Equilibrium electrochemical cell

L electromotive force, emf (in an electrochemical cell) equilibrium electrode potential in volts... 

Each electrode reaction, anode and cathode, or half-cell reaction has an associated energy level or electrical potential (volts) associated with it. Values of the standard equilibrium electrode reduction potentials E° at unit activity and 25°C may be obtained from the literature (de Bethune and Swendeman Loud, Encyclopedia of Electrochemistry, Van Nostrand Reinhold, 1964). The overall electrochemical cell equilibrium potential either can be obtained from AG values or is equal to the cathode half-cell potential minus the anode half-cell potential, as shown above. 

A special example of electrical work occurs when work is done on an electrochemical cell or by such a cell on the surroundings -w in the convention of this article). Themiodynamics applies to such a cell when it is at equilibrium with its surroundings, i.e. when the electrical potential (electromotive force emi) of the cell is... 

As seen in previous sections, the standard entropy AS of a chemical reaction can be detemiined from the equilibrium constant K and its temperature derivative, or equivalently from the temperature derivative of the standard emf of a reversible electrochemical cell. As in the previous case, calorimetric measurements on the separate reactants and products, plus the usual extrapolation, will... 

When the reaction between zinc and copper(II) sulphate was carried out in the form of an electrochemical cell (p. 94), a potential difference between the copper and zinc electrodes was noted. This potential resulted from the differing tendencies of the two metals to form ions. An equilibrium is established when any metal is placed in a solution of its ions. 

Electrochemical cells may be used in either active or passive modes, depending on whether or not a signal, typically a current or voltage, must be actively appHed to the cell in order to evoke an analytically usehil response. Electroanalytical techniques have also been divided into two broad categories, static and dynamic, depending on whether or not current dows in the external circuit (1). In the static case, the system is assumed to be at equilibrium. The term dynamic indicates that the system has been disturbed and is not at equilibrium when the measurement is made. These definitions are often inappropriate because active measurements can be made that hardly disturb the system and passive measurements can be made on systems that are far from equilibrium. The terms static and dynamic also imply some sort of artificial time constraints on the measurement. Active and passive are terms that nonelectrochemists seem to understand more readily than static and dynamic. 

Electrochemical cells are familiar—a flashlight operates on current drawn from electrochemical cells called dry cells, and automobiles are started with the aid of a battery, a set of electrochemical cells in tandem. The last time you changed the dry cells in a flashlight because the old ones were dead, did you wonder what had happened inside those cells Why does electric current flow from a new dry cell but not from one that has been used many hours We shall see that this is an important question in chemistry. By studying the chemical reactions that occur in an electrochemical cell we discover a basis for predicting whether equilibrium in a chemical reaction fa-... 

The value of this list is obvious. Any half-reaction can be combined with the reverse of another half-reaction (in the proportion for which electrons gained is equal to electrons lost) to give a possible chemical reaction. Our list permits us to predict whether equilibrium favors reactants or products. We would like to expand our list and to make it more quantitative. Electrochemical cells help us do this. 

Other measurements of AfG involve measuring AG for equilibrium processes, such as the measurement of equilibrium constants, reversible voltages of electrochemical cells, and phase equilibrium measurements. These methods especially come into play in the measurement of Afand AfG for ions in solution, which are processes that we will now consider. 

Measurement of Equilibrium Constants Electrochemical cells can be used to measure equilibrium constants for chemical reactions. For example, consider the cell... 

Chapters 7 to 9 apply the thermodynamic relationships to mixtures, to phase equilibria, and to chemical equilibrium. In Chapter 7, both nonelectrolyte and electrolyte solutions are described, including the properties of ideal mixtures. The Debye-Hiickel theory is developed and applied to the electrolyte solutions. Thermal properties and osmotic pressure are also described. In Chapter 8, the principles of phase equilibria of pure substances and of mixtures are presented. The phase rule, Clapeyron equation, and phase diagrams are used extensively in the description of representative systems. Chapter 9 uses thermodynamics to describe chemical equilibrium. The equilibrium constant and its relationship to pressure, temperature, and activity is developed, as are the basic equations that apply to electrochemical cells. Examples are given that demonstrate the use of thermodynamics in predicting equilibrium conditions and cell voltages. 

Figure 1. Sketch of an electrochemical cell whose equilibrium (open circuit) potential difference is AE. (a) Conventional configuration and (b) short-circuited configuration with an air gap. M and R are the electrodes, S is the solvent (electrolyte solution). Cu indicates the cables connecting the two electrodes to a measuring instrument (or to each other).

As a reaction proceeds toward equilibrium, the concentrations of its reactants and products change and AG approaches zero. Therefore, as reactants are consumed in a working electrochemical cell, the cell potential also decreases until finally it reaches zero. A dead battery is one in which the cell reaction has reached equilibrium. At equilibrium, a cell generates zero potential difference across its electrodes and the reaction can no longer do work. To describe this behavior quantitatively, we need to find how the cell emf varies with the concentrations of species in the cell. 

In this method the creation of defects is achieved by the application of ultrashort (10 ns) voltage pulses to the tip of an electrochemical STM arrangement. The electrochemical cell composed of the tip and the sample within a nanometer distance is small enough that the double layers may be polarized within nanoseconds. On applying positive pulses to the tip, the electrochemical oxidation reaction of the surface is driven far from equilibrium. This leads to local confinement of the reactions and to the formation of nanostructures. For every pufse applied, just one hole is created directly under the tip. This overcomes the restrictions of conventional electrochemistry (without the ultrashort pulses), where the formation of nanostructures is not possible. The holes generated in this way can then be filled with a metal such as Cu by... 

Potentiometric methods are based on the measurement of the potential of an electrochemical cell consisting of two electrodes immersed in a solution. Since the cell potential is measured under the condition of zero cmrent, usually with a pH/mV meter, potentiometry is an equilibrium method. One electrode, the indicator electrode, is chosen to respond to a particular species in solution whose activity or concentration is to be measured. The other electrode is a reference electrode whose half-cell potential is invariant. 

Having introduced matters pertaining to the electrochemical series earlier, it is only relevant that an appraisal is given on some of its applications. The coverage hereunder describes different examples which include aspects of spontaneity of a galvanic cell reaction, feasibility of different species for reaction, criterion of choice of electrodes to form galvanic cells, sacrificial protection, cementation, concentration and tempera lure effects on emf of electrochemical cells, clues on chemical reaction, caution notes on the use of electrochemical series, and finally determination of equilibrium constants and solubility products. 

Here, an electrochemical cell working under irreversible conditions is considered. Its emf invariably moves away from the equilibrium value, and if the cell is serving as a battery or source of electricity, then its voltage drops below the equilibrium value. If, on the other hand, the cell is in a place where electrolysis is occurring, then the voltage to be applied must exceed the equilibrium value. 

Analytical methods based upon oxidation/reduction reactions include oxidation/reduction titrimetry, potentiometry, coulometry, electrogravimetry and voltammetry. Faradaic oxidation/reduction equilibria are conveniently studied by measuring the potentials of electrochemical cells in which the two half-reactions making up the equilibrium are participants. Electrochemical cells, which are galvanic or electrolytic, reversible or irreversible, consist of two conductors called electrodes, each of which is immersed in an electrolyte solution. In most of the cells, the two electrodes are different and must be separated (by a salt bridge) to avoid direct reaction between the reactants. 

Redox potential (thermodynamic derivation). Suppose we take an electrochemical cell represented by Fig. 2.7. We shall now address the question of both the potential values and the equilibrium state that can be finally attained... 

For a redox reaction in an electrochemical cell the decrease in free enthalpy (- AG) is in accordance with the energy delivered by the transfer of electrons through an external circuit if this takes place in a reversible way, i.e., at a rate slow enough to allow complete attainment of equilibrium, the conversion of 1 gram mole will deliver an electrical energy of - AG = z FE. In total cell reaction mred, + n ox2 m ox, + nred2, where m81 = nS2 electrons are transfered (<5, and S2 represent the respective valence differences of the two redox systems), we have... 

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. 

If A is placed in an open circuit electrochemical cell containing no A+ ions, A will donate electrons to the metal electrode, forming A+ ions. Rather quickly, the electrode will be unable to accept additional electrons and the system will reach equilibrium. This equilibrium potential is a reversible electrode potential. If the electrode potential is made more positive, the electrode will again be able to accept electrons and additional A+ will be produced. Conversely, if the electrode is made more negative, A+ will accept electrons from the electrode. The rate at which A is oxidized is proportional to the current density, i (typically in units of A/cm2), by the relation... 

The electrode potential of an electrode reaction at equilibrium can be measured as the electromotive force of an electrochemical cell composed of both the reaction electrode and the normed hydrogen electrode. The potential of the reaction electrode thus measured is taken as the equilibrium potential of the electrode reaction relative to the normal hydrogen electrode. 

Having revised a few basic electrochemical ideas, such as the nature of reference electrodes, the standard hydrogen electrode and the scale based on it, we next looked briefly at thermodynamic parameters such as the electrode potential E, the standard electrode potential f and emf, and then discussed how AG, AH and AS (where the prime indicates a frustrated cell equilibrium ) may be determined. 

Let us revisit the electrochemical cell shown earlier in Figure 3.1. In this figure, two redox electrodes are immersed in solutions of their respective ions, with the half cells being connected by a salt bridge. If we were to connect an infinite-resistance voltmeter between the cells, then it would be possible to perform potentiometric experiments such as those described in the previous chapter. One electrode would be positive with respect to the other, with the separation in potential between the two electrodes being the emf - but only if the measurement was performed at equilibrium. (As before, we take the word equilibrium to imply that no charge flows.)... 

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