Of the second kind

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 +. 

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. 

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 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. 

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. 

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. 

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. 

Laqua et al. [1292] have made a detailed kinetic study of the interaction between CoO and 3-Ga203. In this reaction of the second kind (i.e. each reactant has been presaturated with the other), growth of the spinel product layer is parabolic and E = 300 kJ mole-1. 

In all these cases the support has a dramatic effect on the activity and selectivity of the active phase. In classical terminology all these are Schwab effects of the second kind where an oxide affects the properties of a metal. Schwab effects of the first kind , where a metal affects the catalytic properties of a catalytic oxide, are less common although in the case of the Au/Sn02 oxidation catalysts9,10 it appears that most of the catalytic action takes place at the metal-oxide-gas three phase boundaries. 

Selective Asymmetric transformation precipitation I of the second kind... 

The Legendre s function of the second kind g (> ) has completely different behavior in particular, it tends to infinity when = 1. In accordance with Equation (2.121), this happens at points of the z-axis. Since the potential has everywhere a finite value the function Qn(ri) cannot describe the attraction field and has to be removed from Equation (2.132). This first simplification gives ... 

The Legendre s function of the second kind has everywhere finite values, except = 0. 

Depending on electrolyte composition, the metal will either dissolve in the anodic reaction, that is, form solution ions [reaction (1.24)], or will form insoluble or poorly soluble salts or oxides precipitating as a new solid phase next to the electrode surface [reaction (1.28)]. Reacting metal electrodes forming soluble products are also known as electrodes of the first kind, and those forming solid products are known as electrodes of the second kind. 

The potential of an electrode of the second kind is determined by the activity (concentration) of anions, or more correctly, by the mean ionic activity of the corresponding electrolyte [see Eq. (3.50)]. The most conunon among electrodes of this type are the calomel REs. In them, a volume of mercury is in contact with KCl solution which has a well-defined concentration and is saturated with calomel Hg2Cl2, a poorly soluble mercury salt. The value of such an electrode is 0.2676 V (aU numerical values refer to 25°C, and potentials are reported on the SHE scale). Three types of calomel electrode are in practical use they differ in KCl concentration and, accordingly, in the values of ionic activity and potential ... 

When the metal is in contact with an electrolyte solution not containing its ions, its equilibrium potential theoretically will be shifted strongly in the negative direction. However, before long a certain number of ions will accumulate close to the metal surface as a result of spontaneous dissolution of the metal. We may assume, provisionally, that the equilibrium potential of such an electrode corresponds to a concentration of ions of this metal of about 10 M. In the case of electrodes of the second kind, the solution is practically always saturated with metal ions, and their potential corresponds to the given anion concentration [an equation of the type (3.35)]. When required, a metal s equilibrium potential can be altered by addition of complexing agents to the solution (see Eq. (3.37)]. 

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