Batteries equilibrium potentials

The electrolyte in lead-acid batteries is dilute sulfuric acid that contains the component "water". Its stability is an important factor since it can be decomposed into hydrogen and oxygen, and the two broken lines in Fig. 1 represent the borderlines of this stability. They show the equilibrium potentials of hydrogen and oxygen evolution and their dependence on the pH value. 

PbO and Pb304 are oxides of lead that are important primary products. Under certain circumstances, PbO is also observed in lead-acid batteries (cf. Sec. 4.4.5.1). Fig. 1 shows that these oxides are only stable in a neutral or alkaline environment. Their equilibrium potentials are represented by curves C-F and their standard values are compiled in Table 3. 

Figure 2. Reactions that occur in lead-acid batteries versus electrode potential (thermodynamic situation). Their equilibrium potentials are inserted as boxed numbers. Equilibrium potentials of the charge-discharge reactions (Pb/PbS04 and PhS04/Pb02) are represented by hatched columns, to indicate their dependence on acid concentration. The inserted equilibrium potentials (-0.32 and +l. 75 V) of the charge discharge reactions correspond to an acid density of 1.23 gem 3.

Thus films can be divided into two groups according to their morphology. Discontinuous films are porous, have a low resistance and are formed at potentials close to the equilibrium potential of the corresponding electrode of the second kind. They often have substantial thickness (up to 1 mm). Films of this kind include halide films on copper, silver, lead and mercury, sulphate films on lead, iron and nickel oxide films on cadmium, zinc and magnesium, etc. Because of their low resistance and the reversible electrode reactions of their formation and dissolution, these films are often very important for electrode systems in storage batteries. 

One can think of the reversible (i.e., equilibrium) potential for a reaction across an interface as a battery with a value of Et, as shown schematically in Fig. 1. Thus, at equilibrium, our metal/solution interface can be modeled as a battery. Because the system is at equilibrium, no net reaction is occurring under these conditions. 

If this cell is now connected to an adjustable voltage (e.g., a battery), the potential E can be changed at will and the reaction system, O R, driven in the forward or reverse direction. Let us assume that the potential at E is made more positive, so that the net reaction at the electrode is the reduction of O to R. Eventually there will be reached a new equilibrium state in which the ratio (0)/(R) will be smaller as indicated by Eq. (XVII.8.4) "... 

When the current does not flow through battery the measurable diflerence in electric potential between the terminals of the two electrodes is the result of all the equilibrium potential differences at the interphase between the conducting phases in contact. In the example of the Daniell cell, with both electrodes having copper terminals, there are three interfacial potential differences (apart from the small liquid junction potential difference at the contact between the two electrolyte phases) one potential difference at the contact between the zinc rod and the copper terminal (Zn/Cu) and two potential differences at the metal-solution interphases (Zn/Zn + and Cu/Cu +), which are mainly due to the charge transfer processes. 

Since it is impossible to measure the individual electric potential differences at the phase boundaries, we shall hereinafter speak only in terms of the difference in electric potential across the two terminals connected to the electrodes of the battery. When in a battery the current is not flowing or tends to zero, the measurable potential difference across the two terminals is called the open-circuit voltage (OCV), fJc, and it represents the battery s equilibrium potential (or voltage). Since it is related to the free energy of the cell reaction, the OCV is a measure of the tendency of the cell reaction to take place. Indeed, while the conversion of chemical into electric energy is regulated by thermodynamics, the behavior of a battery under current flow (the current is a measure of the electrochemical reaction rate) comes under electrochemical kinetics. 

Given that the cell reaetion is eomposed of the two half-reactions at the electrodes, the battery s Vo can also be estimated as the difference in the equilibrium potentials of the positive and negative electrode (Eq. (5)). 

All equilibrium potentials are referred to a standard hydrogen electrode. The Hg Hg2S04 electrode is widely used in lead-acid battery investigations. This electrode has a potential which is 0.620 V more positive than that of the standard hydrogen electrode at pH = 0 [18]. 

Fig. 6.10. Possible reactions in VRLA batteries as function of electrode potential. Origin of arrows represents equilibrium potential of given reaction [22].

If we review the literature sources on lead—acid batteries, we will see that reported data about the value of the equilibrium potential of the Pb02/PbS04 electrode differ by 5—6 mV from the value in Eqn (2.E11). This difference comes from the different AG values reported by the authors for the reactants and products of the electrochemical reaction, as well as whether a value of F = 96500 C is used or the more precise value of 96487 C. 

The potential/pH diagram shows that, at low pH values, the equilibrium potential of the H /H2 electrode has more positive values than that of the Pb/PbS04 electrode. It should be expected that H2 will evolve first during battery charge. However, because of the high over-potential of hydrogen evolution on Pb, the above process does not proceed. Instead, PbS04 is reduced... 

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. 

Also when a potential is to be measured, two PU electrodes must be used. The potential of each electrode is either measured individually with respect to a third electrode and then subtracted or the potential difference between the two PU electrodes are measured directly without the use of a third electrode. DC voltage measured is the sum of the equilibrium potentials of the two electrodes, plus the potential difference in the tissue between them. The tissue potential may be membrane potentials, for instance the skin DC potential. If the two electrodes are made of different metals (e.g., steel and platinum), a DC voltage of hundreds of millivolt may be generated by the electrode pair (battery effect). 

Note Actually not the true equilibrium voltage but only the open circuit voltage can be measured with lead-acid batteries. Due to the unavoidable secondary reactions of hydrogen and oxygen evolution and grid corrosion, mixed potentials are established at both electrodes, which are a little different from the true equilibrium potentials (cf Fig. 1.18). But the differences are small and can be ignored. 

The sign expresses that this potential does not represent a true equilibrium potential and that this value can only be approximated, as already has been indicated above and also in Table 1.1. Actually, after charging, values between 1.3 and 1.4 V are observed, depending on the previous treatment of the battery. But on open circuit the cell voltage decreases to less than 1.3 V within a few days (59). 

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