Hydrogen-reaction equilibrium potential dependence

We then determine the equilibrium potentials V(c) and V (d) for the electrode reactions (c) and (d). These potentials represent equilibrium between Fe(s) and the oxides Fe304(s) and Fe203(s), respectively. Since H" (ac ) is included as a reactant in (c) and (d), the equilibrium potentials depend on the hydrogen ion concentration [H+], and thus on the pH value of the electrolyte. To introduce pH as a variable, the following relation is used... 

The role that acid and base catalysts play can be quantitatively studied by kinetic techniques. It is possible to recognize several distinct types of catalysis by acids and bases. The term specie acid catalysis is used when the reaction rate is dependent on the equilibrium for protonation of the reactant. This type of catalysis is independent of the concentration and specific structure of the various proton donors present in solution. Specific acid catalysis is governed by the hydrogen-ion concentration (pH) of the solution. For example, for a series of reactions in an aqueous buffer system, flie rate of flie reaction would be a fimetion of the pH, but not of the concentration or identity of the acidic and basic components of the buffer. The kinetic expression for any such reaction will include a term for hydrogen-ion concentration, [H+]. The term general acid catalysis is used when the nature and concentration of proton donors present in solution affect the reaction rate. The kinetic expression for such a reaction will include a term for each of the potential proton donors that acts as a catalyst. The terms specific base catalysis and general base catalysis apply in the same way to base-catalyzed reactions. 

Equation (3.3) gives the potential dependence of the reaction free energy of Reaction (3.2). Since this reaction equilibrium defines the standard hydrogen electrode potential, we now have a direct fink between quite simple DFT calculations and the electrode potential. In a similar way, we can now calculate potential-dependent reaction free energies for other reactions, such as O - - H" " + e OH or OH - -+ e HzO. 

Two things to notice are that fc, will depend on the reference electrode chosen and secondly E° is the equilibrium potential not for the standard hydrogen electrode but rather for the electrochemical equilibrium between H+ and H ds. This can be seen by explicitly writing out the equation corresponding to the reverse reaction ... 

E is the standard equilibrium potential, i. e. the potential corresponding to unit activity and RTF. The dissolution reaction leads to the development of an electrical double layer at the iron-solution interface. The potential difference of the Fe/Fe " half cell cannot be measured directly, but if the iron electrode is coupled with a reference electrode (usually the standard hydrogen electrode, SHE), a relative potential difference, E, can be measured. This potential is termed the single potential of the Fe/Fe electrode on the scale of the standard hydrogen couple H2/H, the standard potential of which is taken as zero. The value of the equilibrium potential of an electrochemical cell depends upon the concentrations of the species involved. 

The value of the constant V, and hence the values of standard potentials, depend on the choice of the reference electrode and on the character of electrode reaction, which takes place on it With the reference electrode potential conventionally taken as zero, we can choose, for example, the normal hydrogen electrode (NHE), i.e., an electrode, for which the equilibrium at the interface is attained due to the reversible redox reaction H+ + e = H2, provided the activity of H+ ions in the solution is 1 mol/liter and the pressure of gaseous hydrogen above the solution is 1 atm. Many of the measured potentials are given below relative to the saturated calomel electrode (SCE) its potential relative to the NHE is 0.242 V. 

When a biochemical half-reaction involves the production or consumption of hydrogen ions, the electrode potential depends on the pH. When reactants are weak acids or bases, the pH dependence may be complicated, but this dependence can be calculated if the pKs of both the oxidized and reduced reactants are known. Standard apparent reduction potentials E ° have been determined for a number of oxidation-reduction reactions of biochemical interest at various pH values, but the E ° values for many more biochemical reactions can be calculated from ArG ° values of reactants from the measured apparent equilibrium constants K. Some biochemical redox reactions can be studied potentiometrically, but often reversibility cannot be obtained. Therefore a great deal of the information on reduction potentials in this chapter has come from measurements of apparent equilibrium constants. 

During each run, the membrane is electrochemically loaded with hydrogen from the left side with a constant electrolysis current of 30 mA. The initial potential of the palladium/palladium hydride (vs. Ag/AgCl reference electrode) on carbon dioxide reaction side at the start of the run is defined as E. This potential depends on the hydride content of the membrane and the equilibrium between the metal hydride/bicarbonate solution. 

Moreover, Takehara (125) has investigated the hydrogenation of allyl alcohol. Since the rate was found to depend on the rotational speed of the platinum disk only to a minor extent, the reaction was not diffusion controlled. The potential of the platinum disk was about 50 to 120 mV more noble than the hydrogen equilibrium potential. The potential... 

Consider a hydrogen electrode in equilibrium with H ion at a concentration c and hydrogen gas at a pressure p. The equilibrium potential of this electrode is denoted by 00 The equilibrium is Hj 2H + 2e . If the potential of the electrode is increased (made more positive), this equilibrium will be disturbed. The reaction from left to right will predominate, H2 will be oxidized, and a positive current will flow into the solution. If the potential of the electrode is lowered (made more negative), the equilibrium will be disturbed. The reaction from right to left will predominate, H2 will be liberated, and a positive current will fiow into the electrode or a negative current will flow into the solution. The current that fiows to the electrode, therefore, depends on the departure of the potential from the equilibrium value, 0 — 0o This difference between the applied potential 0 and the equilibrium potential 0 is the overpotential, or overvoltage,... 

Except for the electrochemical reaction (2.6), all other reactions depend on the pH of the solution. A number of electrochemical reactions proceed in this system, which form different electrode systems, depending on lead ion valency, solution composition and pH, and electrode potential. These reactions cover a potential range of 2.0 V. Table 2.4 summarises the electrochemical reactions involving Pb, lead oxides, PbS04 and basic lead sulfates, and the equilibrium potentials of the respective electrode systems. The reactions and the equilibrium potentials for the hydrogen and oxygen electrodes are also given in the table. Several chemical reactions in which basic lead sulfates take part are also included in Table 2.4. 

The driving force for an electrochemical reaction to proceed is polarization of the electrode, i.e. the potential difference between the equilibrium potential of the reaction and the electrode potential. The rate of the electrochemical reaction depends on the hindrances that have to be overcome by the reacting particles for the reaction to proceed. The hydrogen reaction on lead proceeds with great hindrances, i.e. at high overpotential. Hence, the competing reaction of lead sulfate reduction to lead proceeds with high coulombic efficiency and kinetic stability. This, in turn, ensures stable performance of the lead—acid battery. 

Each reaction either produces or consumes electrons hence, the rates of the reactions can be expressed conveniently as an electrical current density. By convention, electron release is assigned a positive current, whereas electron consumption is designated a negative current. In Fignre 16.1, Eh is the equilibrium potential for the hydrogen evolution reaction while Fe is that of iron dissolution. Below Epe, iron does not go into solution, and it represents the threshold potential for the dissolution of iron. The values of these equilibrium potentials can be obtained from the Nemst equation, and they depend on the concentrations of hydrogen and ferric ions in their respective cases. 

It can be seen that the corrosion current and potential depend on both the equilibrium potentials for the hydrogen evolution reaction and metal dissolution calculated from the Nernst equation, and the kinetic parameters, the exchange currents and the Tafel slopes. Table 9.1 shows the corrosion currents calculated for some typical values of these parameters it is also important to note that even a... 

If voltages ate referred to hydrogen half-cell potentials. Eo = . The Pourbaix diagram is a plot of versus pH for solid, gaseous, and dissolved components in equilibrium. It is apparent that if m and n appear on the same side of the equation the ratio m/n will be negative. If n = 0, Eq. (9.3-18) represents a vertical line on a potential-pH diagram which is voltage independent. U m = 0, the reaction is pH dependent. 

PEM fuel cell characteristics are generally described with polarization curves. The thermodynamic equilibrium potential of the hydrogen/oxygen reaction is reduced by various overvoltage terms that depend on mass transport, kinetic, and ohmic phenomena within cell. In other words, the output voltage of a single cell is attributable to different current, temperature, and pressure dependant factors [1]. 

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