Electrochemical reaction equilibrium

We now wish to apply the principles of thermodynamics to determine the minimum electrical work needed or the maximum electrical work obtained in these systems at equilibrium. The differential electrical work can be related to the electric potential difference between the cathode and the anode, E, and the differential amount of charge transferred, d(J, as follows  

The sign convention for Equation (9.30) is chosen so that when the cathode has a positive potential with respect to the anode, the system can generate useful work, while a negative potential indicates that work is required for the process to proceed. 

Electrons that carry the charge in the external circuit result from the oxidation halfreaction thus, the differential charge transferred can be related to the extent of reaction as follows  

We can apply the fugacity coefficient formulation for gases and the activity coefficient formulation for liquids as we did in Section 9.5. Assuming the activity of the solids in the system is 1, this expression becomes  

Systems with solid solutions will need a solid term in Equation (9.32) as well. Recall that the fugacity coefficient formulation uses a standard-state fugacity for the vapor of 1 bar, so all units of pressure are in bar. Electrochemical cells typically operate under ideal gas conditions, so we will assume (pi = 1. For processes at high pressure, the development that follows should be modified to include the fugacity coefficient as well. Additionally, in dilute solutions, the activity of the solvent (yx), is approximately 1. 

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The electrochemical reaction equilibrium condition in phase a can be written by separating the electrons from other reacting species as... 

At open-circuit, the current in the cell is 2ero, and species in adjoining phases are in equilibrium. Eor example, the electrochemical potential of electrons in phases d and P are identical. Furthermore, the two electrochemical reactions are equilibrated. Thus,... 

Thus the tendency for an electrochemical reaction at a metal/solution interface to proceed in a given direction may be defined in terms of the relative values of the actual electrode potential E (experimentally determined and expressed with reference to the S.H.E.) and the reversible or equilibrium potential E, (calculated from E and the activities of the species involved in the equilibrium). 

For simplicity a cell consisting of two identical electrodes of silver immersed in silver nitrate solution will be considered first (Fig. 1.20a), i.e. Agi/AgNOj/Ag,. On open circuit each electrode will be at equilibrium, and the rate of transfer of silver ions from the metal lattice to the solution and from the solution to the metal lattice will be equal, i.e. the electrodes will be in a state of dynamic equilibrium. The rate of charge transfer, which may be regarded as either the rate of transfer of silver cations (positive charge) in one direction, or the transfer of electrons (negative charge) in the opposite direction, in an electrochemical reaction is the current I, so that for the equilibrium at electrode I... 

For the non-electrochemical reaction 1.119, the equilibrium constant (K) for the reaction is written as... 

Exchange Current Density (/ o) the rate of exchange of electrons (expressed as a current per unit area) between the two components of a single electrochemical reaction when the reaction is in equilibrium. The exchange current density flows only at the equilibrium potential. 

Nemst Equation the thermodynamic relationship between the equilibrium potential of an electrochemical reaction and the activities of the species involved in that reaction. 

Potential-pH Equilibrium Diagram (Pourbaix Diagram) diagram of the equilibrium potentials of electrochemical reactions as a function of the pH of the solution. The diagram shows the phases that are thermodynamically stable when a metal reacts with water or an aqueous solution of specified ions. 

Electrical methods of analysis (apart from electrogravimetry referred to above) involve the measurement of current, voltage or resistance in relation to the concentration of a certain species in solution. Techniques which can be included under this general heading are (i) voltammetry (measurement of current at a micro-electrode at a specified voltage) (ii) coulometry (measurement of current and time needed to complete an electrochemical reaction or to generate sufficient material to react completely with a specified reagent) (iii) potentiometry (measurement of the potential of an electrode in equilibrium with an ion to be determined) (iv) conductimetry (measurement of the electrical conductivity of a solution). 

Similarly to chemical reactions, it is possible to treat electrochemical reactions in equilibrium with the help of the thermodynamics. 

As shown in Fig. 33, the decreasing mechanism of this fluctuation is summarized as follows At a place on the electrode surface where metal dissolution happens to occur, the surface concentration of the metal ions simultaneously increases. Then the dissolved part continues to grow. Consequently, as the concentration gradient of the diffusion layer takes a negative value, the electrochemical potential component contributed by the concentration gradient increases. Here it should be noted that the electrochemical potential is composed of two components one comes from the concentration gradient and the other from the surface concentration. Then from the reaction equilibrium at the electrode surface, the electrochemical potential must be kept constant, so that the surface concentration component acts to compensate for the increment of the concen-... 

Models and theories have been developed by scientists that allow a good description of the double layers at each side of the surface either at equilibrium, under steady-state conditions, or under transition conditions. Only the surface has remained out of reach of the science developed, which cannot provide a quantitative model that describes the surface and surface variations during electrochemical reactions. For this reason electrochemistry, in the form of heterogeneous catalysis or heterogeneous catalysis has remained an empirical part of physical chemistry. However, advances in experimental methods during the past decade, which allow the observation... 

The second chapter is by Aogaki and includes a review of nonequilibrium fluctuations in corrosion processes. Aogaki begins by stating that metal corrosion is not a single electrode reaction, but a complex reaction composed of the oxidation of metal atoms and the reduction of oxidants. He provides an example in the dissolution of iron in an acidic solution. He follows this with a discussion of electrochemical theories on corrosion and the different techniques involved in these theories. He proceeds to discuss nonequilibrium fluctuations and concludes that we can again point out that the reactivity in corrosion is determined, not by its distance from the reaction equilibrium but by the growth processes of the nonequilibrium fluctuations. ... 

The Gibbs free energy for the reaction is related to the equilibrium cell potential ( 0) (Equation 6.4). For the reaction between hydrogen and oxygen to produce water, n, the number of electrons per molecule participating in the electrochemical reaction is 2 and AG has a value of —37.2 kJ mol giving Eq a value of 1.23 V... 

For thermodynamic reasons, an electrochemical reaction can occur only within a dehnite region of potentials a cathodic reaction at electrode potentials more negative, an anodic reaction at potentials more positive than the equilibrium potential of that reaction. This condition only implies a possibility that the electrode reaction will occur in the corresponding region of potentials it provides no indication of whether the reaction will actually occur, and if so, what its rate will be. The answers are provided not by thermodynamics but by electrochemical kinetics. 

Other types of polarization are caused by specific features in the various steps of the electrochemical reaction that produce a potential shift relative to the effective equilibrium potential (i.e., that which already accounts for the prevailing values of surface concentrations). These types of polarization, which may differ in character, are jointfy termed activation polarization. The value of activation polarization is sometimes called the overvoltage (this term should be reserved for the complete ceU see Section 2.5.2). 

Experimental studies in electrochemistry deal with the bulk properties of electrolytes (conductivity, etc.) equilibrium and nonequilibrium electrode potentials the structure, properties, and condition of interfaces between different phases (electrolytes and electronic conductors, other electrolytes, or insulators) and the namre, kinetics, and mechanism of electrochemical reactions. 

Electrochemical reactions differ fundamentally from chemical reactions in that the kinetic parameters are not constant (i.e., they are not rate constants ) but depend on the electrode potential. In the typical case this dependence is described by Eq. (6.33). This dependence has an important consequence At given arbitrary values of the concentrations d c, an equilibrium potential Eq exists in the case of electrochemical reactions which is the potential at which substances A and D are in equilibrium with each other. At this point (Eq) the intermediate B is in common equilibrium with substances A and D. For this equilibrium concentration we obtain from Eqs. (13.9) and (13.11),... 

The rates of an electrochemical reaction at potentials away from the equilibrium value are given by Eq. (13.5), which in this case can be written as... 

Consider an electrochemical reaction of the type Red Ox + e under conditions when the chemical reaction (and equilibrium)... 

When the current is anodic, component Red is consumed and the equilibrium in the electrolyte close to the surface is disturbed reaction (13.37) will start to proceed from left to right, producing additional amounts of species Red. In this case the chemical precedes the electrochemical reaction. However, when the current is cathodic, substance Red is produced and the chemical reaction (13.37), now as a subsequent reaction, will occur from right to left. When component Ox rather than component Red is involved in the chemical reaction, this reaction will be the preceding reaction for cathodic currents, but otherwise all the results to be reported below remain valid. 

Equilibrium between substances A and Red will be preserved during current flow not only in the bulk solution but even near the electrode surface when the chemical reaction has a high exchange rate. Therefore, a change in surface concentration of the substance Red which occurs as a result of the electrochemical reaction will give... 

According to these equations, in kinetically controlled reactions the mean-square amplitude is about 10 V, while in reactions occurring under diffusion control it is almost an order of magnitude smaller. Thus, the size of electrochemical (thermal) equilibrium fluctuations is extremely small. 

The concentrations of the reactants and reaction prodncts are determined in general by the solution of the transport diffusion-migration equations. If the ionic distribution is not disturbed by the electrochemical reaction, the problem simplifies and the concentrations can be found through equilibrium statistical mechanics. The main task of the microscopic theory of electrochemical reactions is the description of the mechanism of the elementary reaction act and calculation of the corresponding transition probabilities. 

The ends of a correctly constructed electrochemical circuit measuring electrical potential difference must always have metals or conductors with identical chemical composition. It is usually reached by simple connection of two metals by copper wires. The inclusion between two metal conductors of a third metal conductor according to Volta s law does not change the difference of potentials at the output of a circuit. The difference of potentials in an electrochemical circuit at equilibrium is caused by the change of Gibbs free energy during the appropriate electrochemical reaction ... 

The exchange current density, /0- From equations (1.28) and (1,29) it is clear that /Q is a direct measure of the kinetics of the reaction at the equilibrium potential Er. A high exchange current density indicates a facile electrochemical reaction that will rapidly become limited by transport at potentials away from E°. 

The electrochemical detection of pH can be carried out by voltammetry (amper-ometry) or potentiometry. Voltammetry is the measurement of the current potential relationship in an electrochemical cell. In voltammetry, the potential is applied to the electrochemical cell to force electrochemical reactions at the electrode-electrolyte interface. In potentiometry, the potential is measured between a pH electrode and a reference electrode of an electrochemical cell in response to the activity of an electrolyte in a solution under the condition of zero current. Since no current passes through the cell while the potential is measured, potentiometry is an equilibrium method. 

The standard electrode potential [1] of an electrochemical reaction is commonly measured with respect to the standard hydrogen electrode (SHE) [2], and the corresponding values have been compiled in tables. The choice of this reference is completely arbitrary, and it is natural to look for an absolute standard such as the vacuum level, which is commonly used in other branches of physics and chemistry. To see how this can be done, let us first consider two metals, I and II, of different chemical composition and different work functions 4>i and 4>ii-When the two metals are brought into contact, their Fermi levels must become equal. Hence electrons flow from the metal with the lower work function to that with the higher one, so that a small dipole layer is established at the contact, which gives rise to a difference in the outer potentials of the two phases (see Fig. 2.2). No work is required to transfer an electron from metal I to metal II, since the two systems are in equilibrium. This enables us calculate the outer potential difference between the two metals in the following way. We first take an electron from the Fermi level Ep of metal I to a point in the vacuum just outside metal I. The work required for this is the work function i of metal I. 

We should like to define a work function of an electrochemical reaction which enables us to calculate outer potential differences in the same way for a metal-solution interface, and this work function should also refer to the vacuum. For this purpose we consider a solution containing equal amounts of Fe3+ and Fe2+ ions in contact with a metal M, and suppose that the reaction is at equilibrium. We now transfer an electron from the solution via the vacuum to the metal in the following way ... 

For a metal, the negative of the work function gives the position of the Fermi level with respect to the vacuum outside the metal. Similarly, the negative of the work function of an electrochemical reaction is referred to as the Fermi level Ep (redox) of this reaction, measured with respect to the vacuum in this context Fermi level is used as a synonym for electrochemical potential. If the same reference point is used for the metal s,nd the redox couple, the equilibrium condition for the redox reaction is simply Ep (metal)= Ep(redox). So the notion of a Fermi level for a redox couple is a convenient concept however, this terminology does not imply that there are free electrons in the solution which obey Fermi-Dirac statistics, a misconception sometimes found in the literature. 

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