Voltage equilibrium measurement

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. 

The technique of photovoltage differs from the photocurrent techniques discussed above in that the electrode is held at open circuit and its equilibrium voltage is measured against a reference. The change in this equilibrium voltage on illumination is termed the photovoltage [170, 171]. The... 

The BP mechanism for hysteresis in field-effect devices [6] proposed by us was strongly supported by the experimental determination of a rate eonstant for a second order reaetion of Ps from voltage stress measurements [11, 12] which has been attributed to the BP formation. However, the above mentioned alternative of PPs requires a eritieal revisal of equilibrium for systems with Ps, and doubly eharged polymer states, whieh is presented in Section 16.5. The ki-neties and hysteresis in organie MIS devices due to formation and dissoeiation are then analysed in Section 16.6. Also a further mechanism is considered whieh is eonneeted with the formation of different complexes between Ps, BPs and mobile ions. Conelusions are drawn in Section 16.7. 

In potentiometric devices, an open-circuit voltage is measured. They also consist of an electrolyte (that is also typically made of YSZ) and two electrodes (also typically made of platinum). One of the electrodes is the working electrode (WE) - also called the sensing electrode (SE) - and the other is the reference electrode (RE). Both YSZ and Pt are suitable for high-temperature applications such as exhaust gas detection. They work as follows the electrolyte is an ionic conductor and there is a thermodynamic equilibrium between ambient oxygen, electrons in the electrodes and mobile oxygen ions. In the simplest case, the following reaction takes place in the electrodes ... 

First measiirements were made on Ag2+5S in equilibrium with sulfur. The silver sulfide was first brought into a stationary state involving a small concentration gradient of silver in silver sulfide by impressing a voltage on the cell. Then the circuit was interrupted and the voltage was measured as a ftinction of time. 

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. 

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. 

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). 

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. 

The temperature dependence of the equilibrium cell voltage forms the basis for determining the thermodynamic variables AG, A//, and AS. The values of the equilibrium cell voltage A%, and the temperature coefficient dA< 00/d7 which are necessary for the calculation, can be measured exactly in experiments. 

During charging and discharging of the cell, the terminal voltage U is measured between the poles. It should also be possible to calculate directly the thermodynamic terminal voltage from the thermodynamic data of the cell reaction. This value often differs slightly from the terminal voltage measured between the poles of the cell because of an inhibited equilibrium state or side reactions. 

In practice, for a ternary system, the decomposition voltage of the solid electrolyte may be readily measured with the help of a galvanic cell which makes use of the solid electrolyte under investigation and the adjacent equilibrium phase in the phase diagram as an electrode. A convenient technique is the formation of these phases electrochemically by decomposition of the electrolyte. The sample is polarized between a reversible electrode and an inert electrode such as Pt or Mo in the case of a lithium ion conductor, in the same direction as in polarization experiments. The... 

Equilibrium potentials can be calculated thermodynamically (for more details, see Chapter 3) when the corresponding electrode reaction is known precisely, even when they cannot be reached experimentally (i.e., when the electrode potential is nonequilibrium despite the fact that the current is practically zero). The open-circuit voltage of any galvanic cell where at least one of the two electrodes has an nonequilibrium open-circuit potential will also be nonequilibrium. Particularly in thermodynamic calculations, the term EMF is often used for measured or calculated equilibrium OCV values. 

The condition at equilibrium is that tp(a ) = and fie(a) = jue()3) (the latter equation describes the condition for contact equilibrium between the electrons in phase oc and j3). The measured compensating voltage U,... 

A conductivity cell is set up using an yttria-stabilized zirconia electrolyte. At 900°C the equilibrium pressure in the cell was 1.02 x 10-10 atm, and the reference pressure outside the cell was 7.94 x 10 18 atm. (a) What is the cell voltage The temperature was dropped to 800°C and the reference pressure changed to 1.61 x 10-19 atm. The measured equilibrium voltage was 946 mV. (b) What is the equilibrium oxygen pressure in the cell [Data adapted from D-K. Lee et al., J. Solid State Chem., 178, 185-193 (2005).]... 

An electrode potential E is the energy (expressed as a voltage) when a redox couple is at equilibrium. The value of E cannot be measured directly and must be calculated from an experimental emf. 

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