Concentrations thermodynamic

As noted above, all of the partial molar quantities are concentration dependent. It is convenient to define a thermodynamic concentration called the activity aj in terms of which the chemical potential is correctly given by the relationship... 

The wolume fraction emerges from the Einstein derivation at the natural concentration unit to describe viscosity. This parallels the way volume fraction arises as a natural thermodynamic concentration unit in the Flory-Huggins theory as seen in Sec. 8.3. 

Interionic attraction in dilute solutions al.su leads to an effective ionic concentration or activity that is less than flic stoichiometric value The oriiriiy of an ion species is its thermodynamic concentration. i.e., the ion concentration corrected for the deviation from ideal behavior. For dilute solutions lire activity id ions is less than one. for concentrated solutions it may be greater than one. It is the ionic activity that is used in expressing the variation of electrode potentials, und other electrochemical phenomena, with composition. 

All the routines described for the determination of the thermodynamic (concentration) parameters in metal oxide solutions include some indirectly obtained values. For example, the equilibrium concentration of metal cations is calculated proceeding from the quantity of the oxide-ion donor consumed for titration (precipitation). Direct determination of the concentration of metal cations in the melt (if it is possible) allows one to obtain more correctly the obtained solubility product values. Our paper [332] reports a method for correction of the solubility product values for oxides on the basis of the potentiometric titration data. The modification of the standard routine consists of the simultaneous use of two indicator electrodes, one of which is the membrane oxygen electrode and the other is a metal electrode, reversible to the cations the oxide consists of. This routine was used to estimate the solubility products of copper(I) and nickel(II) oxides in the molten KCl-NaCl equimolar mixture at 700 °C. Investigation of Cu20 by the proposed method is of considerable importance since, as will be shown further, the process of dissociation/dissolution of copper(I) oxide in molten alkali-metal halides differs from the generally accepted one which was considered, e.g. in Ref. [119]. 

These weird standard states have one very attractive feature, which is that because they all have the same value of the activity of A would always be the same in all three phases at equilibrium. The three standard states could also coexist at equilibrium, if they could exist at all. As mentioned earlier, there is no reason why other concentrations or pressures could not be chosen for the standard states, that is, other than one molal or one bar, as long as ideal behavior is still part of the definition. But these other concentrations or pressures would then appear in all activity calculations and all equilibrium constants, and we would have to give up the convenience of being able to think of gaseous activities as approximate or thermodynamic pressures, and of aqueous activities as approximate or thermodynamic concentrations. It seems generally more convenient to add a little diversity to standard states, and keep activity expressions simple, as is the present custom. 

Free enthalpy, according to Equation (1.55), depends on temperature and pjp° ratio. The ratio of partial pressures of the component i in the solution and in its standard state is called thermodynamic concentration, or relative activity, and more often simply activity. Then free enthalpy and chemical potential of the component i under nonstandard conditions are calculated from ... 

In its substance it shows how much energy of the component i under the solution conditions differs from the energy of its formation imder standard conditions. The concept of thermodynamic concentration was introduced by Gilbert Newton Lewis (1875-1946) in 1907 for diluted gas solutions and later expanded for other solutions. In this connection, determination of the activity values depends on the nature and state of the component. In this respect gas, non-polar hydrophobic and polar hydrophilic components should be distinguished. 

Table 1.3 Equations for determination of relative thermodynamic concentrations (activities).

Determination of thermodynamic concentration Connection of a. v t or partia Hth concentration pressure... 

Equilibrium constants play an important role in establishing the direction and rate of spontaneous reactions of the grormd water composition formation. In this connection quite urgent is the task of their determination in specific conditions for different chemical reactions. In practice, hydrogeo-chemical studies used thermodynamic, concentration and tentative constants of equilibrium. 

For comparing concentrations of the same ion in exchange capacity and in water it is more convenient to use relative concentrations, as in their nature they are closer to the concept of relative thermodynamic concentrations, i.e., of the activities. It is usually sufficient to limit to two relative dimensions molar fractions of exchange ions and equivalent fractions of exchange ions. 

Thermodynamical concentration of gas components is described by the value of fugacity. It numerically is equal to pressure in physical atmospheres or bars. That is why the chemical potential of gas components is determined from equation ... 

That is why relative thermodynamical concentration (activity) of nonpolar hydrophobic components may be equated with their molar fractions ... 

The cell voltage is always lower than the OCV because when the electrochemical reaction occurs, the voltage decays by a term A Ere due to thermodynamic concentration polarization ... 

From these examples it will be seen that the activity a is a non-dimensional quantity the activity can be perceived as a generalized thermodynamic concentration parameter which for ideal systems of matter can be described by the relations (5.31)-(5.33). 

PcOi, or the partial pressure of carbon dioxide, represents the activity or thermodynamic concentration of carbon dioxide in the aqueous phase. It is a parameter which is not measured directly in groundwaters without a coexisting gas phase, but is calculated from the following relationship ... 

Use of the potential of a galvanic cell to measure the concentration of an electroactive species developed later than a number of other electrochemical methods. In part, this was because a rational relation between electrode potential and the concentration of an electroactive species required the development of thermodynamics, and, in particular, its application to electrochemical phenomena. The work of J. Willard Gibbs in the 1870s provided the foundation for the Nernst equation. The latter provides a quantitative relationship between potential and the ratio of effective thermodynamic concentrations [activities] for a redox couple [ox]l[red ) and is the basis for potentiometry and poten-tiometric titrations. The utility of potentiometric measurements for the characterization of ionic solutions was established with the invention of the glass electrode in 1909 for a selective potentiometric response to hydronium-ion concentrations. Another milestone in the development of potentiometric measurements was the introduction of the hydrogen electrode for the measurement of hydronium-ion concentrations one of many important contributions by Professor Joel Hildebrand. Subsequent development of special glass formulations has made possible electrodes that are selective to different monovalent cations. The idea is so attractive that intense effort has led to the development of electrodes that are selective for many cations and anions, as well as several gas- and bioselective electrodes. The use of these electrodes and the potentiometric measurement of pH continue to be among the most important applications of electrochemistry. 

When multicomponent diffusion is significant, it is best described with a generalized form of Pick s law containing (n - 1) diffusion coefficients in an -component system. This form of diffusion equation can be rationalized using irreversible thermodynamics. Concentration profiles in these multicomponent cases can be directly inferred from the binary results. However, multicomponent diffusion coefficients are difficult to estimate, and experimental values are fragmentary. As a result, you should make very sure that you need the more complicated theory before you attempt to use it. 

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