Reaction, affinity entropy

Entropy production per unit volume in terms of reaction affinities is... 

Since the reactions at the electrodes may occur at different electrical potentials, we must use the electrochemical affinity to formulate the thermodynamics of an electrochemical cell. If A is the electrochemical affinity and is the extent of reaction, the entropy production is... 

Let us now calculate the excess entropy production for the autocatalytic reaction. The chemical reaction affinity becomes... 

Although the occurrence or nonoccurrence of the proton transfer depends, at any given temperature, on the relative gas-phase basicity values, rather than the proton affinities, entropy changes associated with Equation [8] are typically (although not always) small, and proton affinities are, in practice, often consulted to predict the occurrence or nonoccurrence of particular proton transfer reactions. 

We have already seen in Section 4.2 that, in the case of a chemical reaction, the entropy production, which is zero at equilibrium, can be described at nonequilibrium as a product of the driving force (affinity A), which we will regard in what follows as being given, and the corresponding rate (reaction rate U). This can be generalized for different processes (k) to... 

This behaviour, since it corresponds to the second law, can be put more clearly in thermodynamic language (Chapter 4) [512]. At electrochemical equihbrium (open circuit, no internal fluxes) the equihbrimn voltage E just compensates the reaction affinity (see Section 4.2). The actual driving force for current flow is the electrochemical affinity A = —AG, which represents the deviation from electrochemical equilibrium. It is obtained, accordingly, from the difference between the chemical affinity and the voltage multiphed ly the charge transferred, and is thus proportional to E — U = —7. The entropy production (cf. Section 6.1) then is II = AR. oc /I > 0. This no longer applies in the same manner when permeation cells are concerned (cf. Section 7.2.2) since short ircuit currents occur (II 0), which do not manifest themselves in an external current (1=0). 

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.

Since practically the same protoljrtic reaction takes place for all aromatic substances, it may be assumed that the reaction entropy is largely independent of the structure of the aromatic substance itself. If, however, several points of identical proton affinity are present, then AO will contain an entropy contribution which depends on z. This contribution is given by RT. Inz, so that one obtains the relation... 

CHEMICAL AFFINITY. The entropy production due to a chemical reaction has the form... 

Early chemists thought that the beat of reaction, —AH. should be a measure of the "chemical affinity" of a reaction. With the introduction of the concepl of netropy (q.v.) and ihe application of the second law of thermodynamics lo chemical equilibria, it is easily shown that the true measure of chemical affinity and Ihe driving force for a reaction occurring at constant temperature and pressure is -AG. where AG represents the change in thermodynamic slate function, G. called Gibbs free energy or free enthalpy, and defined as the enthalpy, H, minus the entropy. S. times the temperature, T (G = H — TS). For a chemical reaction at constant pressure and temperature ... 

Horiuti Nakamura [75] have considered the possibility that there may be more than one set of stoicheiometric numbers leading to an overall reaction between the species s s. They find that the number of such reaction routes is the row nullity of the matrix [a ]. Nakamura has also considered the affinity of the overall reaction near equilibrium [79] and with Yamazaki [20] has related this to the theorem of minimum entropy production. 

As we stated earlier, diS > 0. Generalizing the concept of affinity of chemical reactions, the rate of entropy production can be written as7... 

From the temperature dependence of the equilibrium constant for proton exchange between some deuterated and undeuterated primary and secondary amines, monitored by high-pressure mass spectrometry, the reaction enthalpy, or difference in proton affinity, could be measured.101 Protonation of the deuterated amine is favored by 0.2kcalmol-1, varying with structure by 0.1 kcal mol-1 but with no obvious pattern. However, the equilibrium, at least for CH3CD2NHCH3, appears to be entropy driven, not enthalpy. 

In these calculations, the electron affinity of the methyl radical has been taken1 as 27 kcal.mole-1. The other enthalpy terms are all well-known quantities the enthalpies of hydration of individual ions have been assigned as done by Valis ev (see ref. 2) and the enthalpy of hydration of the gaseous methyl anion has been taken as that of the bromide ion. It can be seen from Table 1 that not only is the formation of the methyl anion energetically very unfavoured in the gas phase, but it is also endothermic to the extent of 54 kcal.mole-1 in aqueous solution. A check on this final result can be made by consideration of the standard entropy change for the reaction... 

If the reactions are independent, each term in the sum must be positive. However, if the reactions are coupled, most simply by having reactants and products in common, only the total entropy generation must be positive. Thus, as is well known in biochemical systems, it is possible for reactions with negative affinity (positive free-energy change) to be driven to products by reactions with positive affinity. 

A second qualification is that the OSPE parameter, as well as the CFSE(crystal glass) difference parameters, eq. (8.11), are enthalpy terms and as such cannot be used to determine the affinity of a reaction. Free energy changes must be considered. However, since entropy changes are expected to be similar for all transition metal ions of the same valency, the use of an enthalpy term such as CFSE to interpret element fractionation may be a valid approximation when comparisons are made between transition metal ions of similar radius and charge. 

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