Voltage equilibrium

When the e.m.f. of a cell is measured by balancing it against an external voltage, so that no current flows, the maximum e.m.f. is obtained since the cell is at equilibrium. The maximum work obtainable from the cell is then nFE J, where n is the number of electrons transferred, F is the Faraday unit and E is the maximum cell e.m.f. We saw in Chapter 3 that the maximum amount of work obtainable from a reaction is given by the free energy change, i.e. - AG. Hence... 

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. 

Equation (2-38) is valid for every region of the surface. In this case only weight loss corrosion is possible and not localized corrosion. Figure 2-5 shows total and partial current densities of a mixed electrode. In free corrosion 7 = 0. The free corrosion potential lies between the equilibrium potentials of the partial reactions and U Q, and corresponds in this case to the rest potential. Deviations from the rest potential are called polarization voltage or polarization. At the rest potential = ly l, which is the corrosion rate in free corrosion. With anodic polarization resulting from positive total current densities, the potential becomes more positive and the corrosion rate greater. This effect is known as anodic enhancement of corrosion. For a quantitative view, it is unfortunately often overlooked that neither the corrosion rate nor its increase corresponds to anodic total current density unless the cathodic partial current is negligibly small. Quantitative forecasts are possible only if the Jq U) curve is known. 

This figure demonstrates that also under potentiometric conditions (- no external current flow) electrochemical net reactions occur. The EMF of the zinc-amalgam in a given Zn2 -ion solution depends on the current-voltage characteristic of other ions (in this example, Cu2 and Pb2 are interfering ions with respect to the Zn2 equilibrium potential) at the amalgam electrode. EMF drifts are thus explainable. 

Otherwise it has been shown that the accumulation of electrolytes by many cells runs at the expense of cellular energy and is in no sense an equilibrium condition 113) and that the use of equilibrium thermodynamic equations (e.g., the Nemst-equation) is not allowed in systems with appreciable leaks which indicate a kinetic steady-state 114). In addition, a superposition of partial current-voltage curves was used to explain the excitability of biological membranes112 . In interdisciplinary research the adaptation of a successful theory developed in a neighboring discipline may be beneficial, thus an attempt will be made here, to use the mixed potential model for ion-selective membranes also in the context of biomembrane surfaces. 

According to the exact position of the equilibrium galvani potential for Ca2+-ions on the voltage axis, stimulation or inhibition of the Na+—K+ exchange can be understood. The effect of anions (e.g., MgATP2-) may be similiar as shown in Fig. 4. 

One of the most important characteristics of a cell is its voltage, which is a measure of reaction spontaneity. Cell voltages depend on the nature of the half-reactions occurring at the electrodes (Section 18.2) and on the concentrations of species involved (Section 18.4). From the voltage measured at standard concentrations, it is possible to calculate the standard free energy change and the equilibrium constant (Section 18.3) of the reaction involved. 

As pointed out previously, the value of the standard cell voltage, E°, is a measure of the spontaneity of a cell reaction. In Chapter 17, we showed that the standard free energy change, AG°, is a general criterion for reaction spontaneity. As you might suppose, these two quantities have a simple relation to one another and to the equilibrium constant, K, for the cell reaction. 

Redox reactions, like all reactions, eventually reach a state of equilibrium. It is possible to calculate the equilibrium constant for a redox reaction from the standard voltage. To do that, we start with the relation obtained in Chapter 17 ... 

Only if the standard voltage falls within a rather narrow range, say+0.10 to—0.10 V, will the value of K (and that of AG°) be such that the reaction will produce an equilibrium mixture containing appreciable amounts of both reactants and products. 

When a voltaic cell operates, supplying electrical energy, the concentration of reactants decreases and that of the products increases. As time passes, the voltage drops steadily. Eventually it becomes zero, and we say that the cell is dead. At that point, the redox reaction taking place within the cell is at equilibrium, and there is no driving force to produce a voltage. 

To calculate the current-voltage characteristic of a MESFET, we assume that the conducting channel is at thermal equilibrium, and the space-chaige layer completely depleted. Eq. (14.28) becomes... 

What happens to any cell or battery as it operates The voltage decreases until, finally, it reaches zero. Then we say the cell is dead. Equilibrium has been attained and the reaction that... 

The negative voltage shows that the state of equilibrium favors the reactants more than the products for the reaction as written. For standard conditions, the reaction will not tend to occur spontaneously. However, if we place Ag(s) in 1 M H+, the Ag+ concentration is not 1 M— it is zero. By Le Chatelier s Principle, this increases the tendency to form products, in opposition to our prediction of no reaction. Some silver will dissolve, though only a minute amount because silver metal releases electrons so reluctantly compared with H2. It is such a small amount, in fact, that no silver chloride precipitate forms, even though silver chloride has a very low solubility. 

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). 

The reaction may be regarded as taking place in a voltaic cell, the two half-cells being a C12,2C1 system and a Fe3+,Fe2+ system. The reaction is allowed to proceed to equilibrium, and the total voltage or e.m.f. of the cell will then be zero, i.e. the potentials of the two electrodes will be equal ... 

In galvanic cells it is only possible to determine the potential difference as a voltage between two half-cells, but not the absolute potential of the single electrode. To measure the potential difference it has to be ensured that an electrochemical equilibrium exists at the phase boundaries, e.g., at the electrode/electrolyte interface. At the least it is required that there is no flux of current in the external and internal circuits. 

---