Proton chemical potential difference

Each of the respiratory chain complexes I, III, and IV (Figures 12-7 and 12-8) acts as a proton pump. The inner membrane is impermeable to ions in general but particularly to protons, which accumulate outside the membrane, creating an electrochemical potential difference across the membrane (A iH )-This consists of a chemical potential (difference in pH) and an electrical potential. 

The equations for the fluxes of and and the expression for the diffusion potential will be derived now for a filament on the basis of the assumptions discussed in Section 2.2. Across the length / of the proton-con-ducting filament a chemical potential difference FKh= —i Tln Ch(/)/ch(0) is assumed to be maintained by two synchronized chemical reactions which inject and take out H at z = 0 and z = 1 respectively. The K layer has the radial extension from r = ator = a-ft/ with the thickness d corresponding roughly to the Debye length. The concentration of in the K layer will... 

In some cases, it is possible to observe a small amount of ammonia before imposing a potential. It is likely that the reaction occurs due to the difference in chemical potentials of electro-active ionic species (in this case protons) between two electrodes induces some protons to move from the anode (higher concentration) to the cathode (lower concentration). Theoretically, the reactions at the cathode should not be completed because the transportation of electrons through the electrolyte should be negligibly small, and a high-resistance external source connected to the electrodes also forbids the flow of electrons. Therefore, only the chemical potential difference between the electrodes called a potential open-circuit voltage (Voc) should be measured. In some electrolyte materials, the presence of electrons transport will cause the formation of ammonia at the cathode under open circuit conditions, especially in an elevated temperature sohd oxide proton conductor. 

The relative importance of the disproportionation process (SET between two anion radicals) depends principally on the thermodynamic constant (K). It can be easily determined more or less accurately from the potential difference existing between the first cathodic peak and the second one. (An exact calculation would be possible from the thermodynamic potentials of the two reversible transfers in the absence of proton sources and at reasonable sweep rates so as to inhibit any undesirable chemical reaction.)... 

Note, in using Equations 50 and 53 above, that tabulations of thermodynamic data for electrolytes tend to employ a 1 molar ess concentration for all species in solution. For situations defined to have a standard-state pH value different from 0 (which corresponds to a 1 molar concentration of solvated protons), the standard-state chemical potentials for anions and cations are determined as... 

In thermal equilibrium, within a quantum statistical approach a mass action law can be derived, see [12], The densities of the different components are determined by the chemical potentials ftp and fin and temperature T. The densities of the free protons and neutrons as well as of the bound states follow in the non-relativistic case as... 

In the previous chapter we indicated that the components involved with electron flow are situated in the lamellar membranes of chloroplasts such that they lead to a vectorial or unidirectional movement of electrons and protons (see Fig. 5-19). We now return to this theme and focus on the gradients in H+ (protons) thus created. In the light, the difference in the chemical potential of H+ from the inside to the outside of a thylakoid acts as the energy source to drive photophosphorylation. This was first clearly recognized in the 1960s by Peter Mitchell, who received the 1978 Nobel Prize in chemistry for his enunciation of what has become known as the chemiosmotic hypothesis for interpreting the relationship among electron flow, proton movements, and ATP formation. 

Figure 6-5 indicates that the C>2-evolution step and the electron flow mediated by the plastoquinones and the Cyt b(f complex lead to an accumulation of H+ in the lumen of a thylakoid in the light. This causes the internal H+ concentration, c, or activity, to increase. These steps depend on the light-driven electron flow, which leads to electron movement outward across the thylakoid in each of the two photosystems (see Fig. 5-19). Such movements of electrons out and protons in can increase the electrical potential inside the thylakoid (E ) relative to that outside ( °), allowing an electrical potential difference to develop across a thylakoid membrane. By the definition of chemical potential (fij = jx + RT In cij 4- ZjFE Eq. 2.4 with the pressure and gravitational terms omitted see Chapter 3, Section 3.1), the difference in chemical potential of H+ across a membrane is...

The transport of protons from the matrix to the lumen leads to a difference in the H+ chemical potential across the inner mitochondrial membrane. Using Equation 6.17c and the values in Figure 6-9, we calculate that... 

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