Zero-current cell potential

Measurement of the potential of a galvanic cell, usually at zero current cell potential governed by the potential of an indicator electrode which responds to changes in the activity of the species of interest. 

An electrical potential difference between the electrodes of an electrochemical cell (called the cell potential) causes a flow of electrons in the circuit that connects those electrodes and therefore produces electrical work. If the cell operates under reversible conditions and at constant composition, the work produced reaches a maximum value and, at constant temperature and pressure, can be identified with the Gibbs energy change of the net chemical process that occurs at the electrodes [180,316]. This is only achieved when the cell potential is balanced by the potential of an external source, so that the net current is zero. The value of this potential is known as the zero-current cell potential or the electromotive force (emf) of the cell, and it is represented by E. The relationship between E and the reaction Gibbs energy is given by... 

An interesting result has emerged. When a Zn/Zn2+ interface and a Cu/Cu2+ interface are built into an electrochemical cell or system, one can proceed from the equilibrium electrode potentials and the zero-current cell potential to predict at which interface there will be a tendency for deelectronation (oxidation) and at which a tendency for electronation (reduction), i.e., which electrode will function as the electron source and which as the electron sink. 

Consequently, by measuring the zero-current cell potential we obtain the standard state Gibbs free energy change on reaction (if all the ions are in their standard states). Now if we continue further and measure how the zero-current standard state cell potential varies as a function of temperature, we have... 

E Electrochemical cell potential difference (V) E° Zero-current cell potential (V)... 

This maximum work is obtained if the process is sufficiently slow that there are no irreversibilities, for example, no resistive heating as a result of the current flow. This implies that the rate of reaction is very slow, and that the electrical potential produced is just balanced by an external potential so that the current flow is infinitesimal. This electrical potential produced by the cell (or of the balancing external potential) will.be referred-to as-the zero-current cell potential and designated by E. The work done by... 

D7.6 The potential difference between the electrodes in a working electrochemical cell is called the cell potential. The cell potential is not a constant and changes with time as the cell reaction proceeds. Thus the cell potential is a potential difference measured under non-equilibrium conditions as electric current is drawn from the cell. Electromotive force is the zero-current cell potential and corresponds to the potential difference of the cell when the cell (not the cell reaction) is at equilibrium. Infinitesimally small changes from this equilibrium are reversible with constant concentration and, consequently, it is possible to relate emf to thermodynamic properties. 

The zero-current cell potential is given by the Nemst equation vF vF [H+l pfO,)"/ ... 

As Fig. 2 illustrates, the observed zero-current cell potential (electromotive force, emf) is a sum of each individual potential drop that occurs across the entire cell. Indeed, each vertical line in Fig. 2 represents an interface where a boundary potential develops. It is the potential across the ion-selective membrane that will be directly dependent on the ion composition of the sample and the contacting inner electrolyte. Therefore, all other potential contributions must be reversible and constant, so that observed cell potential ( cell) changes can be attributed to changes in the membrane potential only, which in turn are indicative of changes in the ion activity in the sample phase. 

The reason it is not necessary to include the terminals is that the property whose value we seek, the zero-current cell potential, is the same regardless of the metal used for the terminals. 

Figure 14.3 Potentiometer to measure the zero-current cell potential of a galvanic cell.

Figure 14.3 shows how we can use a potentiometer to determine the equilibrium cell potential. Consider Fig. 14.3(a). Outside the galvanic cell is an external circuit with a battery that allows an electric current to pass through a slidewire resistor. The cell s negative terminal is connected to the negative terminal of the battery. Since the cell is not part of this circuit, no current passes through the cell, and is the zero-current cell potential celi,eq- The left end of the slidewire is at the same electric potential as the left terminal of the cell. 

In practice, it is more convenient to measure the zero-current cell potential with a high-impedance digital voltmeter (a voltmeter that draws negligible current) instead of with a... 

What is the source of an open-circuit, zero-current cell potential When no electric current passes through the cell, the electric potential must be uniform within each bulk phase that is an electrical conductor, because otherwise there would be a spontaneous movement of charged particles (electrons or ions) through the phase. Electric potential differences in a cell without current therefore exist only at phase boundaries. The equilibrium cell potential is the cumulative result of these potential differences at interfaces between different conducting phases within the cell. 

An interfacial potential difference appears as a vertical step in a profile of the Galvani potential, as shown schematically in Fig. 14.4(a). The zero-current cell potential, E ceii.eq is the algebraic sum of the interfacial potential differences within the cell. 

Fig. 5.10 The zero-current ceU potential is measured by balancing the ceU against an external potential that opposes the reaction in the ceU. When there is no current flow, the external potential difference is equal to the zero-current cell potential.

Equation 5.12 provides an electrical method for measuring a reaction Gibbs energy at any composition of the reaction mixture we simply measure the zero-current cell potential and convert it to Afi. Gonversely, if we know the value of AfG at a particular composition, then we can predict the cell potential. 

A power supply may generate a potential difference that perfectly counterbalances that existing between the two electrodes. In these conditions, no current flows. The situation is equivalent to that encountered when the two electrodes are not connected. We say that the system is at equilibrium. Sometimes, the potential difference E determined at equilibrium (the zero-current cell potential) is still called the electromotive force of the cell. In the case of a chemically reversible cell, it is endowed with a very well-determined meaning (see Chap. 2 and later in this chapter) It permits us to obtain the standard electrode potentials. Establishing the latter is in the realm of the application of Nernst s law. 

Nernst s law permits the calculation of a redox potential when, and only when, there is equilibrium. This is the reason why the potentials calculated by the above relations are called equilibrium potentials. This means that the potential of by an electrode that dips into an electrochemical compartment is given by Nernst s law when no current flows through the cell (i = 0). With respect to this point, we must recall that the standard potentials, which differ from the equilibrium potentials due to the presence of the logarithmic terms in the latter, are obtained from zero-current cell potential values (see Chap. 2). 

These potential values are those of reduction potentials. Hence, these values are those of zero-current cell potentials in which the hydrogen electrode is located on the left and that under study on the right (see Fig. 2.5 in Chap. 2). Moreover, all the species that participate in the half-reduction equilibria are in their standard states their activities are equal to unity. We have already seen that the hydrogen electrode necessarily plays the part of the anode and the electrode under study that of the cathode. Hence, the studied system suffers the electrodic reaction... 

By convention, the zero-current cell potential (formerly electromotive force) is equal, in sign and magnitude, to the potential difference between the cathode and the anode ... 

Applying Nernst s law immediately let us calculate the zero-current cell potential, provided the species activities are known. 

In order to overcome the difficulty due to the discrepancy of the values of activities and concentrations, which may be important, the concept of formal potentials E° has been devised. (The symbol E° of formal potentials is, unfortunately, the same as that used for standard biological potentials.) The formal potential is that which is experimentally observed with solutions containing both Ox and Red forms of the couple at the unit concentration and that also may contain other species whose concentrations are specified. They take into account the variations in activity coefficients with the ionic strength, the acid-base equilibria involving the Ox and/or Red form(s), and their possible complexations with the other solution species. They are experimentally determined using electrochemical cells of the classes described above, after measurements of their zero-current cell potentials. The formal potentials can be used only when the experimental conditions of the redox reaction under study are the same as those under which they have been determined. 

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