Electrochemical cell Nernst equation

In potentiometry the potential of an electrochemical cell is measured under static conditions. Because no current, or only a negligible current, flows while measuring a solution s potential, its composition remains unchanged. For this reason, potentiometry is a useful quantitative method. The first quantitative potentiometric applications appeared soon after the formulation, in 1889, of the Nernst equation relating an electrochemical cell s potential to the concentration of electroactive species in the cell. ... 

Potential and Concentration—The Nernst Equation The potential of a potentio-metric electrochemical cell is given as... 

Making appropriate substitutions into the Nernst equation for the electrochemical cell (see Example 11.2)... 

Despite the apparent ease of determining an analyte s concentration using the Nernst equation, several problems make this approach impractical. One problem is that standard-state potentials are temperature-dependent, and most values listed in reference tables are for a temperature of 25 °C. This difficulty can be overcome by maintaining the electrochemical cell at a temperature of 25 °C or by measuring the standard-state potential at the desired temperature. 

Electrochemical methods covered in this chapter include poten-tiometry, coulometry, and voltammetry. Potentiometric methods are based on the measurement of an electrochemical cell s potential when only a negligible current is allowed to flow, fn principle the Nernst equation can be used to calculate the concentration of species in the electrochemical cell by measuring its potential and solving the Nernst equation the presence of liquid junction potentials, however, necessitates the use of an external standardization or the use of standard additions. 

As a consequence, the equilibrium potential of the single half-cell also depends on the concentrations of the compounds involved. The Nernst equation [Eq. (24)], which is one of the most important electrochemical relations, explains this context... 

Nernst equation The equation expressing the emf of an electrochemical cell in terms of the concentrations of the reagents taking part in the cell reaction E = E° - (RT/nF) In Q. 

R is the ideal gas constant, T is the Kelvin temperature, n is the number of electrons transferred, F is Faraday s constant, and Q is the activity quotient. The second form, involving the log Q, is the more useful form. If you know the cell reaction, the concentrations of ions, and the E°ell, then you can calculate the actual cell potential. Another useful application of the Nernst equation is in the calculation of the concentration of one of the reactants from cell potential measurements. Knowing the actual cell potential and the E°ell, allows you to calculate Q, the activity quotient. Knowing Q and all but one of the concentrations, allows you to calculate the unknown concentration. Another application of the Nernst equation is concentration cells. A concentration cell is an electrochemical cell in which the same chemical species are used in both cell compartments, but differing in concentration. Because the half reactions are the same, the E°ell = 0.00 V. Then simply substituting the appropriate concentrations into the activity quotient allows calculation of the actual cell potential. 

Electrochemical experiments fall into two broad categories. Some experiments are concerned with standard cell voltages, while other experiments use the Nernst equation directly or indirectly. Experiment 21 in the Experimental chapter uses these concepts. 

Tower, Stephen. All About Electrochemistry. Available online. URL http //www.cheml.com/acad/webtext/elchem/. Accessed May 28, 2009. Part of a virtual chemistry textbook, this excellent resource explains the basics of electrochemistry, which is important in understanding how fuel cells work. Discussions include galvanic cells and electrodes, cell potentials and thermodynamics, the Nernst equation and its applications, batteries and fuel cells, electrochemical corrosion, and electrolytic cells and electrolysis. 

The foregoing considerations are based on the concepts of reversible thermodynamics the electrochemical cells are considered to be operating reversibly, which means in effect that no net current is drawn. Real cell EMFs, however, can differ substantially from the predictions of the Nernst equation because of electrochemical kinetic factors that emerge when a nonnegligible current is drawn. An electrical current represents electrons transferred per unit of time, that is, it is proportional to the extent of electrochemical reaction per unit of time, or reaction rate. The major factors that can influence the cell EMF through the current drawn are... 

One important application of the Nernst equation is the measurement of pH (and, through pH, acidity constants). The pH of a solution can be measured electrochemically with a device called a pH meter. The technique makes use of a cell in which one electrode is sensitive to the H30+ concentration and the second electrode serves as a reference. An electrode sensitive to the concentration of a particular ion is called an ion-selective electrode. One combination is a hydrogen electrode connected through a salt bridge to a calomel electrode. The reduction half-reaction for the calomel electrode is... 

The electrochemical determination of pH using a pH meter is a particularly important application of the Nernst equation. Consider, for example, a cell with a hydrogen electrode as the anode and a second reference electrode as the cathode ... 

The potential of this electrode is defined (Section 5.2) as the voltage of the cell Pt H2(l atm) H+(<2 = 1) MZ+ M, where the left-hand electrode, Et = 0, is the normal hydrogen reference electrode (described in Section 5.6). We will derive the Nernst equation on the basis of the electrochemical kinetics in Chapter 6. Here we will use a simplified approach and consider that Eq. (5.9) can be used to determine the potential E of the M/Mz+ electrode as a function of the activity of the products and reactants in the equilibrium equation (5.10). Since in reaction (5.10) there are two reactants, Mz+ and e, and only one product of reaction, M, Eq. (5.9) yields... 

This interface is also known as the perm-selective interface (Fig. 6.1a). It is found in ion-selective sensors, such as ion-selective electrodes and ion-selective field-effect transistors. It is the site of the Nernst potential, which we now derive from the thermodynamic point of view. Because the zero-current axis in Fig. 5.1 represents the electrochemical cell at equilibrium, the partitioning of charged species between the two phases is described by the Gibbs equation (A.20), from which it follows that the electrochemical potential of the species i in the sample phase (S) and in the electrode phase (m) must be equal. 

It has been reported (4,5) that solid electrolyte sensors using stabilized zirconia can detect reducible gases in ambient atmosphere by making use of an anomalous EMF which is unusually larger than is expected from the Nernst equation. However, these sensors should be operated in a temperature range above ca. 300°C mainly because the ionic conductivity of stabilized zirconia is too small at lower temperatures. On the other hand, solid state proton conductors such as antimonic acid (6,1), zirconium phosphate (8), and dodecamolybdo-phosphoric acid (9) are known to exhibit relatively high protonic conductivities at room temperature. We recently found that the electrochemical cell using these proton conductors could detect... 

Potentiometric measurements are based on the Nernst equation, which was developed from thermodynamic relationships and is therefore valid only under equilibrium (read thermodynamic) conditions. As mentioned above, the Nernst equation relates potential to the concentration of electroactive species. For electroanalytical purposes, it is most appropriate to consider the redox process that occurs at a single electrode, although two electrodes are always essential for an electrochemical cell. However, by considering each electrode individually, the two-electrode processes are easily combined to obtain the entire cell process. Half reactions of electrode processes should be written in a consistent manner. Here, they are always written as reduction processes, with the oxidised species, O, reduced by n electrons to give a reduced species, R ... 

The cell reaction is the transfer of oxygen from one side to the other. (See also Lambda probe). In the case of an - electrochemical equilibrium (subentry of -> equilibrium) the measured -> open circuit potential (subentry of - potential) or -> equilibrium potential (subentry of -> potential) Ueq or E (emf) can be calculated by the -> Nernst equation ... 

Half-cell reaction — The redox reaction (- electrode reaction) proceeding in a half-cell. The half-cell reaction changes the ratio of the activities of the reduced and oxidized forms. When the half-cell reaction is electrochemically reversible (see reversibility), the -> Nernst equation will describe the dependence of the -> electrode potential on the ratio of the activities of the reduced and oxidized forms. 

Nernst equation — A fundamental equation in -> electrochemistry derived by - Nernst at the end of the nineteenth century assuming an osmotic equilibrium between the metal and solution phases (- Nernst equilibrium). This equation describes the dependence of the equilibrium electrode - potential on the composition of the contacting phases. The Nernst equation can be derived from the - potential of the cell reaction (Ecen = AG/nF) where AG is the - Gibbs energy change of the - cell reaction, n is the charge number of the electrochemical cell reaction, and F is the - Faraday constant. 

Reversibility — This concept is used in several ways. We may speak of chemical reversibility when the same reaction (e.g., -> cell reaction) can take place in both directions. Thermodynamic reversibility means that an infinitesimal reversal of a driving force causes the process to reverse its direction. The reaction proceeds through a series of equilibrium states, however, such a path would require an infinite length of time. The electrochemical reversibility is a practical concept. In short, it means that the -> Nernst equation can be applied also when the actual electrode potential (E) is higher (anodic reaction) or lower (cathodic reaction) than the - equilibrium potential (Ee), E > Ee. Therefore, such a process is called a reversible or nernstian reaction (reversible or nerns-tian system, behavior). It is the case when the - activation energy is small, consequently the -> standard rate constants (ks) and the -> exchange current density (jo) are high. 

Because the potential of an electrochemical cell depends on the concentrations of the participating ions, the observed potential can be used as a sensitive method for measuring ion concentrations in solution. We have already mentioned the ion-selective electrodes that work by this principle. Another application of the relationship between cell potential and concentration is the determination of equilibrium constants for reactions that are not redox reactions. For example, consider a modified version of the silver concentration cell shown in Fig. 11.11. If the 0.10 M AgN03 solution in the left-hand compartment is replaced by 1.0 M NaCl and an excess of solid AgCl is added to the cell, the observed cell potential can be used to determine the concentration of Ag+ in equilibrium with the AgCl(s). In other words, at 25°C we can write the Nernst equation as... 

Nernst equation an equation relating the potential of an electrochemical cell to the concentrations of the cell components... 

The Nernst equation gives the electromotive force (EMF) G of an electrochemical cell as a function of the absolute temperature T as... 

Another approach to electrochemical transduction by chemical recognition is the incorporation of the imprinted polymer as the active ingredient in a membrane of an ISE. ISEs are devices which, when incorporated in an electrochemical cell with an appropriate reference electrode, produce a potential that varies predictably with the concentration of a certain ion in solution. If the response of the electrode follows theory, the response is Nernstian and is given by the Nernst equation ... 

Electrode Potential Nernst Equation and the Electrochemical Cell 441 Tableau 8.5. Redox Equilibria of Cl Species... 

THE ELECTRODE POTENTIAL THE NERNST EQUATION AND THE ELECTROCHEMICAL CELL... 

Electrode Potential Nernst Equation and the Electrochemical Cell 447... 

Potentiometric transducers measure the potential under conditions of constant current. This device can be used to determine the analytical quantity of interest, generally the concentration of a certain analyte. The potential that develops in the electrochemical cell is the result of the free-energy change that would occur if the chemical phenomena were to proceed until the equilibrium condition is satisfied. For electrochemical cells containing an anode and a cathode, the potential difference between the cathode electrode potential and the anode electrode potential is the potential of the electrochemical cell. If the reaction is conducted under standard-state conditions, then this equation allows the calculation of the standard cell potential. When the reaction conditions are not standard state, however, one must use the Nernst equation to determine the cell potential. Physical phenomena that do not involve explicit redox reactions, but whose initial conditions have a non-zero free energy, also will generate a potential. An example of this would be ion-concentration gradients across a semi-permeable membrane this can also be a potentiometric phenomenon and is the basis of measurements that use ion-selective electrodes (ISEs). 

Apply the Nernst equation to calculate the voltage of a cell in which reactants and products are not in their standard states and to calculate the value of an equilibrium constant from the voltage of an electrochemical cell (Section 17.3, problems 27-38). 

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