, of pH, or of optical rotation. The most common other variables are partial pressure p and mole fraction Ni. The relations between these units... 

Table 14-3 presents a typical range of values for chemically reacting systems. The first two entries in the table represent systems that can be designed by the use of purely physical design methods, for they are completely gas-phase mass-transfer limited. To ensure a negligible liquid-phase resistance in these two tests, the HCl was absorbed into a solution maintained at less than 8 percent weight HCl and the NH3 was absorbed into a water solution maintained below pH 7 by the addition of acid. The last two entries in Table 14-3 represent liquid-phase mass-transfer hmited systems. 

TABLE 14-2 Typical Effects of Packing Type, Size, and Liquid Rate on K o in a Chemically Reacting System, KgO, kmol/(h m )... 

Danckwerts and Gillham did not investigate the influence of the gas-phase resistance in their study (for some processes gas-phase resistance may be neglected). However, in 1975 Danckwerts and Alper [Trans. Tn.st. Chem. Eng., 53, 34 (1975)] showed that by placing a stirrer in the gas space of the stirred-cell laboratoiy absorber, the gas-phase mass-transfer coefficient fcc in the laboratoiy unit could be made identical to that in a packed-tower absorber. When this was done, laboratoiy data obtained for chemically reacting systems having a significant gas-side resistance coiild successfully be sc ed up to predict the performance of a commercial packed-tower absorber. 

There are a number of different types of experimental laboratory units that could be used to develop design data for chemically reacting systems. Charpentier [ACS Symp. Sen, 72, 223-261 (1978)] has summarized the state of the art with respect to methods of scaUng up lab-oratoiy data and tabulated typical values of the mass-transfer coefficients, interfacial areas, and contact times to be found in various commercial gas absorbers as well as in currently available laboratoiy units. 

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