Cell Potential and Free Energy

10 Key excerpts on "Cell Potential and Free Energy"

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  Electrochemical Engineering

  • Thomas F. Fuller, John N. Harb(Authors)
  • 2018(Publication Date)
  • Wiley

    (Publisher)

  Chapter 2 Cell Potential and Thermodynamics The objectives of this chapter are to introduce the poten- tial of an electrochemical cell and to develop a relationship between the cell potential and its chemical environment at equilibrium. The thermodynamics of electrochemical sys- tems is no different than that of other systems—a dynamic equilibrium exists where an infinitesimal change in any driving force will force the system to shift reversibly to establish a new balance. One characteristic of electro- chemical systems is that charged species and electron- transfer reactions are included. Hence, a new property, the electrical state, is important in describing equilibrium in electrochemical systems. For an electrochemical system to be in equilibrium, there can be no net current flow. The condition of a cell where the external current is zero is termed open circuit, and the associated potential is the open-circuit potential. The equilibrium potential that we are interested in here is even more restrictive than the open-circuit potential. Not only is the external current zero, but a more general dynamic equilibrium exists in the cell. The equilibrium or thermodynamic potential is a critical characteristic that affects the design and operation of electrochemical devices. In this chapter, we use thermodynamics to calcu- late the cell potential as a function of the chemical com- ponents that make up the cell. As you will remember, an electrochemical cell is used to convert between chemical energy and electrical energy in order to (i) produce energy from stored chemicals, or (ii) use energy to produce chemical changes. The distinction pivots around the ther- modynamic potential of the cell. 2.1 ELECTROCHEMICAL REACTIONS An electrochemical reaction is a reaction where the transfer of electrons from a species being oxidized to a species undergoing reduction takes place through an electronic conductor.

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  Electrochemical Methods

  Fundamentals and Applications

  • Allen J. Bard, Larry R. Faulkner, Henry S. White(Authors)
  • 2022(Publication Date)
  • Wiley

    (Publisher)

  61 2 Potentials and Thermodynamics of Cells In Chapter 1, we focused on potential as an electrochemical variable. Here we look more closely at the physical meaning of potential, the origins of potential differences, and access, through potential, to chemical information. Initially, we will approach these matters through thermodynamics, which will teach us that potential differences manifest free energy changes. That linkage will open a path to chemical information through electrochemical measurements. Subsequently, we will explore the physical mechanism by which potential differences are established, and we will gain insights relevant to the measurement and control of potential. 2.1 Basic Electrochemical Thermodynamics 2.1.1 Reversibility Thermodynamics strictly applies only to systems at equilibrium, which involves the idea that a process can move readily in opposite directions from the equilibrium position. The adjective reversible relates to this core idea; however, the word carries several different, but related, mean-ings. We distinguish three of them now. (a) Chemical Reversibility Consider the electrochemical cell shown in Figure 1.1.1 b : Pt ∕ H 2 ∕ H + , Cl − ∕ AgCl ∕ Ag (2.1.1) Experimentally, one finds that the difference in potential between the silver wire and the platinum wire is 0.222 V when all substances are in their standard states.

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  Nanostructured Ceramic Oxides for Supercapacitor Applications

  • Avinash Balakrishnan, K.R.V. Subramanian(Authors)
  • 2014(Publication Date)
  • CRC Press

    (Publisher)

  The force on the electrons causing them to move is referred to as electromotive force or EMF (E). One can measure the magnitude of the EMF causing electron flow by measuring the voltage. Electricity is generated due to the electric potential difference between the two electrodes and this difference in potential is called the cell potential. This electric potential varies with temperature, pressure, and concentration of the cell. As mentioned earlier, these redox reactions can be broken down into two half-reactions. 40–43 2.9 Standard Half-Cell Potential When a net reaction proceeds in an electrochemical cell, oxidation occurs at one electrode (the anode) and reduction takes place at the other electrode (the cathode). The electrochemical cell consists of two half-cells joined together by an external circuit through which electrons flow and an internal pathway that allows ions to migrate between them so as to preserve electroneutrality. Cell potential is the difference between anode and cathode potential: 44–47 = -E E E cell cathode anode (2.19) when half-reactions are written as reductions. Example, → + + -Zn Zn e 2 , 2 = + + E V 0.76 Zn Zn 2 (2.20) + → + -H e H 2 2 , 2 = + ( ) E V 0.00 SHE 0 (2.21) The net reaction is, + → + + + Zn H Zn H 2 2 2 (2.22) = -+ = -+ = -( )       + E E E V 0.76 0.00 0.76 Zn Zn SHE cell 0 2 (2.23) 24 Nanostructured Ceramic Oxides for Supercapacitor Applications 2.10 Concentration Effects on Cell Potential (Nernst Equation) Nernst equation relates free energy change in a chemical reaction to the EMF of a cell. To derive this equation, a reduction reaction is considered as a suitable example.

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  Electrochemical Methods

  Fundamentals and Applications

  • Allen J. Bard, Larry R. Faulkner(Authors)
  • 2012(Publication Date)
  • Wiley

    (Publisher)

  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 direction  DG   nF E   DG   charge passed  reversible potential difference 48  Chapter 2. Potentials and Thermodynamics of Cells of 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 confusion about sign conventions of cell potentials if one understands this formal relationship be- tween electrostatic measurements and thermodynamic concepts (3,4). Because our convention implies a positive emf when a reaction is spontaneous, (2.1.24) or as above, when all substances are at unit activity, (2.1.25) where is called the standard emf of the cell reaction. Other thermodynamic quantities can be derived from electrochemical measurements now that we have linked the potential difference across the cell to the free energy. For example, the entropy change in the cell reaction is given by the temperature dependence of G: (2.1.26) hence (2.1.27) and (2.1.28) The equilibrium constant of the reaction is given by (2.1.29) Note that these relations are also useful for predicting electrochemical properties from thermochemical data. Several problems following this chapter illustrate the usefulness of that approach. Large tabulations of thermodynamic quantities exist (5–8). 2.1.4 Half-Reactions and Reduction Potentials Just as the overall cell reaction comprises two independent half-reactions, one might think it reasonable that the cell potential could be broken into two individual electrode poten- tials. This view has experimental support, in that a self-consistent set of half-reaction emfs and half-cell potentials has been devised.

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  Analytical and Physical Electrochemistry

  • Hubert H. Girault(Author)
  • 2002(Publication Date)
  • EPFL PRESS

    (Publisher)

  1 Electrochemical Potential CHAPTER 1 ELECTROCHEMICAL POTENTIAL 1.1 ELECTROCHEMICAL POTENTIAL OF IONS The chemical potential is the main thermodynamic tool used to treat chemical equilibria. It allows us to predict whether a reaction can happen spontaneously, or to predict the composition of reactants and products at equilibrium. In this book, we shall consider electrochemical reactions that involve charged species, such as electrons and ions. In order to be able to call on the thermochemical methodology, it is convenient to define first of all the notion of electrochemical potential, which will be the essential tool used for characterising the reactions at electrodes as well as the partition equilibria between phases. To do this, let us recall first of all, what a chemical potential is, and in particular the chemical potential of a species in solution. 1.1.1 Chemical potential Thermodynamic definition Let us consider a phase composed of chemical species j. By adding to this phase one mole of a chemical species i whilst keeping the extensive properties of the phase constant, i.e. the properties linked to its dimensions (V, S, n j ), we increase the internal energy U of the phase. In effect, we are adding the kinetic energy E trans , the rotational energy E rot and the vibrational energy E vib if i is a molecule, the interaction energy between the species E int , perhaps the electronic energy E el if we have excited electronic states and the energy linked to the atomic mass of the atoms E mass if we consider radiochemical aspects, such that: U E E E E E E = + + + + + trans rot vib el mass int (1.1) Thus, we define the chemical potential of the species i as being the increase in inter- nal energy due to the addition of this species µ ∂ ∂ i i V S n U n j i =       ≠ , , (1.2) In general, the variation in internal energy can be written in the form of a differential:

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  Physical Chemistry

  How Chemistry Works

  • Kurt W. Kolasinski(Author)
  • 2016(Publication Date)
  • Wiley

    (Publisher)

  For example, for Eq. (15.79) (15.82) A reaction producing H + has a value of E ° less than E °' by 0.414 V/ z per mole of H + formed, and is more spontaneous at pH 7 than at pH 0. Note that corrections of this type only need to be made when trying to compare values of standard electrode potentials from one scale to the other, or when calculations of expected cell potentials must be constructed by using standard potentials from both scales. 15.8.2 Gibbs energy change in terminal respiratory cycle The conversion of nicotinamide adenine dinucleotide, reduced form (NADH) to its oxidized form (NAD +) releases two electrons, which are used to reduce O 2 to H 2 O. The half-reactions involved are and which corresponds to the overall reaction The Gibbs energy change is Energy can effectively be stored by running an endothermic reaction, such as ATP synthesis (Δ r G°' = 31.4 kJ mol –1). Remember that energy is not released by breaking bonds. Rather, it is released when high-enthalpy species are transformed into lower-enthalpy species via chemical reactions, when weak bonds are replaced by stronger bonds. If the above electron transfers were performed in one step, much energy would be lost as heat. Performing it in a number of steps involving NADH, flavin adenine dinucleotide (FAD), cytochrome b, cytochrome c as well as cytochrome a and cytochrome a 3, releases the energy in smaller steps. This allows for the synthesis of several molecules of ATP along the way in a highly efficient manner, with minimal losses to heat generation. 15.8.3 Membrane potentials Nerve cells and muscle cells are excitable. They can transmit a change of electrical potential along their membranes. The electrical potential established by the difference in ionic concentrations across the membrane is known as the membrane potential. Differences in ionic concentrations inside and outside the cell can be established because the cell membrane has different permeabilities for different ions

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  Polymer Electrolyte Fuel Cells

  Physical Principles of Materials and Operation

  • Michael Eikerling, Andrei Kulikovsky(Authors)
  • 2014(Publication Date)
  • CRC Press

    (Publisher)

  (1.9) 4 Polymer Electrolyte Fuel Cells Equation 1.8 together with Equation 1.9 form the famous Nernst equation , which relates the equilibrium potential difference of an electrochemical cell to standard equilibrium potential, cell composition and temperature. In deriving Equation 1.8, it was assumed that both electrodes are made of identical metals and that they are in contact with electrolyte with identical composition and Galvani potential, . Therefore, specific terms, depending on chemical potentials of electrolyte protons or metal electrons will cancel out of this equation. Indeed, the difference in electrochemical potentials ˜ μ e − of metal electrons at cathode and anode is proportional to the EMF: ˜ μ c e − − ˜ μ a e − = μ c e − − μ a e − − F ( φ c , eq − φ a , eq ) = FE eq O 2 , H 2 . (1.10) If both electrodes are made of the same material, corresponding to the case consid-ered above, electrons must have the same chemical potential at anode and cathode, μ c e − = μ a e − . Therefore, the difference in electrochemical potential or EMF is equal to the difference in electrostatic Galvani potentials φ between the metal electrodes at equilibrium: E eq O 2 , H 2 = φ c , eq − φ a , eq . (1.11) This Galvani potential difference can be measured with a voltmeter. It represents the maximal driving force of the electron flux from anode to cathode. Since it is reasonable to assume that electron transport in metal wires occurs under negligible ohmic resistance losses, the potential difference between metal ports at anode and cathode is almost completely available to perform electrical work in electrical loads or appliances, indicated in Figure 1.1. The standard EMF of the H 2 / O 2 fuel cell is E 0 O 2 , H 2 = 1.23 V. In order for a constant electron current to flow through the external wiring, in the direction indicated in Figure 1.1, the difference in reactant gas compositions at the electrodes must be maintained in a steady state.

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  Electrochemical Kinetics

  Theoretical Aspects

  • Klaus J. Vetter(Author)
  • 2013(Publication Date)
  • Academic Press

    (Publisher)

  E Q U I L I B R I U M P O T E N T I A L S € , ¼ 17 13. The Electrochemical Potential ç Ü The electrochemical potential ç ß9 introduced by Guggenheim 1 » 2 can be used advantageously in many cases in place of the chemical potential ì } . As with ì, , ç, is also a partial molar quantity (for example, dG/dn,) . However, in the formation of ^ the reversible electrical work zjF-ö is also taken into consideration. Therefore, the electrochemical potential is by definition In Eq. (1.19), ö is the (inner) Galvani potential (Sections 3 and 4) of the phase in question and z, is the charge of the species s s in fundamental units with due consideration of the sign. F again is the faraday. For unchanged materials, æ , = 0 and thus ç, = ì ^ At equilibrium, the change in free enthalpy, AG = 0 , and there-fore Óí,ì, = 0. A quite analogous relationship exists during the attainment of an electrochemical equilibrium between Phases 1 and 2. This equilibrium is attained after an equilibrium Galvani potential difference å 0 = ÷ ö -2 ö has formed between the two phases. Then, one obtains* Thus, the reversible electrochemical work must be zero. The stoichiometric factors of the reaction products are again positive, those of the reacting substances negative. Equation (1.20) should only be applied to the reaction at one phase boundary, which gives the potential difference between these two phases. An application of Eq. (1.20) to all successive phase boundaries of a galvanic cell gives the equilibrium cell voltage only by the addition of all individual potential differences. Therefore, Eq. (1.11) and (1.20) are not equivalent in the method of their application, even though both lead to the same end results. While sign errors may happen easily in the calculation of the potential difference in Eq. (1.11), the formal application of Eq. (1.20) leads to the correct sign of the potential difference in every case.

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  Electrochemistry

  A Guide for Newcomers

  • Helmut Baumgärtel(Author)
  • 2019(Publication Date)
  • De Gruyter

    (Publisher)

  This effect will be the topic of this chapter. In Fig. 2.24(a) and (b), the shift of the cell potential in a galvanic cell and in an electrolytic cell is shown. Remember, there exists an activation energy for the transfer of charge across the interface. 2.5.3 Charge transfer and activation energy Now some questions appear: Which are the components of energy forming this bar-rier? and “ How is the heights of this barrier influenced by the potential of the elec-trode? ” Figures 2.25 and 2.26 give answers to these questions. Figure 2.25 a schematic illustration of the energies involved in the transfer of electrons across the electrode/ electrolyte interface at a redox electrode. It must be emphasized that no potential from outside is put on the metal. It is just the Galvani potential in the interior of the CI 2 +2e 2CI – 2H +2e +2e CI 2 φ 0 CI 2 /CI φ 0 H 2 /H E kl = E Z x + Σ |η| E Kl E 0 E Z E 0 – Σ |η| = η CI 2 η CI 2 η H 2 H 2 η H 2 2CI H 2 2H +2e Current Current Electrode potential (a) (b) Fig. 2.24: Schematic representation of the course of the overvoltage in the galvanic cell H 2 /HCl (a) and of the terminal potential difference in the HCl electrolytic cell (b). 66 2 Fundamentals Energy Electrolyte ( S 0 , S T ) η Me = –H e –Fφ Me = = –φ–Fψ Me Metal 2 3 Anode Cathode ξ E – η El = –(H T –H 0 +I)–F φ El Δ η = η Me –η El = = T.ΔS–Fη 1 E + (anode) Rigid double layer Fig. 2.25: Schematic representation of the energies that influence the electron transfer in a redox reaction. Electrolyte (S 0 ,S T ) i + Metal E + i – E – 3 2 1 ξ αFΔφ s (1–α)FΔφ s 0 E + 0 E – Rigid double layer +ZFΔφ s =–FΔφ s Fig. 2.26: The dependence of the anodic activation en-ergies E + and the cathodic activation energy E – on the potential difference Δ φ r in the rigid double layer. 2.5 Kinetics of electrode processes 67 metal that determines the energy level of the electron in the metal. Some further com-ments that are helpful for understanding are given in Figure 2.25.

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  Ion Exchange

  Highlights Of Russian Science

  • Dimitri Muraviev, Vladimir Gorshkov, Abraham Warshawsky(Authors)
  • 1999(Publication Date)
  • CRC Press

    (Publisher)

  ELECTROCHEMICAL AND TWIN CHEMICAL POTENTIALS AS THERMODYNAMIC DRIVING FORCES Yurii A. Kokotov Institute of Agrophysics, St. Petersburg, Russia ABSTRACT This paper discusses the problem of rigorous thermodynamic description of ionic systems in terms of ions as system constituents. This description can be based on the use of either electrochemical potentials (ECP) as a whole (without their division into chemical and electrical constituents), or twin chemical potentials (TCP) concept (introduced by the author) as thermodynamic driving forces of mass-transfer processes in ionic systems, including ion exchange. The main advantages of the approach proposed in comparison with traditional description of ionic systems is demonstrated and discussed. 1. INTRODUCTION Ionic systems represent the main and the most active part of the matter in the terrestrial environment. We can find different types of ionic systems ranging from relatively simple (e.g., ionic solutions and melts), to extremely complex. Some examples of the latter are solid crystalline substances like porous and layered crystals, glasses, natural and synthetic non-crosslinked polyelectrolytes, crosslinked polyelectrolyes (ion 847 848 KOKOTOV exchangers) and liquid ion exchangers. The thermodynamics of ionic systems (TIS) has been developed during over the last hundred years. Nevertheless, until now it is yet characterized by some unclear and difficult for understanding parts. The description of different ionic processes at the macroscopic level in terms of chemical potentials as their driving forces represents one of the most obscure and incomplete parts of modern thermodynamics. The general state-of-the-art of this problem will be considered below. The basic notion of TIS is the electrochemical potential (ECP) of the ion of "i" type determined through the internal energy of the system or by means of some other thermodynamic potentials, which (unlike non-ionic systems) must include the energy of the electric field.

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