Wagner activity coefficients

Wagner factor — or thermodynamic factor, denotes usually the - concentration derivative of -> activity or - chemical potential of a component of an electrochemical system. This factor is necessary to describe the - diffusion in nonideal systems, where the - activity coefficients are not equal to unity, via Fick s laws. In such cases, the thermodynamic factor is understood as the proportionality coefficient between the selfdiffusion coefficient D of species B and the real - diffusion coefficient, equal to the ratio of the flux and concentration gradient of these species (chemical diffusion coefficient DB) ... 

Up to this point, no definite advantage can be perceived by the use of a 1 weight percent solution as the standard state. But if more than one solute is present, Wagner (1952) found that the activity coefficient is changed by the following expression... 

The evaluation of mixing properties of melts and solid solutions from measured ion intensities and temperatures are described in the reviews by Chatillon et al. [12], Sidorov and Korobov [115], as well as Raychaudhuri and Stafford [13] and the references quoted in these articles. The chemical activities, or activity coefficients, can be obtained from the partial pressures of the mixture components. The pressure calibration constant (see Sect. 2.4) has to be determined in this case. The pressure calibration can be avoided by the use of the ion intensity ratio method described by Lyubimov et al. [116]j Belton and Fruehan [117], as well as Neckel and Wagner [118, 119]. The Gibbs-Duhem relation is used to obtain the activity coefficient f of the component A in the mixture... 

The Wagner first order interaction parameter has first been experimentally determined at 1592°C by [1963Wei] and at 1600°C by [1965Bur], It is defined by = 5 logio/n / d (% Cu) where (% Cu) represents the copper content of the alloy expressed in mass% and n the activity coefficient of H in die alloy defined hyfn = (% H in pure iron) / (% H in die alloy). It is calculated from die solubility measurements at constant temperature and hydrogen pressure and its most probable value is = -0.0004 at 1600°C [1974Boo] for less than 12 tnass% Cu in the alloy. 

Wagner has derived the following expression for the activity coefficient of... 

The Wagner expansion is another form of limited expansion, this time used to represent the logarithms of the activity coefficients for the solutes in a solvent, as reference (II) - an infinitely-dilute solution. 

Activity coefficients are likewise assessed using thermodynamics, either using Margules or Wagner limited development, or by assessing the free molar enthalpy of the component in excess using the following relation ... 

As discussed in Section 8.2 the relation between the chemical diffusion coefficient and diffusivity (sometimes also called the component diffusion coefficient) is given by the Wagner factor (which is also known in metallurgy in the special case of predominant electronic conductivity as the thermodynamic factor) W = d n ajd In where A represents the electroactive component. W may be readily derived from the slope of the coulometric titration curve since the activity of A is related to the cell voltage E (Nernst s law) and the concentration is proportional to the stoichiometry of the electrode material ... 

T Tobias number (ratio of mass transport to ohmic resistance), dimensionless Wa Wagner number, (ratio of activation to ohmic resistance), dimensionless aa,ac, transfer coefficients, anodic and cathodic, respectively, dimensionless 8C equivalent mass transfer boundary layer thickness (Nemst-type), cm r overpotential, V... 

Bokhoven and Rayen [97] measured reaction rates on 0.5-0.7 mm and 2.4-2.8 mm particles at 1, and 30 atm and 325-550 °C. The effective diffusion coefficient of NH3 was calculated from the results of O2 diffusion measurements on a catalyst with the same surface area and porosity as the catalyst used in the activity measurements. The authors approximated the reaction rate by a pseudo first-order reaction suggested by Wagner [103] to calculate the effectiveness factor. Good agreement between measured and calculated data was obtained. However, the approximation above is only good, if the reaction is near equilibrium. 

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