Second kind

There are three types of reference electrodes discussed reference electrodes of the first kind, reference electrodes of the second kind, and redox reference electrodes. The first two are used with potentiometric chemical sensors, whereas the last one helps us to get around the difficult problem of comparing potentials in different solvents. There is also a pseudo-reference electrode that does not have a stable, defined, reproducible potential. It serves only as the signal return to satisfy the condition of closing the electrical circuit (see Section 5.2). Because the liquid junction always causes some leakage of the internal solution, electrodes of the first kind are particularly affected. 

The potential of an electrode of the first kind is determined by the redox equilibrium between the cation with its metal. The simplest example is the equilibrium 

A reference electrode based on (6.28) can be realized by immersing Ag wire in a solution of AgN03. In order to maintain its activity constant this solution is placed in the inner reference electrode compartment, which is then connected to the sample solution through the liquid junction. Because of its good solubility, silver nitrate has often been used in reference electrodes for nonaqueous solvents. 

In order to avoid confusion in reporting of electrochemical data, the Standard Hydrogen Electrode (SHE) has been selected as the primary reference electrode, which means that its standard potential has been arbitrarily set to zero, thus establishing the hydrogen scale of standard potentials. It is based on the equilibrium 

Its realization is shown in Fig. 6.9. This electrode is impractical and secondary reference electrodes such as those discussed in these sections are used instead. 

---

Mobility of this second kind is illustrated in Fig. XVIII-14, which shows NO molecules diffusing around on terraces with intervals of being trapped at steps. Surface diffusion can be seen in field emission microscopy (FEM) and can be measured by observing the growth rate of patches or fluctuations in emission from a small area [136,138] (see Section V111-2C), field ion microscopy [138], Auger and work function measurements, and laser-induced desorption... 

There are many equivalent statements of the second law, some of which involve statements about heat engines and perpetual motion machines of the second kind that appear superficially quite different from equation (A2.T21). They will not be dealt with here, but two variant fonns of equation (A2.T21) may be noted in... 

Electrodes of the Second Kind An electrode of the first kind involving an M"+/M redox couple will respond to the concentration of another species if that species is in equilibrium with M"+. For example, the potential of a silver electrode in a solution of Ag+ is given by... 

When the potential of an electrode of the first kind responds to the potential of another ion that is in equilibrium with M"+, it is called an electrode of the second kind. Two common electrodes of the second kind are the calomel and silver/silver chloride reference electrodes. Electrodes of the second kind also can be based on complexation reactions. Eor example, an electrode for EDTA is constructed by coupling a Hg +/Hg electrode of the first kind to EDTA by taking advantage of its formation of a stable complex with Hg +. 

Redox Electrodes Electrodes of the first and second kind develop a potential as the result of a redox reaction in which the metallic electrode undergoes a change in its oxidation state. Metallic electrodes also can serve simply as a source of, or a sink for, electrons in other redox reactions. Such electrodes are called redox electrodes. The Pt cathode in Example 11.1 is an example of a redox electrode because its potential is determined by the concentrations of Ee + and Ee + in the indicator half-cell. Note that the potential of a redox electrode generally responds to the concentration of more than one ion, limiting their usefulness for direct potentiometry. 

The relative measurement error in concentration, therefore, is determined by the magnitude of the error in measuring the cell s potential and by the charge of the analyte. Representative values are shown in Table 11.7 for ions with charges of+1 and +2, at a temperature of 25 °C. Accuracies of 1-5% for monovalent ions and 2-10% for divalent ions are typical. Although equation 11.22 was developed for membrane electrodes, it also applies to metallic electrodes of the first and second kind when z is replaced by n. 

Potentiometric electrodes are divided into two classes metallic electrodes and membrane electrodes. The smaller of these classes are the metallic electrodes. Electrodes of the first kind respond to the concentration of their cation in solution thus the potential of an Ag wire is determined by the concentration of Ag+ in solution. When another species is present in solution and in equilibrium with the metal ion, then the electrode s potential will respond to the concentration of that ion. Eor example, an Ag wire in contact with a solution of Ck will respond to the concentration of Ck since the relative concentrations of Ag+ and Ck are fixed by the solubility product for AgCl. Such electrodes are called electrodes of the second kind. 

Another widely studied phenomenon in alkah borate glasses is the mixed alkah effect, the nonlinear change in glass properties when a second kind of alkah oxide is added into the single-alkali glass. Models have been suggested to explain the mixed alkah effect (144), but a universally accepted model has not been developed as of this writing. 

Atkinson, K. E. A Sui oey of Numeiical Methods foi the Solution ofFied-holm Integial Equations of the Second Kind, SIAM, Philadelphia (1976). 

This integral equation is a Volterra equation of the second land. Thus the initial-value problem is eqmvalent to a Volterra integral equation of the second kind. 

In a second kind of infrared ellipsometer a dynamic retarder, consisting of a photoelastic modulator (PEM), replaces the static one. The PEM produces a sinusoidal phase shift of approximately 40 kHz and supplies the detector exit with signals of the ground frequency and the second harmonic. From these two frequencies and two settings of the polarizer and PEM the ellipsometric spectra are determined [4.316]. This ellipsometer system is mainly used for rapid and relative measurements. 

The second kind of modeling is focused on the needs of the planner and HVAC engineer, who has to comply with certain criteria for heat delivery or removal for comfort and energy efficiency and from this has to select a certain type of component available on the market. Once the component is selected, only the performance of this component under variable load is of interest. This kind of modeling normally requires much less input, because actually only the change in performance from a given design point to a point for the actual load has to be determined. 

In these examples B is a base. The first example is called a secondary isotope effect of the first kind, the next one is a secondary isotope effect of the second kind. The distinction between these is that in the first kind bonds to the isotopic atom have undergone spatial (i.e., structural) change. Halevi has reviewed secondary isotope effects on equilibria and rates. 

Calculate tire Fatal Accident Rate (FAR) for tlie second kind of accident. 

Electrodes such as Cu VCu which are reversible with respect to the ions of the metal phase, are referred to as electrodes of the first kind, whereas electrodes such as Ag/AgCl, Cl" that are based on a sparingly soluble salt in equilibrium with its saturated solution are referred to as electrodes of the second kind. All reference electrodes must have reproducible potentials that are defined by the activity of the species involved in the equilibrium and the potential must remain constant during, and subsequent to, the passage of small quantities of charge during the measurement of another potential. 

The Ag/AgCl, Cl" electrode, which may be regarded as typical of electrodes of the second kind, consists of AgCl in contact with a soluble chloride, usually KCl. This electrode is essentially an Ag -F e Ag electrode, in which the 0 is controlled by the solubility product of AgCl and by the flci- Thus... 

Metals in practice are usually coated with an oxide film that affects the potential, and metals such as Sb, Bi, As, W and Te behave as reversible A//A/,Oy/OH electrodes whose potentials are pH dependent electrodes of this type may be used to determine the solution s pH in the same way as the reversible hydrogen electrode. According to Ives and Janz these electrodes may be regarded as a particular case of electrodes of the second kind, since the oxygen in the metal oxide participates in the self-ionisation of water. 

A second kind of covalent bonding in peptides occurs when a disulfide linkage, RS-SR, is formed between two cysteine residues. As we saiv in Section 18.8, a disulfide is formed by mild oxidation of a thiol, RSH, and is cleaved by mild reduction. 

The second kind of interaction takes place between solids and as a pure solid phase interaction, does not release any C02. 

Precipitated, washed and filtrated hydroxides consisting of wet powder contain two kinds of water. The first is moisture, i.e. water remainders that include adsorbed water. This kind of water can be successfully removed by diying at 100-200°C. The second type is molecules of water that are incorporated with tantalum or niobium to form hydroxides. Because hydroxyl groups form relatively strong bonds with tantalum or niobium, the separation of the second kind of water requires thermal treatment at higher temperatures [501],... 

It is also possible in appropriate cases to measure by direct potentiometry the concentration of an ion which is not directly concerned in the electrode reaction. This involves the use of an electrode of the second kind , an example of which is the silver-silver chloride electrode which is formed by coating a silver wire with silver chloride this electrode can be used to measure the concentration of chloride ions in solution. 

Indicator electrodes for anions may take the form of a gas electrode (e.g. oxygen electrode for OH- chlorine electrode for Cl-), but in many instances consist of an appropriate electrode of the second kind thus as shown in Section 15.1, the potential of a silver-silver chloride electrode is governed by the chloride-ion activity of the solution. Selective-ion electrodes are also available for many anions. 

The pressed disc (or pellet) type of crystalline membrane electrode is illustrated by silver sulphide, in which substance silver ions can migrate. The pellet is sealed into the base of a plastic container as in the case of the lanthanum fluoride electrode, and contact is made by means of a silver wire with its lower end embedded in the pellet this wire establishes equilibrium with silver ions in the pellet and thus functions as an internal reference electrode. Placed in a solution containing silver ions the electrode acquires a potential which is dictated by the activity of the silver ions in the test solution. Placed in a solution containing sulphide ions, the electrode acquires a potential which is governed by the silver ion activity in the solution, and this is itself dictated by the activity of the sulphide ions in the test solution and the solubility product of silver sulphide — i.e. it is an electrode of the second kind (Section 15.1). 

There are two principal types of bifurcation phenomena those of the first kind and those of the second kind. ... 

In the bifurcation of the second kind th critical coalescence for A = A0 involves two adjoining limit cycles, one that is stable and the other, unstable. We can consider the same configuration as before, the only difference being that the coalescence is now one of two cycles that destroy each other this gives ... 

The bifurcation of the second kind was established by Poincar6, but the bifurcation of the first kind was established more recently (1937) by A. Andronov.4 For further discussion, see this reference, or reference 6. The direct analytical approach to the theory of bifurcation is very difficult, and the only known case in which it could be carried through is that of Andronov. 

Bernoulli s method, 79 Konig s Theorem and Hadahiard s generalization, 81 Bethe, H. A., 641 Bethenod, T., 380 Bifurcation, 342 diagram, 342 first kind, 339 point, 342 second kind, 339 theory of, 338 value, 338 Binary digits... 

For if a cyclic process could be performed in a heat reservoir of uniform temperature so as to give out work, it would constitute a perpetanm mobile of the second kind, the existence of which is denied by the second law. And if the cyclic process absorbed work when performed at a uniform temperature, it would, by reason of its reversibility, give out an equal amount of work when reversed this would, however, be the case first considered. Hence the production of work in either cycle is impossible, which establishes the theorem. 

---