Ideal systems affinity

The forces can be controlled in various ways to find a proper pathway leading to quasi-linear force-flow relationships so that the theory of linear nonequilibrium thermodynamics can be applied. For a first-order reaction S -> P, doubling the concentrations of S and P will double the reaction rate for an ideal system, although the affinity remains the same, and a distinction must be made between thermodynamic and kinetic linearity. Proper pathways are associated with thermodynamic linearity. The rate of a process depends not only on the force but also on the reference state the flow of a solute across a membrane depends on its chemical potential and on its thermodynamic state on both sides of the membrane. 

We now extend the above results to an ideal system of cj) phases. Using equations (6.69) and (7.3) we have for the affinity of a reaction taking place in the ideal system... 

Equation (7.80) holds whether a system is ideal or not, for the standard affinity of a reaction in a non-ideal system is the same as that in the corresponding reference system. 

Equation (10.40) will be recognized as the general form for the affinity of reaction in an ideal system. 

The solution-difTusion model is valid only in strictly ideal systems, namely when dealing with solutions of infinite dilution. As soon as one departs from such ideal solutions, it becomes to some extent subjective what can still be considered as almost ideal and highly dilute . For the pervaporation of isobutyl alcohol, for example, a feed concentration of 50 mg kg would lead to a membrane surface concentration of 50 mg kg (according to the sorption coefficient listed in Table 3.6-2). For the same feed concentration, ethyl hexanoate would yield a membrane surface concentration about 240 times higher, namely 12 g kg which may not be considered ideal anymore. The stronger the (desired) solute-polymer affinity, the more pronounced can be the non-ideal phenomena, with the most relevant being discussed below. 

It will be clear that all systems having a negative heat of absorption (generally those having a smaller affinity than the ideal system), will also yield sorption isotherms convex to the pressure axis. Curves concave to the pressure axis hence indicate an affinity sensibly larger than that of the ideal system. 

For a reaction I sS i pP, the affinity is A = ytis — Mp- After substituting the chemical potentials of the substrate and product in an ideal system, = jx° + nc, where (f is any reference state, or the component compositions in the form (Sieniutycz, 2004)... 

In addition to stabilizing lower oxidation states, crown thioethers can also be used to manipulate the coordination geometry of a metal ion. The elegant work of Rorabacher, Ochrymowycz, and coworkers demonstrates the use of closely related crown thioethers to study how coordinative plasticity affects the thermodynamics and kinetics of electron transfer [149,170], The same approach could be used with equal profit on fundamental studies on the interrelation of ligand conformation and binding affinity. The importance of such studies transcends crown thioether chemistry, which merely provides ideal systems in which to work out the requisite concepts. 

---