Thermodynamics reversible cell

An e.m.f. measurement is only useful for a thermodynamically reversible cell, when E is related to the free energy change of the chemical reaction by... 

Equations 20.176 and 20.179 emphasise the essentially thermodynamic nature of the standard equilibrium e.m.f. of a cell or the standard equilibrium potential of a half-reaction E, which may be evaluated directly from e.m.f. meeisurements of a reversible cell or indirectly from AG , which in turn must be evaluated from the enthalpy of the reaction and the entropies of the species involved (see equation 20.147). Thus for the equilibrium Cu -)-2e Cu, the standard electrode potential u2+/cu> hence can be determined by an e.m.f. method by harnessing the reaction... 

Applying the common equations for the thermodynamics of reversible cells, it is possible to extract energetic parameters for the adatom redox reaction. This approach requires the measurement of voltammograms at different temperatures. If we consider that the adatom oxidation reaction involves the formation of the hydroxide, we can write the following equation for the overall cell reaction ... 

Reversible cell potentials have been the source of much thermodynamic data on aqueous electrolytes. In recent years, this technique has been extended to nonaqueous solutions and to molten salt systems. Its use for aqueous solutions, relative to other techniques, has decreased. Various ion specific electrodes have been developed in recent years. These are used primarily in analytical chemistry and have not produced much thermodynamic data. 

Consequently, a wealth of information on the energetics of electron transfer for individual redox couples ("half-reactions") can be extracted from measurements of reversible cell potentials and electrochemical rate constant-overpotential relationships, both studied as a function of temperature. Such electrochemical measurements can, therefore, provide information on the contributions of each redox couple to the energetics of the bimolecular homogeneous reactions which is unobtainable from ordinary chemical thermodynamic and kinetic measurements. 

Assuming thermodynamic reversibility of the cell reaction and with the help of eqs 1 and 3, we can obtain the reversible heat effect. 

A process is thermodynamically reversible when an infinitesimal reversal in a driving force causes the process to reverse its direction. Since all actual processes occur at finite rates, they cannot proceed with strict thermodynamic reversibility and thus additional nonrevers-ible effects have to be regarded. In this case, under practical operation conditions, voltage losses at internal resistances in the cell (these kinetic effects are discussed below) lead to the irreversible heat production (so-called Joule heat) in addition to the thermodynamic reversible heat effect. 

This is, in fact, the way electrode potentials are measured in practice. A cell is made up of the electrode of interest (the working electrode, e.g., Cu in Fig. 7.14) and a reference electrode made of Pt over which is bubbled Hj- No current passes through the reference electrode, which is therefore at its thermodynamically reversible potential. A counter-electrode (not shown in Fig. 7.14) is coupled through a power source... 

Note that some electrochemical cells use, instead of conventional reference electrodes, indicator electrodes. These are electrodes that are not thermodynamically reversible but which may hold then-potential constant 1 mV for some minutes—enough to make some nonsteady-state measurements (see Chapter 8). Such electrodes can simply be wires of inert materials, e.g.. smooth platinum without the conditions necessary to make it a standard electrode exhibiting a thermodynamically reversible potential. However, many different electrode materials may serve m this relatively undemanding role. 

Cells in which at least two electrolytic solutions are in contact are known as cells with liquid junction or with transference. Such cells are inherently irreversible and a complete thermodynamic development of them is beyond the scope of this book. However, cells with liquid junction are of sufficient importance that we discuss here the type that approximates a reversible cell most closely. 

From the basic principles we can make preliminary design estimates. Inefficiencies in a system arise because of voltage losses and because all of the current does not enter into the desired reactions. The minimum potential required to perform an electrolytic reaction is given by the reversible cell potential, a thermodynamic quantity. Additional voltage that must be applied at the electrodes represents a loss that is manifested in a higher energy requirement. The main causes of voltage loss are ohmic drops and overpotentials. The applied potential is equal to the sum of the losses plus the thermodynamic requirement ... 

This deviation from the thermodynamic reversible behavior leads to a decrease of the cell voltage by ca. 0.4-0.6 V, which reduces the energy efficiency of the fuel cell by a factor eE = E(j)/ Eeq, called voltage efficiency (eE = 0.80/1.23 = 0.65 for a cell voltage of 0.80 V), so that the overall energy efficiency at 25°C for the H2/02 fuel cell becomes 0.83 x 0.65 = 0.54. 

Going downhill, i.e., discharging the cell, is subject to similar thinking but of course reversed. The potential available at the terminals of a battery in discharge will be the thermodynamically reversible potential but now diminished by the sum of the overpotential and the IR drop. 

The reversible potential ofBr2 + 2e —> 2 Br is 1.08 V atm. The pH of sea water is near 7 and 25 °C hence the reversible potential of 2H+ + 2e —> Hj is about -0.42 V. The reversible cell potential would be then about 1.5 V. The idea here is to reduce the potential below the thermodynamically reversible value by photoillumination ofthe anode (photoassisted water decomposition Szklarczyk, 1983). 

When applying thermodynamic laws to the so called reversible galvanic cells their EMF can be deduced mathematically from characteristics of the system. Reversible cells are those in which the direction of reactions proceeding in them can be reversed when a voltage of an opposite direction is applied to the electrodes, which is only higher by an infinitesimal value then the EMF of the system proper. 

The galvanic cell operating at constant temperature either absorbs heat from the surroundings, or evolves it this absorbed or evolved heat is called latent heat. It follows from the thermodynamics laws that the sum total of free energy change AC , converted in a reversible cell quantitatively into the electrical work and of latent heat Qtev ) equals the enthalpy change AH ... 

The open circuit voltage (OCV) of a fuel cell is identical to the reversible cell potential, provided that the cell is in thermodynamic equilibrium. That is usually achieved, especially at high temperatures. There are some causes which... 

Reversibility — This concept is used in several ways. We may speak of chemical reversibility when the same reaction (e.g., -> cell reaction) can take place in both directions. Thermodynamic reversibility means that an infinitesimal reversal of a driving force causes the process to reverse its direction. The reaction proceeds through a series of equilibrium states, however, such a path would require an infinite length of time. The electrochemical reversibility is a practical concept. In short, it means that the -> Nernst equation can be applied also when the actual electrode potential (E) is higher (anodic reaction) or lower (cathodic reaction) than the - equilibrium potential (Ee), E > Ee. Therefore, such a process is called a reversible or nernstian reaction (reversible or nerns-tian system, behavior). It is the case when the - activation energy is small, consequently the -> standard rate constants (ks) and the -> exchange current density (jo) are high. 

With its reactant and product connections isolated, but equilibrium concentrations remaining in the cell, the cell voltage is a maximum, namely V , at open-circuit, zero-flow equilibrium (Table A.1). Equilibrium entails the presence of a thermodynamically reversible, symmetrical or balanced exchange current, described by Marcus (1964 1982) as being an equilibrium exchange between electrode electrons and vibrating... 

Hydrogen and carbonmonoxide are fuels which must be made at thermodynamic and economic cost. A principal industrial route is via the fired steam reform of natural gas, a highly irreversible process. The related thermodynamically reversible route to methane reform, and electrochemical oxidation, Figure A.3, is examined. An electrically driven electrochemical reformer at standard conditions is the model. The reformer supplies a pair of fuel cells separately utilising carbon monoxide and hydrogen. The thermodynamic data confirm that there is plenty of electricity available... 

Reversible cell. One in which the half-cell reactions are reversed by reversing the current flow such a cell is said to be in thermodynamic equilibrium. Standard Hydrogen Electrode SHE). This consists of a platinum electrode coated with platinum black to catalyse the electrode reaction and over the... 

The single thermodynamically reversible electrode potential as measured against the standard hydrogen electrode is equal to the emf of the cell,... 

Furthermore, when an electrochemical cell works in a thermodynamically reversible way (see Vol. 2, Chapter 7),... 

However, there is a direct method to obtain A5, via the thermodynamics of reversibly behaving cells without any special assumptions. Thus, consider a cell that is assumed to be run in a thermodynamically reversible way ... 

Table 1 Thermodynamics and theoretically reversible cell potential for fuel cell reactions... 

The values for the Daniel cell are taken from the latest and most accurate measurements of Cohen, Chattaway, and TombrokJ In dilute solutions the Daniel cell has a very small temperature coefficient, so that nE is nearly equal to Q. This accounts for the apparent confirmation of the old erroneous equation Q = nE. It is important to note that the Helmholtz equation is strictly accurate, as it depends solely on the two laws of thermodynamics. It is, of course, only applicable to reversible cells. 

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