Reversibility in Chemical Reactions

open access bookIn this chapter we give an overview of techniques for the modelling and reasoning about reversibility of systems, including outof- causal-order reversibility, as it appears in chemical reactions. We consider the autoprotolysis of water reaction, and model it with the Calculus of Covalent Bonding, the Bonding Calculus, and Reversing Petri Nets. This exercise demonstrates that the formalisms, developed for expressing advanced forms of reversibility, are able to model autoprotolysis of water very accurately. Characteristics and expressiveness of the three formalisms are discussed and illustrated

Numerical calculation of simultaneous mass transfer of two gases accompanied by complex reversible reactions

A discretization technique is described, which makes it possible to calculate numerically mass transfer behaviour between two media in which complex chemical reactions occur. To show the stability of the technique it has been applied to the industrially well-known system of simultaneous absorption or desorption of H2S and CO2 to or from an amine solution, accompanied by simultaneously occurring strongly interfering overall chemical reaction(s) of complex, non elementary kinetics. For previously published limit cases of the transfer system considered, i.e. for the single transfer of H2S or CO2 accompanied by reversible chemical reaction, a comparison has been made with analytical and approximate solutions of previous authors. The agreement is very good. In studying simultaneous transfer of H2S and CO2, on which hardly any previous work was available, special attention has been paid to the effects of the reversibility of the reactions involved. It has been shown how, under certain conditions due to reversibility occurring in the transferzone, desorption takes place though absorption would be expected on basis of the driving forces. This revealed that not only enhancement factors larger than unity but also smaller, even negative values are possible

Reversibility and Non-reversibility in Stochastic Chemical Kinetics

Mathematical problems with mean field and local type interaction related to stochastic chemical kinetics,are considered. Our main concern various definitions of reversibility, their corollaries (Boltzmann type equations, fluctuations, Onsager relations, etc.) and emergence of irreversibility

Reciprocal Relations Between Kinetic Curves

We study coupled irreversible processes. For linear or linearized kinetics with microreversibility, $\dot{x}=Kx$, the kinetic operator $K$ is symmetric in the entropic inner product. This form of Onsager's reciprocal relations implies that the shift in time, $\exp (Kt)$, is also a symmetric operator. This generates the reciprocity relations between the kinetic curves. For example, for the Master equation, if we start the process from the $i$th pure state and measure the probability $p_j(t)$ of the $j$th state ($j\neq i$), and, similarly, measure $p_i(t)$ for the process, which starts at the $j$th pure state, then the ratio of these two probabilities $p_j(t)/p_i(t)$ is constant in time and coincides with the ratio of the equilibrium probabilities. We study similar and more general reciprocal relations between the kinetic curves. The experimental evidence provided as an example is from the reversible water gas shift reaction over iron oxide catalyst. The experimental data are obtained using Temporal Analysis of Products (TAP) pulse-response studies. These offer excellent confirmation within the experimental error.Comment: 6 pages, 1 figure, the final versio

A statistical mechanics description of environmental variability in metabolic networks

Many of the chemical reactions that take place within a living cell are irreversible. Due to evolutionary pressures, the number of allowable reactions within these systems are highly constrained and thus the resulting metabolic networks display considerable asymmetry. In this paper, we explore possible evolutionary factors pertaining to the reduced symmetry observed in these networks, and demonstrate the important role environmental variability plays in shaping their structural organization. Interpreting the returnability index as an equilibrium constant for a reaction network in equilibrium with a hypothetical reference system, enables us to quantify the extent to which a metabolic network is in disequilibrium. Further, by introducing a new directed centrality measure via an extension of the subgraph centrality metric to directed networks, we are able to characterise individual metabolites by their participation within metabolic pathways. To demonstrate these ideas, we study 116 metabolic networks of bacteria. In particular, we find that the equilibrium constant for the metabolic networks decreases significantly in-line with variability in bacterial habitats, supporting the view that environmental variability promotes disequilibrium within these biochemical reaction system

On the kinetics between CO2 and alkanolamines both in aqueous and non-aqueous solutions—I. Primary and secondary amines

The reaction between CO2 and primary and secondary alkanolamines (DEA and DIPA) has been studied both in aqueous and non-aqueous solutions (ethanol and n-butanol) at various temperatures. Reaction kinetics have been established by chemically enhanced mass transfer of CO2 into the various solutions. The experiments were performed in a stirred vessel operated with a horizontal interface which appeared to the eye to be completely smooth. The reaction can be described with the zwitterion-mechanism originally proposed by Caplow (1968) and reintroduced by Danckwerts (1979). Literature data on the reaction rates can be correlated fairly well with this mechanism. As all amines react with CO2 in a reversible way, and the mass transfer models used for the interpretation of the experimental data neglect this reversibility and take only the forward reaction rate into account, the influence of the reversibility is studied. With the aid of numerical mass transfer models (Versteeg et al., 1987b,c) the experimental method with its underlying assumptions have been verified and the applicability and the limits of this method were determined. Special attention has been paid to the influence of small amounts of impurities (amines) on the measured mass transfer rates. A Brønsted relationship exists between the second-order rate constant, k2, for the formation of the zwitterion and the acid dissociation constant of the alkanolamine

Symmetry relations in chemical kinetics arising from microscopic reversibility

It is shown that the kinetics of time-reversible chemical reactions having the same equilibrium constant but different initial conditions are closely related to one another by a directly measurable symmetry relation analogous to chemical detailed balance. In contrast to detailed balance, however, this relation does not require knowledge of the elementary steps that underlie the reaction, and remains valid in regimes where the concept of rate constants is ill-defined, such as at very short times and in the presence of low activation barriers. Numerical simulations of a model of isomerization in solution are provided to illustrate the symmetry under such conditions, and potential applications in protein folding-unfolding are pointed out.Comment: 4 pages, 1 figure, accepted to Phys Rev Let

The kinetics of the reaction between CO2 and diethanolamine in aqueous ethyleneglycol at 298 K: a viscous gas—liquid reaction system for the determination of interfacial areas in gas—liquid contactors

The reaction between CO2 and diethanolamine (DEA) in aqueous ethyleneglycol (ETG) at 298 K has been studied over the complete composition range. The application of this reaction as a viscous gas—liquid system for the determination of interfacial areas in gas—liquid contactors by the chemical method is discussed. The reaction kinetics have been determined by mass transfer experiments of CO2 into solutions of DEA in aqueous ETG. To this end laboratory-scale stirred cell reactors with a flat surface have been used. In accordance with the same reaction in water at 298 K the reaction between CO2 and DEA in aqueous ETG at 298 K can be described by the zwitterion mechanism of Caplow. Special attention has been paid to the reversibility of the reaction between CO2 and DEA. Calculation show that the influence of the reversibility on the mass transfer rate can be neglected for partial pressures of CO2 below 3 kPa. It is demonstrated that the reaction between CO2 and DEA in aqueous ETG can be used for the determination of interfacial areas in gas—liquid contactors at higher viscosities