Electrochemical cell chemical potential

If a solution forms part of an electrochemical cell, the potential of the cell, the current flowing through it and its resistance are all determined by the chemical composition of the solution. Quantitative and qualitative information can thus be obtained by measuring one or more of these electrical properties under controlled conditions. Direct measurements can be made in which sample solutions are compared with standards alternatively, the changes in an electrical property during the course of a titration can be followed to enable the equivalence point to be detected. Before considering the individual electrochemical techniques, some fundamental aspects of electrochemistry will be summarized in this section. 

Determining the cell potential requites knowledge of the thermodynamic and transport properties of the system. The analysis of the thermodynamics of electrochemical systems is analogous to that of neutral systems. Eor ionic species, however, the electrochemical potential replaces the chemical potential (1). 

An electrochemical reaction is said to be polarized or retarded when it is limited by various physical and chemical factors. In other words, the reduction in potential difference in volts due to net current flow between the two electrodes of the corrosion cell is termed polarization. Thus, the corrosion cell is in a state of nonequilibrium due to this polarization. Figure 4-415 is a schematic illustration of a Daniel cell. The potential difference (emf) between zinc and copper electrodes is about one volt. Upon allowing current to flow through the external resistance, the potential difference falls below one volt. As the current is increased, the voltage continues to drop and upon completely short circuiting (R = 0, therefore maximum flow of current) the potential difference falls toward about zero. This phenomenon can be plotted as a polarization diagram shown in Figure 4-416. 

Figure 7.9. Schematic representation of the density of states N(E) in the conduction band of two transition metal electrodes (W and R) and of the definitions of work function O, chemical potential of electrons p, electrochemical potential of electrons or Fermi level p, surface potential x, Galvani (or inner) potential (p and Volta (or outer) potential for the catalyst (W) and for the reference electrode (R). The measured potential difference UWr is by definition the difference in p q>, p and p are spatially uniform O and can vary locally on the metal surfaces 21 the T terms are equal, see Fig. 5.18, for the case of fast spillover, in which case they also vanish for an overall neutral cell Reprinted with permission from The Electrochemical Society.

Figure 7.14. Schematic representation of the spatial variation of electrode potential, chemical potential of oxygen and electrochemical potential of O2 for the cell 02, M1YSZ1M, 02 (=1 atm).

Electrochemical cells can be constructed using an almost limitless combination of electrodes and solutions, and each combination generates a specific potential. Keeping track of the electrical potentials of all cells under all possible situations would be extremely tedious without a set of standard reference conditions. By definition, the standard electrical potential is the potential developed by a cell In which all chemical species are present under standard thermodynamic conditions. Recall that standard conditions for thermodynamic properties include concentrations of 1 M for solutes in solution and pressures of 1 bar for gases. Chemists use the same standard conditions for electrochemical properties. As in thermodynamics, standard conditions are designated with a superscript °. A standard electrical potential is designated E °. 

This is a quantitative problem, so we follow the standard strategy. The problem asks about an actual potential under nonstandard conditions. Before we determine the potential, we must visualize the electrochemical cell and determine the balanced chemical reaction. The half-reactions are given in the problem. To obtain the balanced equation, reverse the direction of the reduction half-reaction with the... 

The two terms in the final expression of Equation 9.11 can compete against one another and with only a small membrane potential the concentration gradient chemical potential can be overcome. Electrochemical energy is thus harnessed to allow nutrients to flow into a cell and increase the local concentration. 

Chemical potential gradients The chemical potential of a species can vary from place to place, e.g. inside and outside a cell, giving rise to a concentration difference and hence a concentration gradient. The inclusion of ions adds an electrochemical gradient and the two may oppose one another... 

Wagner pioneered the use of solid electrolytes for thermochemical studies of solids [62], Electrochemical methods for the determination of the Gibbs energy of solids utilize the measurement of the electromotive force set up across an electrolyte in a chemical potential gradient. The electrochemical potential of an electrochemical cell is given by ... 

Potentiometry deals with the electromotive force (EMF) generated in a galvanic cell where a spontaneous chemical reaction is taking place. In practice, potentiometry employs the EMF response of a galvanostatic cell that is based on the measurement of an electrochemical cell potential under zero-current conditions to determine the concentration of analytes in measuring samples. Because an electrode potential generated on the metal electrode surface,... 

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. 

An electrical potential difference between the electrodes of an electrochemical cell (called the cell potential) causes a flow of electrons in the circuit that connects those electrodes and therefore produces electrical work. If the cell operates under reversible conditions and at constant composition, the work produced reaches a maximum value and, at constant temperature and pressure, can be identified with the Gibbs energy change of the net chemical process that occurs at the electrodes [180,316]. This is only achieved when the cell potential is balanced by the potential of an external source, so that the net current is zero. The value of this potential is known as the zero-current cell potential or the electromotive force (emf) of the cell, and it is represented by E. The relationship between E and the reaction Gibbs energy is given by... 

This exposition has been greatly simplified. At equilibrium, the sums of the electrochemical potentials, p, within each of the two half cells comprising the overall cell are the same, and p is related to the chemical potential n a by the relationship p = n + nF. The occurrence of a potential E at the electrode is a manifestation of the difference in electric field, A0 between the electrodes and their respective couples in solution, as a function of their separation distances. 

The electrochemical cell with zinc and copper electrodes had an overall potential difference that was positive (+1.10 volts), so the spontaneous chemical reactions produced an electric current. Such a cell is called a voltaic cell. In contrast, electrolytic cells use an externally generated electrical current to produce a chemical reaction that would not otherwise take place. 

Equation (5) shows the fundamental relationship between Gibbs free energy change of the chemical reaction and the cell potential under reversible conditions (potential of the electrochemical cell reaction). 

Electrodeposition of Pa metal has been performed from both aqueous and nonaqueous solutions. An isopropanol solution of 10-20 p,gmL Pa from 8M HCl/0.01 M HE/Pa stock was employed for quantitative electrodeposition [41]. The cell consisted of a gold-plated A1 cathode and a Pt wire anode. During deposition the current was maintained at 1 mA, which produced a potential of 400-600 V during the 90-min electrolysis. The progress of the electrolysis was externally monitored by alpha-counting of the electrolysis solution before and during the electrodeposition. Deposition studies of metal from aqueous solutions are more common. Pa was electrodeposited on platinum in 95% yield at tracer concentrations from an electrolyte of [NH4]C1/HC1 [42]. Electrochemical and chemical conditions of the plating process were described for Pu solutions, which served as a model for the other actinide elements studied. Another tracer... 

Much of the recent research in solid state chemistry is related to the ionic conductivity properties of solids, and new electrochemical cells and devices are being developed that contain solid, instead of liquid, electrolytes. Solid-state batteries are potentially useful because they can perform over a wide temperature range, they have a long shelf life, it is possible to make them very small, and they are spill-proof We use batteries all the time—to start cars, in toys, watches, cardiac pacemakers, and so on. Increasingly we need lightweight, small but powerful batteries for a variety of uses such as computer memory chips, laptop computers, and mobile phones. Once a primary battery has discharged, the reaction cannot be reversed and it has to be thrown away, so there is also interest in solid electrolytes in the production of secondary or storage batteries, which are reversible because once the chemical reaction has taken place the reactant concentrations can be... 

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