A.J. Bard, L.R. Faulkner - Electrochemical methods - Fundamentals and Applications (794273), страница 14
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In the reversible process, the springis never prone to contract more than an infinitesimal distance, because the large weight isremoved progressively in infinitesimal portions.Now if the same final state is reached by simply removing the weight all at once,equation 2.1.14 applies at no time during the process, which is characterized by severedisequilibrium and is grossly irreversible.On the other hand, one could remove the weight as pieces, and if there were enoughpieces, the thermodynamic relation, (2.1.14), would begin to apply a very large fraction ofthe time.
In fact, one might not be able to distinguish the real (but slightly irreversible)process from the strictly reversible path. One could then legitimately label the real transformation as "practically reversible."In electrochemistry, one frequently relies on the Nernst equation:Е = Е°' + Щ;]п^(2.1.15)to provide a linkage between electrode potential E and the concentrations of participantsin the electrode process:O + m><=±R(2.1.16)If a system follows the Nernst equation or an equation derived from it, the electrodereaction is often said to be thermodynamically or electrochemically reversible (ornernstian).Whether a process appears reversible or not depends on one's ability to detect thesigns of disequilibrium.
In turn, that ability depends on the time domain of the possiblemeasurements, the rate of change of the force driving the observed process, and the speedwith which the system can reestablish equilibrium. If the perturbation applied to the system is small enough, or if the system can attain equilibrium rapidly enough compared to2.1 Basic Electrochemical Thermodynamics47the measuring time, thermodynamic relations will apply. A given system may behave reversibly in one experiment and irreversibly in another, even of the same genre, if the experimental conditions have a wide latitude. This theme will be met again and againthroughout this book.2.1.2Reversibility and Gibbs Free EnergyConsider three different methods (1) of carrying out the reaction Zn + 2AgCl —> Z n 2 ++ 2Ag + 2СГ:(a)Suppose zinc and silver chloride are mixed directly in a calorimeter atconstant, atmospheric pressure and at 25°C.
Assume also that the extent ofreaction is so small that the activities of all species remain unchanged duringthe experiment. It is found that the amount of heat liberated when all substances are in their standard states is 233 kJ/mol of Zn reacted.
Thus,AH0 = -233 kJ. 2(b) Suppose we now construct the cell of Figure 1.1.1a, that is,Zn/Zn 2+ (a = 1), CT(a = l)/AgCl/Ag(2.1.17)and discharge it through a resistance R. Again assume that the extent of reactionis small enough to keep the activities essentially unchanged. During the discharge, heat will evolve from the resistor and from the cell, and we could measure the total heat change by placing the entire apparatus inside a calorimeter.We would find that the heat evolved is 233 kJ/mol of Zn, independent of R. Thatis, A#° = —233 kJ, regardless of the rate of cell discharge.(c)Let us now repeat the experiment with the cell and the resistor in separatecalorimeters. Assume that the wires connecting them have no resistance and donot conduct any heat between the calorimeters. If we take Qc as the heat changein the cell and QR as that in the resistor, we find that Qc + QR = -233 kJ/molof Zn reacted, independent ofR.
However, the balance between these quantitiesdoes depend on the rate of discharge. As R increases, \QC\ decreases and |Q R | increases. In the limit of infinite R, QQ approaches —43 kJ (per mole of zinc) andQR tends toward -190 kJ.In this example, the energy QR was dissipated as heat, but it was obtained as electrical energy, and it might have been converted to light or mechanical work. In contrast, Qcis an energy change that is inevitably thermal. Since discharge through R —» °° corresponds to a thermodynamically reversible process, the energy that must appear as heat intraversing a reversible path, <2rev, is identified as lim Qc. The entropy change, AS, is defined as Qrev /T (2), therefore for our example, where all species are in their standard states,TAS° = lim Qc = - 4 3 kJ(2.1.18)AG° = -190kJ = lim QR(2.1.19)Because AG° = AH0 - TAS°,Note that we have now identified — AG with the maximum net work obtainable fromthe cell, where net work is defined as work other than PV work (2).
For any finite R, \QR\2We adopt the thermodynamic convention in which absorbed quantities are positive.48Chapter 2. Potentials and Thermodynamics of Cells(and the net work) is less than the limiting value. Note also that the cell may absorb orevolve heat as it discharges. In the former case, |AG°| > |A#° .2.1.3Free Energy and Cell emfWe found just above that if we discharged the electrochemical cell (2.1.17) through an infinite load resistance, the discharge would be reversible.
The potential difference is therefore always the equilibrium (open-circuit) value. Since the extent of reaction is supposedto be small enough that all activities remain constant, the potential also remains constant.Then, the energy dissipated in R is given by| AG\ = charge passed X reversible potential difference(2.1.20)(2.L21)where n is the number of electrons passed per atom of zinc reacted (or the number ofmoles of electrons per mole of Zn reacted), and F is the charge on a mole of electrons,which is about 96,500 C. However, we also recognize that the free energy change has asign associated with the direction of the net cell reaction.
We can reverse the sign by reversing the direction. On the other hand, only an infinitesimal change in the overall cellpotential is required to reverse the direction of the reaction; hence E is essentially constantand independent of the direction of a (reversible) transformation. We have a quandary.We want to relate a direction-sensitive quantity (AG) to a direction-insensitive observable(E). This desire is the origin of almost all of the confusion that exists over electrochemicalsign conventions.
Moreover the actual meaning of the signs — and + is different for freeenergy and potential. For free energy, — and + signify energy lost or gained from the system, a convention that traces back to the early days of thermodynamics. For potential, —and + signify the excess or deficiency of electronic charge, an electrostatic conventionproposed by Benjamin Franklin even before the discovery of the electron. In most scientific discussions, this difference in meaning is not important, since the context, thermodynamic vs. electrostatic, is clear.
But when one considers electrochemical cells, where boththermodynamic and electrostatic concepts are needed, it is necessary to distinguish clearlybetween these two conventions.When we are interested in thermodynamic aspects of electrochemical systems, we rationalize this difficulty by inventing a thermodynamic construct called the emf of the cellreaction. This quantity is assigned to the reaction (not to the physical cell); hence it has adirectional aspect. In a formal way, we also associate a given chemical reaction with eachcell schematic. For the one in (2.1.17), the reaction isZn + 2AgCl -> Z n 2 + + 2Ag + 2 С Г(2.1.22)The right electrode corresponds to reduction in the implied cell reaction, and the left electrode is identified with oxidation.
Thus, the reverse of (2.1.22) would be associated withthe opposite schematic:Ag/AgCl/Cl"(a = 1), Zn 2 + (« = 1)/Zn(2.1.23)The cell reaction emf, £ rxn , is then defined as the electrostatic potential of the electrodewritten on the right in the cell schematic with respect to that on the left.For example, in the cell of (2.1.17), the measured potential difference is 0.985 V andthe zinc electrode is negative; thus the emf of reaction 2.1.22, the spontaneous direction,is +0.985 V. Likewise, the emf corresponding to (2.1.23) and the reverse of (2.1.22) is—0.985 V.
By adopting this convention, we have managed to rationalize an (observable)electrostatic quantity (the cell potential difference), which is not sensitive to the direction2.1 Basic Electrochemical Thermodynamics49of the cell's operation, with a (defined) thermodynamic quantity (the Gibbs free energy),which is sensitive to that direction. One can avoid completely the common confusionabout sign conventions of cell potentials if one understands this formal relationship between electrostatic measurements and thermodynamic concepts (3,4).Because our convention implies a positive emf when a reaction is spontaneous,AG = -nFEr,(2.1.24)or as above, when all substances are at unit activity,AG° = -(2.1.25)where E®xn is called the standard emf of the cell reaction.Other thermodynamic quantities can be derived from electrochemical measurementsnow that we have linked the potential difference across the cell to the free energy. Forexample, the entropy change in the cell reaction is given by the temperature dependenceof AG:дс -P(2.1.26)hence(2.1.27)and(2.1.28)AH = AG + TAS = nF\ TThe equilibrium constant of the reaction is given byRT\nKrxn=-AG°=(2.1.29)Note that these relations are also useful for predicting electrochemical properties fromthermochemical data.
Several problems following this chapter illustrate the usefulness ofthat approach. Large tabulations of thermodynamic quantities exist (5-8).2.1.4Half-Reactions and Reduction PotentialsJust as the overall cell reaction comprises two independent half-reactions, one might thinkit reasonable that the cell potential could be broken into two individual electrode potentials.
This view has experimental support, in that a self-consistent set of half-reactionemfs and half-cell potentials has been devised.To establish the absolute potential of any conducting phase according to definition, one must evaluate the work required to bring a unit positive charge, without associated matter, from the point at infinity to the interior of the phase.
Although thisquantity is not measurable by thermodynamically rigorous means, it can sometimes beestimated from a series of nonelectrochemical measurements and theoretical calculations, if the demand for thermodynamic rigor is relaxed. Even if we could determinethese absolute phase potentials, they would have limited utility because they would50Chapter 2. Potentials and Thermodynamics of Cellsdepend on magnitudes of the adventitious fields in which the phase is immersed (seeSection 2.2).
Much more meaningful is the difference in absolute phase potentials between an electrode and its electrolyte, for this difference is the chief factor determining the state of an electrochemical equilibrium. Unfortunately, we will find that it alsois not rigorously measurable. Experimentally, we can find only the absolute potentialdifference between two electronic conductors. Still, a useful scale results when onerefers electrode potentials and half-reaction emfs to a standard reference electrode featuring a standard half-reaction.The primary reference, chosen by convention, is the normal hydrogen electrode(NHE), also called the standard hydrogen electrode (SHE):+Pt/H2(a = 1)/Н (я - 1)(2.1.30)Its potential (the electrostatic standard) is taken as zero at all temperatures.
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