Activity coefficients concentration dependence

Generally, the activity coefficient y depends on the composition of solution. In the ranges of our narrow purposes of investigations of the macromolecules chemical potential conformation term influence on the osmotic pressure of polymeric solutions we will be neglect by the change of y lying y = const in all range of the macromolecules concentrations into solution. This permits to write... 

The activity 3j of an ion i is related to its concentration q by the relationship d = where 7, is the activity coefficient which depends on the total ionic strength /. This latter term is a measure of the quantity and charge of all ions present in the medium / = 0.5 Cizf- Therefore, for ion i of charge z, equation (18.1) becomes ... 

In view of the large dopant concentration it may appear surprising that the Pq dependencies of [v0], [h ], [e ] (see Figure 13) behave ideally. The reason is that the activity coefficient mainly depends on the dopant and temperature and will not be affected by minor changes in the redox-chemistry. Hence the Pq dependencies are indeed expected to be ideal while severe... 

The finite-ion-size model yielded agreement with experiment at concentrations up to 0.1 N. It also introduced through the value of a, the ion size parameter, a specificity to the eiectrolyte (making NaCi different from KCl), whereas the point-charge model yielded activity coefficients that depended only upon the valence type of electrolyte. Thus, while the limiting law sees only the charges on the ions, it is biind... 

The activity coefficients, 7 , depend on the concentration. For nonideal systems, it is necessary to develop a model and derive an equation for the activity coefficients in the adsorbed phase. The definition of these coefficients must satisfy three thermodynamic conditions ... 

The values of y are nearly independent of the kind of ions in the compound so long as the compounds are of the same valence type. For example, KCl and NaBr have nearly the same activity coefficients at the same concentration, as do K2SO4 and Ca(N03)2. In Section 16.7 we shall see that the theory of Deby e and Huckel predicts that in a sufficiently dilute solution the mean ionic activity coefficient should depend only on the charges on the ions and their concentration, but not on any other individual characteristics of the ions. 

Electrolysis of solutions can be used for electrodeposition of a trace metal on an electrode. The selectivity and efficiency which would be present for electrolytic deposition of macro amounts of ions at a controlled potratial is not present, however, for trace amounts. The activity of trace amounts of the species is an unknown quantity even if the concentration is known, since the activity coefficient is dependent upon the behavior of the mixed electrolyte system. Moreover, the concentration of the tracer in solution may not be known accurately since there is always the possibility of some loss through adsorption, complex formation with impurities, etc. Nevertheless, despite these uncertainties it has been found that the Nemst equation can be used, with some caution, for calculating the conditions necessary for electrolytic deposition of trace metals. 

The activity coefficient is depending on the section j and can differ from section j to section j + because the adsorbate concentration differs too. 

No further difficulties arise when we come to discuss steady state diffusion in a system in which the activity coefficient is dependent upon concentration. In such a system, Di (1 +... 

This is indeed the case, as shown again in Figure 13.2. [There are, however, a few rare cases where - due to a combination of physical and chemical interactions - the activity coefficient s dependency on concentration passes through a maximum or minimum (see, for example, the system acetone-methanol in Severns et al, 1955).]... 

Debye-Hiickel theory The activity coefficient of an electrolyte depends markedly upon concentration. Jn dilute solutions, due to the Coulombic forces of attraction and repulsion, the ions tend to surround themselves with an atmosphere of oppositely charged ions. Debye and Hiickel showed that it was possible to explain the abnormal activity coefficients at least for very dilute solutions of electrolytes. 

That the rate profiles are close to parallel shows that the variations in rates reflect the changing concentration of nitronium ions, rather than idiosyncrasies in the behaviour of the activity coefficients of the aromatic compounds. The acidity-dependences of the activity coefficients of / -nitrotoluene, o- and -chloronitrobenzene (fig. 2.2, 2.3.2), are fairly shallow in concentrations up to about 75 %, and seem to be parallel. In more concentrated solutions the coefficients change more rapidly and it... 

The true thermodynamic equilibrium constant is a function of activity rather than concentration. The activity of a species, a, is defined as the product of its molar concentration, [A], and a solution-dependent activity coefficient, Ya. 

For gases, pure solids, pure liquids, and nonionic solutes, activity coefficients are approximately unity under most reasonable experimental conditions. For reactions involving only these species, differences between activity and concentration are negligible. Activity coefficients for ionic solutes, however, depend on the ionic composition of the solution. It is possible, using the extended Debye-Htickel theory, to calculate activity coefficients using equation 6.50... 

A quantitative solution to an equilibrium problem may give an answer that does not agree with the value measured experimentally. This result occurs when the equilibrium constant based on concentrations is matrix-dependent. The true, thermodynamic equilibrium constant is based on the activities, a, of the reactants and products. A species activity is related to its molar concentration by an activity coefficient, where a = Yi[ ] Activity coefficients often can be calculated, making possible a more rigorous treatment of equilibria. 

Concentrated, Binary Mixtures of Nonelectrolytes Several correlations that predict the composition dependence of Dab. re summarized in Table 5-19. Most are based on known values of D°g and Dba- In fact, a rule of thumb states that, for many binary systems, D°g and Dba bound the Dab vs. Xa cuiwe. CuUinan s equation predicts dif-fusivities even in hen of values at infinite dilution, but requires accurate density, viscosity, and activity coefficient data. 

Since activity coefficients have a strong dependence on composition, the effect of the solvent on the activity coefficients is generally more pronounced. However, the magnitude and direc tion of change is highly dependent on the solvent concentration, as well as the liquid-phase interactions between the key components and the solvent. The solvent acts to lessen the nonideahties of the key component whose liquid-phase behavior is similar to the solvent, while enhancing the nonideal behavior of the dissimilar key. 

The last term in Eq. (6-32) describes the temperature dependence of the molar concentration in water, this contributes only about —45 cal mol to E at room temperature. In a strong mineral acid solution, the temperature dependence of the activity coefficient term contributes about —90 cal mol . These are small quantities relative to the uncertainty in E s-... 

Throughout this section the hydronium ion and hydroxide ion concentrations appear in rate equations. For convenience these are written [H ] and [OH ]. Usually, of course, these quantities have been estimated from a measured pH, so they are conventional activities rather than concentrations. However, our present concern is with the formal analysis of rate equations, and we can conveniently assume that activity coefficients are unity or are at least constant. The basic experimental information is k, the pseudo-first-order rate constant, as a function of pH. Within a senes of such measurements the ionic strength should be held constant. If the pH is maintained constant with a buffer, k should be measured at more than one buffer concentration (but at constant pH) to see if the buffer affects the rate. If such a dependence is observed, the rate constant should be measured at several buffer concentrations and extrapolated to zero buffer to give the correct k for that pH. 

The symbol used is dependent upon the method of expressing the concentration of the solution. The recommendations of the IUPAC Commision on Symbols, Terminology and Units (1969) are as follows concentration in moles per litre (molarity), activity coefficient represented by y, concentration in mols per kilogram (molality), activity coefficient represented by y, concentration expressed as mole fraction, activity coefficient represented by f... 

The pH will depend upon the ionic strength of the solution (which is, of course, related to the activity coefficient — see Section 2.5). Hence, when making a colour comparison for the determination of the pH of a solution, not only must the indicator concentration be the same in the two solutions but the ionic strength must also be equal or approximately equal. The equation incidentally provides an explanation of the so-called salt and solvent effects which are observed with indicators. The colour-change equilibrium at any particular ionic strength (constant activity-coefficient term) can be expressed by a condensed form of equation (4) ... 

It is typical that in this region the curves of electrolytes of the same valence type almost coincide (i.e., at a given concentration the activity coefficients depend only on the electrolyte s valence type, not on its identity). 

The formal Galvani potential, described by Eq. (22), practically does not depend on the concentration of ions of the electrolyte MX. Since the term containing the activity coefficients of ions in both solutions is, as experimentally shown, equal to zero it may be neglected. This results predominantly from the cross-symmetry of this term and is even more evident when the ion activity coefficients are replaced by their mean values. A decrease of the difference in the activity coefficients in both phase is, in addition, favored by partial hydration of the ions in the organic phase [31 33]. Thus, a liquid interface is practically characterized by the standard Galvani potential, usually known as the distribution potential. 

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