Cell voltage equilibrium electrode potential

The thermodynamic data also determine the temperature coefficient of the equilibrium cell voltage or electrode potential according to the relation... 

Equation (5.9) is the general Nemst equation giving the concentration dependence of the equilibrium cell voltage. It will be used in Section 5.4 to derive the equilibrium electrode potential for metal/metal-ion and redox electrodes. 

The equilibrium potential of an electrode (e.g., M/M ) is defined in Section 5.2 as the voltage of the cell, Pt H2(l atm) H+(a = 1) M M, where a is the activity. Three issues have to be resolved to measure this equilibrium electrode potential (1) the selection of a reference electrode (2) the coupling of the reference electrode with the electrode whose potential is being measured, in this case M/M + and (3) the experimental method for the voltage measurement. 

Considering Equation (4), it is clear that one has to operate a galvanic cell at the maximum possible cell voltage in order to maximize the electric energy yield. As shown previously (Figure 3.1.6), the maximum value of U is the equilibrium electrode potential difference E or E°. Thus, one may formulate the fundamental relationship between chemical and electric energy ... 

We now estimate the anode/cathode potential difference during current flow for driven and self-driven cells. First, we define the cell potential (V) as the difference in the anode and cathode potentials. For a self-driven cell, the cell voltage at a given current density will be less than the difference in equilibrium electrode potentials (AEJ due to the presence of various overpotentials. 

Voltage drop caused by mixed potential and fuel crossover. The mixed potential at electrodes is due to unavoidable parasitic reactions that tend to lower the equilibrium electrode potential. For a mixed cathode potential, a local-cell mechanism has been put forward to explain the Pt-02 reaction mechanism at the electrode in an 02-saturated acidic solution [20, 21], The mixed potential is composed of both the cathodic O2/H2O reaction potential (O2+ 4H -l- 4e 2H2O,... 

In Chapter 8 (pages 119-123) we saw that the position of an equilibrium reaction is affected by changes in concentration, temperature and pressure. Redox equilibria are no different. When we compare the voltage of a standard half-cell, X, with a standard hydrogen electrode, we are measuring E for the half-cell X. If we change the concentration or temperature of half-cell X, the electrode potential also changes. Under these nonstandard conditions we use the symbol E for the electrode potential. 

Equilibrium potentials can be calculated thermodynamically (for more details, see Chapter 3) when the corresponding electrode reaction is known precisely, even when they cannot be reached experimentally (i.e., when the electrode potential is nonequilibrium despite the fact that the current is practically zero). The open-circuit voltage of any galvanic cell where at least one of the two electrodes has an nonequilibrium open-circuit potential will also be nonequilibrium. Particularly in thermodynamic calculations, the term EMF is often used for measured or calculated equilibrium OCV values. 

However, under working conditions, with a current density j, the cell voltage E(j) decreases greatly as the result of three limiting factors the charge transfer overpotentials r]a,act and Pc,act at the two electrodes due to slow kinetics of the electrochemical processes (p, is defined as the difference between the working electrode potential ( j), and the equilibrium potential eq,i). the ohmic drop Rf. j, with the ohmic resistance of the electrolyte and interface, and the mass transfer limitations for reactants and products. The cell voltage can thus be expressed as... 

The first difference between these two batteries is the voltage they produce a watch battery produces about 3 V and a lead-acid cell about 2 V. The obvious cause of the difference in emf are the different half-cells. The electrode potential E is the energy, expressed as a voltage, when a redox couple is at equilibrium. 

Electrode potential, E The energy, expressed as a voltage, of a redox couple at equilibrium. E is the potential of the electrode when measured relative to a standard (ultimately the SHE). E depends on temperature, activity and solvent. By convention, the half cell must first be written as a reduction, and the potential is then designated as positive if the reaction proceeds spontaneously with respect to the SHE. Otherwise, E is negative. 

Thus measuring the cell voltage at equilibrium vs charge passed between the electrodes is equivalent to measuring the chemical potential as a function of x, the Li content of a compound like Li Mo Seg. Thermodynamics requires that p increase with concentration of guest ions, and so E decreases as ions are added to the positive electrode. 

The galvanic cell pictured in Figure 7.1 is not at equilibrium. If switch S is closed, electrons will spontaneously flow from the zinc (anode) to the copper (cathode) electrode. This flow will continue imtil the reactants and products attain their equilibrium concentrations. If switch S is opened before the cell reaches equilibrium, the electron flow will be interrupted. The voltmeter would register a positive voltage, which is a measure of the degree to which the redox reaction drives electrons from the anode to the cathode. Since this voltage is a type of energy that has the potential to do work, it is referred to as a redox potential or cell potential, denoted as... 

This equation has a standard electrode potential of -0.447 V. Thus, the solution containing mercuric and chloride ions in contact with iron forms a battery. The reduction of the complex ions to metallic mercury is the cathodic reaction. The dissolution of iron is the anodic reaction. The overall reaction in the battery is given by the addition of Equation (13.42) and Equation (13.43). Due to the high value of its reversible cell voltage under standard conditions (0.85 V), it is expected that a very low equilibrium concentration of the complex ion can be achieved. 

Equation 2.16 shows that potentiometry is a valuable method for the determination of equilibrium constants, ffowever, it should be borne in mind that the system should be in equilibrium. Some other conditions, which are described below, also need to be fulhlled for use of potentiometry in any application. The basic measurement system must include an indicator electrode that is capable of monitoring the activity of the species of interest, and a reference electrode that gives a constant, known half-cell potential to which the measured indicator electrode potential can be referred. The voltage resulting from the combination of these two electrodes must be measured in a manner that minimises the amount of current drawn by the measuring system. This condition includes that the impedance of the measuring device should be much higher than that of the electrode. 

The SOFC consists of cathode, electrolyte and anode collectively referred to as the PEN - positive electrode, electrolyte, negative electrode. A single cell operated with hydrogen and oxygen provides at equilibrium a theoretical reversible (Nernst) or open circuit voltage (OCV) of 1.229 V at standard conditions (STP, T = 273.15 K. i> = 1 atm). With the standard electrode potential E°, universal gas constant R. temperature T. Faraday s constant F, molar concentration x and pressure p, the OCV is given by... 

When the equivalence point is reached, the Fe2+ will have been totally consumed (the large equilibrium constant ensures that this will be so), and the potential will then be controlled by the concentration ratio of Ce3+/Ce4+. The idea is that both species of a redox couple must be present in reasonable concentrations for a concentration to control the potential of an electrode of this kind. If one works out the actual cell potentials for various concentrations of all these species, the resulting titration curve looks much like the familiar acid-base titration curve. The end point is found not by measuring a particular cell voltage, but by finding what volume of titrant gives the steepest part of the curve. 

The oxidation rate depends not only on the gas composition and the temperature parameter, but also on the electric potential difference between the electronically conductive part of the anode electrode and the ionically conductive electrolyte. Defining the electric potential of the solid part of the anode electrode as zero potential, the reaction rate depends on the electric potential in the electrolyte, other hand, the reduction reaction rate depends on the electric potential difference at the cathode electrode, which is the difference between the given cell voltage, Uceii, and the electrolyte potential, equilibrium constants are determined by the... 

If both electrode processes operate under standard conditions, this voltage is E°, the equilibrium standard electrode potential difference. Values of E and E° may be conveniently measured with electrometers of so large an internal resistance that the current flow is nearly zero. Figure 3.1.6 illustrates the measurement and the equilibrium state. The value of E° is a most significant quantity characterizing the thermodynamics of an electrochemical cell. Various important features of E and E° will be addressed in the following chapters. 

The standard equilibrium cell voltage resulting from a combination of any two electrodes is the difference between the two standard potentials, E°(2) - E°( 1). For instance, the standard cell equilibrium voltage of the combination F2/F with the Li+/Li electrode would be 5,911 V. Correspondingly, the standard free energy change of the underlying chemical reaction, 1/2 F2 + Li —> F + Li+, is AG° = -570 KJ (g-equivalent)-1. 

If the electrode reactants and products are not in the standard state, the equilibrium cell voltage will be the difference between the E values (i.e. the corresponding activity terms have to be included). Consider again the cell consisting of the half reactions Ag+/Ag and H+/H2. The equilibrium potential difference between the two electrodes, E - E(2) - E(l), is represented in Equation (20). Considering that czAg - 1 and 0(H+/H2) = 0 V, Equation (20) is identical to Equation (18). 

Electrochemical cells may consist of two electrodes of the same type, but with different concentrations of the electroactive species in the electrolyte. Such cells are known as concentration cells. For example, two platinum electrodes operate in two H+/H2 solutions of different activity, separated by a membrane. The equilibrium cell voltage is defined by Equation (21a). As the standard potential is the same for both electrode reactions, the measurable cell voltage will depend only on the activity ratios, Equation (21b). If in this system both electrolytes were in equilibrium with the same EE pressure, the measured E would respond linearly to the pH difference between the two electrolytes, Equation (21c) (i.e. a pH electrode). 

The equilibrium situation in an electrochemical cell is obtained, if the electrical current is interrupted, if all local actions (e.g. transport in the electrode) have come to an end and no internal short circuits occur. Then, as mentioned (Figure 3.5.10), the cell voltage is determined by the difference in the lithium potential (chemical potential of lithium) between the left-hand side (Ihs) and right-hand side (rhs) of the electrochemical cell (E - open cell voltage, F - Faraday constant) ... 

The electric potential difference of a -> galvanic cell (cell voltage) is the difference of electric potential between a metallic terminal attached to the right-hand electrode in the -> cell diagram and identical metallic terminal attached to the left-hand electrode. E includes the condition when current flows through the cell. The value of E measured when the left-hand electrode is at virtual equilibrium, and hence acting as a -> reference electrode, may be called the potential of the (right-hand) electrode with respect to the (left-hand) reference electrode. 

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