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Electrochemistry Electrochemistry Department of Physical Chemistry, Institute of Chemistry, Eötvös Loránd University, Budapest, Hungary Professor Dr. György Inzelt Készült 2015-ben az ELTE Felsőoktatási Struktúraátalakítási Alapból támogatott programja keretében. Thermodynamic description of homogeneous and heterogeneous electrochemical systems. From the potential of cell reaction to the electrode potential 1. Introduction The term thermodynamics was introduced by William Thomson (1824–1907, from 1892 Lord Kelvin) in 1849 in order to emphasize the dynamic nature of heat, while working on the problem of conversion of heat to mechanical energy which had a high scientific and technologial relevance. Another field of exceptional interest in the 19th century was electrochemistry. The generation of electricity, the use of the current to induce chemical changes was something very new for the scientists. New elements were discovered by the help of electrolysis which opened up new vistas in chemistry. At the second half of the 19th century — due to the development of both disciplines — a bridge was established between thermodynamics and electrochemistry in which Walther Nernst (1864–1941), Josiah Willard Gibbs (1839–1903) and others played an outstanding role. Nevertheless, thermodynamics and electrochemistry are — in a certain extent — still treated separately at the universities. Thermodynamics applied in chemistry and called chemical thermodynamics is taught in the course of physical chemistry. It mainly covers phase and chemical equilibria, the spontaneous transformations 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. The reason for this lies in the special treatment necessary to describe the systems of charged species or interphases. First, at least one or two additional work terms appear in the fundamental equation of thermodynamics, i.e., beside the heat and mechanical work as well as the conversion of components due to a chemical reaction; electrical work and surface work should be considered. However, the real problem is caused by the electroneutrality principle. Fom this follows that an individual electrode potential, individual activity coefficients of ions, hydration energy of a single ion etc. cannot be determined. A further problems also arise, e.g., regarding the accurate determination of the equilibrium cell potential (electromotive force) due to the junction potential at liquid-liquid interfaces or the surface stress of solid electrodes. (We will return to these problems later.) The separate teaching of electrochemistry is also due 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 occuring in a flask and an electrochemical cell is the same chemical reaction, consequently the possible maximum work produced under the same conditions (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. 2. Definition of an electrochemical cell Electrochemical cells consist of at least two (usually metallic) electron conductors in contact with ionic conductors (electrolytes). The current flow 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 spontaneously and chemical energy is converted into electrical energy (Fig. 1), or they are operated as electrolytic cells (also called electrolysis cells), in which electrical energy is converted into chemical energy (Fig. 2). In both cases part of the energy becomes converted into (positive or negative) heat [1-7]. 2 Fig. 1. Galvanic cell from a hydrogen electrode (left) and a calomel electrode (right). Hydrogen electrode: platinized platinum (1), electrolyte, 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) solution (4) connected with an electrolyte. V is a high resistance voltmeter Cell reaction (spontaneous direction): Hg2Cl2 + H2 2Hg + 2HCl 3 Fig. 2. Electrolysis cell from a hydrogen electrode (left) and a calomel electrode (right). Hydrogen electrode: platinized platinum (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 power source (battery or potentiostat) Cell reaction (forced direction): 2Hg + 2HCl Hg2Cl2 + H2 3. 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 + Zn Cu + ZnSO4 (1) We will see that copper deposits on the surface of the zinc granule. Eventually all the metallic zinc will be dissolved, and copper metal deposit will appear instead if CuSO4 is added at high excess. During this process an increase of temperature of the solution (heat evolution) can be measured (Fig. 3). There is no useful work, the energy liberated will be 4 converted into heat. In an electrochemical cell the same reaction can be executed in such a way that electrical energy (work) can be generated beside heat (Figs. 4 and 5). Fig. 3 A Zn granule in water. Temperature: 23.7 oC (actual room temperature). 5 Then CuSO4 solution of the same temperature was added to the system. Due to the chemical reaction between Zn and CuSO4, the reaction heat causes an increase of temperature upto 36.2 oC within 2 min. A red colored deposition appears on the original silvery sheen Zn granule, i.e., Cu deposited on the Zn granule. Fig. 4 The photo of a very simple Daniell cell when there is no connection (salt bridge) between the electrolytes. Of course, in this case the voltmeter shows 0 V. 6 Fig. 5 The same cell shown in Fig. 3 when the two compartments are connected with a salt bridge. The measured voltage was 1.062 V. Please note that the simplest salt bridge was applied, i.e., a just a wool string soaked in aqueous KCl solution. The cell consists of two beakers containing CuSO4 and ZnSO4 solutions in which Cu and Zn plates were immersed, respectively. The general form of an stoichiometric equation of a chemical reaction — which is called cell reaction if it proceeds in an electrochemical cell — can be written as follows [2]: α α ∑ ∑ 휈i Ai = 0 α i (2) where Ai is for the chemical formula of i-th species participating in the reaction and νi is the respective stoichiometric number which is negative for reactants and positive for the products, and α denotes the phases. Homogeneous reactions occur in a single phase α, while heterogeneous reactions involve two or more phases (α, β, γ etc.). Because electrochemical cell reactions belong to the latter category, it is useful to consider the general case. The Gibbs energy of the (cell) reaction [1- 4] can be expressed as 휕퐺 ( ) = Δ퐺 = ∑ ∑ 휈α휇α 휕휉 i i 푝,푇 α i (3) where G is the Gibbs energy (free enthalpy) of the reaction and i is the chemical potential of i-th species in phase α. At equilibrium between each contacting phases for the common constituents holds the relation: α α ∑ ∑ 휈i 휇i = 0 α i (4) If we consider a cell without liquid junction [8] — which is in fact nonexistent but the effect of the liquid junction potential can be made negligible — we may write as follows α α Δ퐺 = ∑ ∑ 휈i 휇i = −푛퐹퐸cell α i (5) 7 where n is the charge number of the cell reaction, F is the Faraday constant, and 퐸cell 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 νi, 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, AgCl + ½ H2 Ag + HCl n = 1 (6) 2AgCl + H2 2Ag + 2HCl n = 2 (7) Please note that 퐸cell always has the same value independent of the formulation of the reaction, while G is proportional to the amount of substances involved. The minus (–) sign in equation (5) is a convention, i.e., for a spontaneous reaction, where G is negative, 퐸cell is positive. The expression, „cell reaction” is used almost exclusively for the spontaneous reactions occurring in galvanic cells. However, also in electrolysis cells chemical transformations take place, when current is passed through the cell from an external source. Evidently, we may also speak of cell reactions even in this case, albeit additional energy is needed for the reaction to proceed since ΔG > 0. The cell reaction in a galvanic cell is spontaneous, i.e., ΔG is negative. The reaction equation should be written in such a way that ΔG < 0 when it proceeds from left to right. The peculiarity of the cell reaction is that the oxidation and reduction take place spatially separated at the electrodes in such a way that they are interconnected by the ion transport through the solution separating the two electrodes. They are called half-reactions or electrode reactions. Oxidation takes place at the anode, and reduction at the cathode. Taking into account the relationship between µi and the relative activity of species i, ai, i.e., 휇i = 휇i + 푅푇 ln 푎i (8) where 휇i is the standard chemical potential of species i, R is the gas constant and T is the thermodynamic temperature, it follows that (for the sake of simplicity neglecting the indication of phases further on) 1 푅푇 푅푇 퐸 = − ∑ 휈 휇 − ∑ 휈 ln 푎 = 퐸 − ∑ 휈 ln 푎 (9) cell 푛퐹 i i 푛퐹 i i cell 푛퐹 i i Now we have the relationship between the potential of cell reaction (퐸cell) and the composition of the chemical system, and introduced the standard potential of cell reaction (퐸cell) [1-7, 9-11].
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