Free energy reaction pathways

Figure 3.3.10 (A) The electrode potential dependence of the Gibbs free energy reaction pathway of the ORR. While the overall reaction has elementary steps that are energetically uphill at +1.23 V (red pathway), all elementary steps become downhill at +0.81 V (yellow pathway) (i.e. at an overpotential of approximately -0.42 V. At this point, the reaction is not limited by kinetics anymore. (B) The experimentally observed current-potential (j-E) relation of the ORR is consistent with the computational conclusions from (A) between +1.23 V and +0.81 V the j-E curve shows an exponential behavior, while at electrode potentials below +0.81 V, the ORR reaction rate becomes oxygen mass-transport limited, which is reflected by a flat ( j-E) profile. Figure adapted with permission from [19]. 

Fig. 9.1. Free energy/reaction coordinate profile for two competing associative pathways the dashed line leads to less stable products via a less stable intermediate than the full line, but is faster because of smaller activation barriers.

Fig. 1. Schematic free energy-reaction coordinate profiles for a single-electron electroreduction involving solution reactant O and product R at a given electrode potential E, occurring via three different reaction pathways, PAS, P A S, and P A S". Pathway PAS involves energetically favorable precursor and successor states (P and S) but with a weak-overlap transition state. Pathways P A S and P A"S involve energetically similar precursor and successor states, but with the latter involving strong overlap in the transiton state.

Fig. 2. Schematic plots outlining outer-shell free energy-reaction coordinate profiles for the redox couple O + e R on the basis of the hypothetical two-step charging process (Sect. 3.2) [40b]. The y axis is (a) the ionic free energy and (b) the electrochemical free energy (i.e. including free energy of reacting electron), such that the electrochemical driving force, AG° = F(E - E°), equals zero. The arrowed pathways OT S and OTS represent hypothetical charging processes by which the transition state, T, is formed from the reactant.

Studies show that the measured composition of the product mixture at constant temperature depended on the water density (Fig. 7.7). This was taken as an indication that these products could be formed by competing ionic and free-radical reaction pathways. Usually in gas-phase kinetics the product composition changes with temperature because of the different activation energies and, to a minor extent with pressure, mainly because of the concentration effect on bimolecular elementary reaction steps. In water, the drastic dependence on pressure is likely a consequence of the competition between reactions with different polarity. Free radical reaction rates (involving large free radicals beyond the RRKM high-pressure limit, see, for example, [25]) should decrease with pressure as a result... 

In vivo, under steady-state conditions, there is a net flux from left to right because there is a continuous supply of A and removal of D. In practice, there are invariably one or more nonequilibrium reactions in a metabolic pathway, where the reactants are present in concentrations that are far from equilibrium. In attempting to reach equilibrium, large losses of free energy occur as heat, making this type of reaction essentially irreversible, eg. 

Figure 18.2 Summary of respiratory energy flows. Foods ate converted into the reduced form of nicotinamide adenine dinucleotide (NADH), a strong reductant, which is the most reducing of the respiratory electron carriers (donors). Respiration can he based on a variety of terminal oxidants, such as O2, nitrate, or fumarate. Of those, O2 is the strongest, so that aerobic respiration extracts the largest amount of free energy from a given amount of food. In aerobic respiration, NADH is not oxidized directly by O2 rather, the reaction proceeds through intermediate electron carriers, such as the quinone/quinol couple and cytochrome c. The most efficient respiratory pathway is based on oxidation of ferrocytochrome c (Fe ) with O2 catalyzed by cytochrome c oxidase (CcO). Of the 550 mV difference between the standard potentials of c)Tochrome c and O2, CcO converts 450 mV into proton-motive force (see the text for further details).

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