Reaction affinities

Although from the thermodynamic point of view one can speak only about the reversibility of a process (cf. Section 3.1.4), in electrochemistry the term reversible electrode has come to stay. By this term we understand an electrode at which the equilibrium of a given reversible process is established with a rate satisfying the requirements of a given application. If equilibrium is established slowly between the metal and the solution, or is not established at all in the given time period, the electrode will in practice not attain a defined potential and cannot be used to measure individual thermodynamic quantities such as the reaction affinity, ion activity in solution, etc. A special case that is encountered most often is that of electrodes exhibiting a mixed potential, where the measured potential depends on the kinetics of several electrode reactions (see Section 5.8.4). 

This partial differential is called the reaction affinity in older texts and in newer texts is called the reaction free energy. 

In Eqn. 7-9 A and A are defined as the forward and the backward reaction affinities, respectively. A corresponds to the energy (fiee enthalpy) of the reactant particles and A corresponds to the energy (fioe enthalpy) of the product particles as shown in Eqn. 7-10 ... 

In general, the forward and backward reaction affinities A and A are directly related to the forward and backward reaction rates, respectively. 

This equation indicates that the reaction rate is proportional to the reaction affinity A near the equilibrimn (Alinear kinetics similar to Ohm s law in the electric current versus voltage relationship. 

Fig. 7-S. Reaction rate as a function of reaction affinity curve (a) = regime of linear kinetics near reaction equilibrium curve (b) = regime of nonlinear exponential kinetics away from reaction equilibrium v = reaction rate A= affinity.

Further, the overall reaction affinity, - 4G, is represented by the sum total of the step affinities, - 4g, multiplied by the respective stoichiometric numbers, v, of elementary steps as e q)ressed in Eqn. 7-21 ... 

If there is an elementary step r which determines the overall reaction rate because its rate is much smaller than the rates of the other elementary steps, the overall reaction affinity - AG will be located at the rate>determining step r as expressed in Eqn. 7-22 ... 

Such a single rate-determining step scarcely occurs in ordinary reactions usually, the overall reaction affinity is distributed in multiple rate-determining steps rather than localized at a single step as is described in Sec. 7.4. 

With a single rate-determining step, the affinity of elementary steps other than the rate-determining step is negligible, and the overall reaction affinity — AG approximately equals the affinity - 4gr multiplied by the stoichiometric number of the rate-determining step in Eqn. 7-44 as has been shown in Eqn. 

The reaction affinity - AG and the ratio v /vj of the forward to the backward rate can be estimated, regardless of whether the reaction rate is determined by a single step or multiple steps. Thus, Eqn. 7-51 can be used to determine the mean stoichiometric number of the multiple rate-determining steps. 

Fig. 7-12. Potential energy curves for a two-step reaction (a) near equilibrium indicating reaction affinity distributed to step 1 and (b) away from equilibrium indicating reaction affinity distributed to step 1 and step 2 - dG = affinity of overall reaction m = (dgi / dgj).

As the reaction affinity increases in the forward direction, the forward rates I l and vl of the two steps increase, while the backward rates oj and vi decrease, giving rise to an increase of co 1 and a decrease of ( vl vl)/(Uj vl) 1. Then, for the range of affinity in which the forward affinity is high, Eqn. 7-56 yields Eqn. 7-57 ... 

In order that the oxidative and the reductive dissolution reactions may proceed, the affinity for the reaction is required to be positive the reaction affinity is represented by the difference between the Fermi level, ef(sc), of the electrode and the equivalent Fermi level Er(dK) of the ion transfer reaction (Refer to Sec. 4.4.). 

Because reduction of the oligosaccharide occurs in the reductive-amination reaction, affinity adsorbents prepared by this route contain one glycosyl residue fewer than the original oligosaccharide. Adsorbents having such ligands may have low utility. The structure of the product obtained from lactose and 2-aminoethylpoly(acrylamide) by the reductive-amination route is shown in 6. 

In these equations we see the regularity that the partial differential of these four thermodynamic potentials with respect to their respective extensive variables gives us their conjugated intensive variables and vice versa. We thus obtain minus the affinity of an irreversible process in terms of the partial differentials of U, H, F, and G with respect to the extent of reaction affinity is an extensive variable. 

The electromotive force /sHj(0i is thus related to the reaction affinity ... 

The temperature dependence of the reaction affinity is given by Eq. 4.8, and the result for the hydrogen-oxygen cell is shown in Eq. 9.28 ... 

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

The combination of hydrogen and nitrogen under pressure was effected by Le Chatelier5 in 1901, but owing to an explosion the method was not worked commercially. In 1905 the subject was further studied by Haber and van Oordt, who found that at red heat the velocity of combination is too slow" to admit of measurement, and that at higher temperatures the amount of ammonia formed is small, either on account of rapid dissociation or because the reaction-affinity is small. 

Berger G., Cadore E., Schott J., and Dove P. M. (1994) Dissolution rate of quartz in lead and sodium electrolyte solutions between 25 and 300 °C effect of the nature of surface complexes and reaction affinity. Geochim. Cosmochim. Acta 58, 541-551. 

Sometimes the state of a reaction relative to equilibrium is described in terms of reaction affinity (see Stumm and Morgan 1981). The affinity, A, simply equals -AG,. 

Ace denotes the reaction affinity for germanium F(Ge4+) is the Fermi level of the reaction in equilibrium F is the Fermi level of the germanium electrode... 

The third stage in the reaction represents conversion of Alb to Ale by growth of individual units to a size displaying solid-state behavior. At 25°C the critical level for A for Ale formation was near 1.30 kcal. Table IV summarizes the affinity data for all the experiments considered here. The reaction affinities are affected by pH, temperature and rate of Af addition, and these factors need to be considered in any interpretation of the data. 

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