ChemTexts (2014) 1:2 DOI 10.1007/s40828-014-0002-9 LECTURE TEXT Crossing the bridge between thermodynamics and electrochemistry. From the potential of the cell reaction to the electrode potential Gyo¨rgy Inzelt Received: 18 September 2014 / Accepted: 8 October 2014 Ó Springer International Publishing 2014 Abstract Thermodynamics plays a similar role in physical technological relevance. Another field of exceptional chemistry like mathematics in science, however, the inherent interest in the 19th century was electrochemistry. The link between thermodynamics and electrochemistry is not generation of electricity, the use of the current to induce entirely obvious. Less attention is paid to such physical chemical changes was something very new for the scien- quantities as pressure, volume, enthalpy, chemical potential tists. New elements were discovered by the help of elec- etc. in electrochemistry; on the other hand new quantities trolysis which opened up new vistas in chemistry. At the (charge, current, electric potential etc.) and terms (galvanic second half of the 19th century—due to the development of cell. electrode, ion etc.) appear. It is the main goal of this both disciplines—a bridge was established between ther- lecture to present a systematic thermodynamical treatment modynamics and electrochemistry in which Walther Nernst regarding the electrochemical cells; and to give the defini- (1864–1941), Josiah Willard Gibbs (1839–1903) and others tions accepted presently for physical quantities, e.g., poten- played an outstanding role. Nevertheless, thermodynamics tial of the cell reaction, electrode potential, electrochemical and electrochemistry are—in a certain extent—still treated potential as well as terms such as electrode. separately at the universities. Thermodynamics applied in chemistry and called chemical thermodynamics is taught in Keywords Electrochemical cells Á Potential of the cell the course of physical chemistry. It mainly covers phase reaction Á Electrodes Á Electrode potential Á Interfacial and chemical equilibria, the spontaneous transformations equilibria Á Electrochemical potentials of one phase to another or the direction of spontaneous chemical reactions. Electrochemistry is either a separate part of this course or being held as an individual lecture. Introduction The reason for this lies in the special treatment necessary to describe the systems of charged species or interphases. The term thermodynamics was introduced by William First, at least one or two additional work terms appear in Thomson (1824–1907, from 1892 Lord Kelvin) in 1849 in the fundamental equation of thermodynamics, i.e., beside order to emphasize the dynamic nature of heat, while the heat and mechanical work as well as the conversion of working on the problem of conversion of heat to components due to a chemical reaction; electrical work and mechanical energy which had a high scientific and surface work should be considered. However, the real problem is caused by the electroneutrality principle. From this follows that an individual electrode potential, indi- Electronic supplementary material The online version of this vidual activity coefficients of ions, hydration energy of a article (doi:10.1007/s40828-014-0002-9) contains supplementary material, which is available to authorized users. single ion etc. cannot be determined. Further problems also arise, e.g., regarding the accurate determination of the G. Inzelt (&) equilibrium cell potential (electromotive force) due to the Department of Physical Chemistry, Institute of Chemistry, junction potential at liquid–liquid interfaces or the surface Eo¨tvo¨s Lora´nd University, Pa´zma´ny Pe´ter se´ta´ny 1/A, Budapest 1117, Hungary stress of solid electrodes. (We will return to these problems e-mail: [email protected] later). The separate teaching of electrochemistry is also due 123 2 Page 2 of 11 ChemTexts (2014) 1:2 to the fact that several new terms have to be introduced and defined. The latter seems to be an easy task, however, it is not. Perhaps it is enough to mention the exact and perfect definition of the term electrode. The chemical reaction occurring in a flask and an elec- trochemical cell is the same chemical reaction, consequently the possible maximum work produced under the same con- ditions (temperature, pressure etc.) should be the same. Therefore, we can take this as a starting-point. In fact, this idea serves as the inherent link between the ‘‘classical’’ thermodynamics and electrochemical thermodynamics. Definition of an electrochemical cell Electrochemical cells consist of at least two (usually metallic) electron conductors in contact with ionic conductors (elec- trolytes). Beside metals the electron conductor can be also different forms of carbon, semiconductor materials etc. (see Fig. 1 Galvanic cell from a hydrogen electrode (left) and a calomel later), while the electrolyte usually an aqueous or nonaqueous electrode (right). Hydrogen electrode: platinized platinum 1 electro- solution of compounds which dissociate into ions in the sol- lyte, e.g., HCl (aq) 2 Calomel electrode: (Hg (liq) |Hg2Cl2 (s)| KCl (aq): metal wire (1), calomel [Hg2Cl2](2), Hg (liq) (3) and KCl (aq) vent and which provides by this ionic conductivity. Melts, solution (4) connected with an electrolyte. V is a high resistance ionic liquids and solid electrolytes are also used as electro- voltmeter. Cell reaction (spontaneous direction): Hg2Cl2 ? H2 lytes. For the sake of simplicity we restrict our examples to 2Hg ? 2HCl aqueous electrolyte solutions below. The current flows through the electrochemical cells may be zero or non-zero. Electrochemical cells with current flow can operate either as galvanic cells, in which chemical reactions proceed sponta- neously and chemical energy is converted into electrical energy, or they are operated as electrolytic cells (also called electrolysis cells), in which electrical energy is converted into chemical energy. In both cases part of the energy becomes converted into (positive or negative) heat [1–7](Figs.1, 2). The reaction occurring in electrochemical cells: the cell reaction and its thermodynamic description If we drop a piece of zinc into the aqueous solution of CuSO4 the following chemical reaction will take place spontaneously CuSO4 þ Zn Cu þ ZnSO4 ð1Þ We will see that copper deposits on the surface of the Fig. 2 Electrolysis cell from a hydrogen electrode (left) and a zinc granule. Eventually all the metallic zinc will be dis- calomel electrode (right). Hydrogen electrode: platinized platinum solved, and copper metal deposit will appear instead if (1), electrolyte, e.g., HCl (aq) (2). Calomel electrode: metal wire (1), calomel [Hg2Cl2](2), Hg (liq) (3) and KCl (aq) solution (4). E is a CuSO4 is added at high excess. During this process an power source (battery or potentiostat) Cell reaction (forced direction): increase of temperature of the solution (heat evolution) can 2Hg ? 2HCl Hg2Cl2 ? H2 be measured. There is no useful work, the energy liberated will be converted into heat. In an electrochemical cell the The general form of an stoichiometric equation of a same reaction can be executed in such a way that electrical chemical reaction—which is called cell reaction if it energy (work) can be generated beside heat (see Fig. 3 later proceeds in an electrochemical cell—can be written as as well as Figs. 4–8 in the Supplementary material). follows [2]: 123 ChemTexts (2014) 1:2 Page 3 of 11 2 X X a a DG ¼ mi li ¼nFEcell ð5Þ a i where n is the charge number of the cell reaction, F is the Faraday constant, and Ecell is the potential of the cell reaction (SI unit is V). The charge number which is the number of electrons transferred in the cell reaction— which is generally mi, since it is the stoichiometric number of the electron in the electrode reaction—depends on the way of the formulation of the cell reaction. For instance, 1 AgCl þ =2 H2 Ag þ HCl n ¼ 1 ð6Þ 2AgCl þ H2 2Ag þ 2HCl n ¼ 2 ð7Þ Please note that Ecell always has the same value inde- Fig. 3 The Daniell cell. Processes occurring during the measure- pendent of the formulation of the reaction, while DG is ments of the cell voltage with a high resistance voltmeter or when the proportional to the amount of substances involved. The two electrodes are connected by a salt bridge and a metal wire minus (–) sign in Eq. (5) is a convention, i.e., for a G E X X spontaneous reaction, where D is negative, cell is a a positive. The expression, ‘‘cell reaction’’ is used almost mi Ai ¼ 0 ð2Þ a i exclusively for the spontaneous reactions occurring in galvanic cells. However, also in electrolysis cells chemical where A is for the chemical formula of ith species par- i transformations take place, when current is passed through ticipating in the reaction and m is the respective stoichi- i the cell from an external source. Evidently, we may also ometric number which is negative for reactants and speak of cell reactions even in this case, albeit additional positive for the products, and a denotes the phases. For energy is needed for the reaction to proceed since instance, for reaction (1)A represents CuSO with m = i 4 i DG [ 0. The cell reaction in a galvanic cell is spontane- -1, Zn with m =-1. Cu with m = 1 and ZnSO with i i 4 ous, i.e., DG is negative. The reaction equation should be m = 1, respectively, where the salts are in the same i written in such a way that DG \ 0 when it proceeds from aqueous phase while the metals form the respective solid left to right. The peculiarity of the cell reaction is that the metallic phases (Cu and Zn). In the case of the Daniell cell oxidation and reduction take place spatially separated at (see later), where the same reaction occurs, the components the electrodes in such a way that they are interconnected and their respective stoichiometric numbers are the same, by the ion transport through the solution separating the however, CuSO and ZnSO solutions form two different 4 4 two electrodes.