Affinity and the progress variable

Consider the two-component system Nj-Hj. Components N2 and H2 refer to the result you would get if you analyzed the system for total nitrogen and total hydrogen. The actual molecular form taken by each element in the system is irrelevant. However, Nj and H2 might also refer to the species in the system, i.e., diatomic nitrogen molecules and diatomic hydrogen molecules. In real systems, species N2 and Hj combine to form ammonia. 

However, the equation can also be used with i representing some or all of the species in the system, rather than independent components, as long as the species are related to one another in balanced chemical reactions, such that the number of independent compositional parameters remains equal to c. Thus the final term on the right side of (4.65) could also read 

Changing from components to species in this way provides for some flexibility we shall take advantage of shortly. In a closed system, we cannot change the chemical potentials of components N2 and H2, and the last term in (4.65) is zero. However, the chemical potentials of the species in (18.54) can change in a closed system, if the reaction progresses to the left or the right from some metastable state towards the stable equilibrium state. The last term in (4.65) 

Considering a system at constant T and P, Equation (4.65) now shows that 

Recalling that our V are positive for products and negative for reactants, the quantity J2t Vifii is simply the difference in partial molar Gibbs energy between products and reactants. For (18.5) this is 

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We have tried to show that the affinity is a convenient representation of how far a system is from stable equilibrium, and increments in the progress variable allows us to consider the system at various stages as it progresses towards stable equilibrium. This progress is a part of the model we call a quasistatic reaction—a continuous succession of metastable equilibrium states in an overall irreversible reaction. 

The chemical work term that we mentioned in 3.4.1 is -Ad, where A is the affinity and is the progress variable, resulting in... 

Electronic factors and the relative lipophilicity of the molecule probably help to determine the affinity of the substrate for the enzyme as well as turnover properties. It is likely that the fundamental instability of the enzyme has hampered progress in the characterization of human liver aldehyde oxidase. At least in animals, the specific activity of the enzyme is quite dependent on the way the tissue is procured, processed, and stored this may lead to considerable intersample variability. Enzyme instability may at least in part explain why aldehyde oxidase activity from different species is so variable (Duley et al. 1985). However, it is likely that in addition to intrinsic differences in stability, the determination of aldehyde oxidase activity for a given substrate in various tissue preparations is dependent on the analytical methodology employed to assay the enzyme and the likelihood of the presence of different forms of the enzyme that possess distinct substrate specificity and kinetic properties (Johns 1967 Beedham 1985). For example, in the... 

The second and third groups include slow chemical processes, for which the relaxation time is significantly different from 0 (At > 0). Over the time At values of chemical affinity A., saturation index SI. and rate of reaction tend to 0. That is why the considered closed models of mass transfer may be considered titration models, in which added portions of minerals sequentially lower values A., SI. or A. (equation (1.112)). Usually in a study of interaction between water and rock the researcher uses the overall progress variable of mass transfer (equation (2.256)), which in the course of computation sequentially lowered to 0. 

In systems having several simultaneous reactions, affinities and progress variables for each reaction as well as for the whole system may be calculated. Unfortunately, affinities of individual reactions in such systems are not related in any simple way to the order in which those reactions will reach equilibrium, due to the effects of reaction coupling (Helgeson, 1979). Similarly, although the affinity is commonly used in theoretical expressions for reaction rate constants, it is never the only determining factor. Nevertheless, it is always a central concept in thinking about irreversible processes. 

For chemists, the problem of affinity, or what Meyer called variable valence, was the central problem of chemistry, one in which, Ostwald claimed, chemists made no progress while seeking to measure chemical "forces." Meyer, who often is identified with the tradition of physical chemistry and theoretical chemistry, as noted in chapter 3, was confident that the answer to affinity lay in theories of motion, not in species or types, just as Nemst later was to identify the end of affinity theory with its reduction to physical causes. 

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