Indifferent systems

Binary systems that have a maximum or minimum in the temperature-composition or pressure-composition curves become indifferent at the composition of the maximum or minimum. The Gibbs-Duhem equations applicable to each phase are Equations (10.124) and (10.125). The compositions of the two phases are equal at the maximum or minimum and, therefore, the solution of these two equations becomes 

This equation gives the change of pressure with a change of temperature at the maximum or minimum. The system becomes univariant. However, because of the cancellation of the terms containing the chemical potentials, the determination of the change of the composition of the phases at the maximum or minimum with change of temperature or pressure cannot be determined from the Gibbs-Duhem equations alone. In order to do so we introduce the equality of the differentials of the chemical potentials in the two phases for one of the components, so 

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THE.5. R. Defay et I. Prigogine, Systemes monovariants et systemes indifferents (Monovariant systems and indifferent systems). Bull. Cl. Set Acad. Roy. Belg. 29, 525—535 (1943). 

The inverse of this theorem is clearly not true, for in 5 we have already seen examples of indifferent systems in which no pair of phases has the same composition. In two-phase non-reacting systems all indifferent states are states of uniform composition, for in the case of only two phases (29.19) reduces to... 

The lines of coexistence AaEcB and AbEdB correspond to the curves rViPwiW, qq otupi and the point of uniform composition E corresponds to the indifferent system aej8. 

To examine more deeply the relations between monovariant and indifferent systems we shall now introduce the idea of a subsystem. ... 

Therefore, the triatorrtic functionalities behave like electron-rich molecular systems, whereas typical unsaturated moieties, such as benzenes and ethylenes, act as rather indifferent systems with respect to their tt donating or accepting abilities. 

It is conventional to use molality—moles of solute per kilogram of solvent (symbol m)—as the concentration unit in electrolyte thermodynamics. Accordingly, we shall represent the concentrations of both the indifferent electrolyte and the polymer in these units in this section m3 and m2, respectively. In the same dilute (with respect to polymer) approximation that we have used elsewhere in this chapter, m2 is related to the mass volume system of units C2 by... 

What makes the latter items particularly important is the fact that the charge and electrolyte content of an unknown polymer may not be known hence it is important to design an osmotic pressure experiment correctly for such a system. It is often easier to add swamping amounts of electrolyte than to totally eliminate all traces of electrolyte. Under the former conditions a true molecular weight is obtained. Trouble arises only when the experimenter is indifferent toward indifferent electrolyte this sort of carelessness can be the source of much confusion. 

The human element, seen in errors, ignorance, lack of training, lethargy, illiteracy or indiscipline, or indifference, must be monitored carefully. This may require either an adequately qualified and experienced person or proper job training. Indifference, for reasons other than the above, would be a matter for human resource development, where a worker s skills and habits may have to be adapted to fit into the system. 

Equation (3.5) can be used to establish a one-to-one correspondence among all composition scales for which mass exchange is feasible. Since most environmental applications involve dilute systems, one can assume that these systems behave ideally. Hence, the transfer of the pollutant is indifferent to the existence of other species in the waste stream. In other words, even if two waste streams contain species that are not identical, but share the same composition of a particular pollutant, the equilibrium composition of the pollutant in an MSA will be the same for both waste streams. Hence, a single composition scale, y, can be used to represent the concentration of the pollutant in any waste stream. Next, (3.5) can be employed to generate Ns scales for the MSAs. For a given set of corresponding composition scales y,x, X2,..., xj,..., it is thermodynamically and practically feasible to transfer the pollutant from any waste stream to any MSA. In addition, it is also feasible to transfer the pollutant from any waste stream of a composition y/ to any MSA which has a composition less than the xy obtained from (3.5b). 

This has been despite the fact that the UK has developed with a culture that is indifferent to engineering, the respectable professions being those such as law or medicine offering more money and prestige. This deeply rooted attitude was supported by an education system in which on the whole applied science - engineering - was not studied in schools or universities. This contrasts with the rest of world, where such studies were an important part of the curricula of many schools and universities as early as the eighteenth century. Engineering was not considered suitable for those with the ability to enter a university, where arts and sciences were studied. 

If a heterogeneous equilibrium is such that the pressure of the system depends on the temperature alone, and is unchanged when the phases alter in relative amount, it is called a completely heterogeneous equilibrium (Roozeboom), or an indifferent equilibrium (Duhem). 

Let us suppose the apparatus described in 188 is enclosed in a vessel into which an indifferent ga3 may be pumped, so that the whole system can be exposed to any total external pressure desired. If there is a change of total volume when solute passes into solution, it will give rise to the performance of work by, or against, the total pressure, quite independently of the osmotic work derivable from the apparatus inside. 

It is very often necessary to characterize the redox properties of a given system with unknown activity coefficients in a state far from standard conditions. For this purpose, formal (solution with unit concentrations of all the species appearing in the Nernst equation its value depends on the overall composition of the solution. If the solution also contains additional species that do not appear in the Nernst equation (indifferent electrolyte, buffer components, etc.), their concentrations must be precisely specified in the formal potential data. The formal potential, denoted as E0, is best characterized by an expression in parentheses, giving both the half-cell reaction and the composition of the medium, for example E0,(Zn2+ + 2e = Zn, 10-3M H2S04). 

Assume that both the initial substances and the products of the electrode reaction are soluble either in the solution or in the electrode. The system will be restricted to two substances whose electrode reaction is described by Eq. (5.2.1). The solution will contain a sufficient concentration of indifferent electrolyte so that migration can be neglected. The surface of the electrode is identified with the reference plane, defined in Section 2.5.1. In this plane a definite amount of the oxidized component, corresponding to the material flux J0x and equivalent to the current density j, is formed or... 

The first two terms on the right-hand side of this equation express the proper overpotential of the electrode reaction rjr (also called the activation overpotential) while the last term, r)c, is the EMF of the concentration cell without transport, if the components of the redox system in one cell compartment have concentrations (cOx)x=0 and (cRed)x=0 and, in the other compartment, Cqx and cRcd. The overpotential given by this expression includes the excess work carried out as a result of concentration changes at the electrode. This type of overpotential was called the concentration overpotential by Nernst. The expression for a concentration cell without transport can be used here under the assumption that a sufficiently high concentration of the indifferent electrolyte suppresses migration. 

An awkward situation arises when dealing with a dilute solution where it has been observed that the depletion of the electrode layer ultimately leads to an enhancement of the resistance of the solution and thereby affecting subsequently an alteration in the Ohm s Law potential drop (I x R) in the cell. This ultimately gives rise to a doubtful observed potential operative at the electrode. In order to overcome this serious anomaly, it is a normal practice to add an excess of an indifferent electrolyte to the system, such as 0.1 M KC1, which renders the solution to remain stable at a low and constant resistance, whereas the migration current (Im) of the species under examination almost vanishes i.e., I = Id. 

Intensive culture of bananas, as with many other crops, is beset with many problems. Even in isolated plantings, pests of one kind or another reduce the potential crop or even destroy it entirely. In the majority of cases pest control has been confined to large acreages in more intensified banana culture. Many factors have contributed to retarding the use of pest control, such as weather and ground conditions that prevent the use of portable equipment without expensive road systems, small plantations, lack of finances, indifference on the part of grower, and no local demand for quality fruit. 

Ideal potentiometric measurements, especially in analytical chemistry, would require that the potential of the reference electrode be fixed and known, and that the composition of the studied solution affect only the potential of the indicator electrode. This would occur only if the liquid-junction potential could be completely neglected. In practice this situation can be attained only if the whole system contains an indifferent electrolyte in a much larger concentration than that of the other electrolytes, so that the concentration of a particular component in the analysed solution, which is not present in the reference electrode solution, has only a negligible effect on the liquid-junction potential Such a situation rarely occurs, so that it is necessary to know or at least fix the liquid junction potential... 

If the sample solutions contain an indifferent electrolyte at a sufficiently high and constant concentration, then it can be assumed that the activity coefficients and Uquid-junction potentials are also constant and can be included in the value of the standard potential of the given ISE. It is then possible to calibrate the system using solutions with known concentrations of the ion sensed by the ISE and thus to obtain sample concentration values directly. 

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