Chemical drive temperature coefficient

The index is added for clarification to avoid confusion with the molar concentration Ci and the temperature coefficient a, of the chemical potential. For the drive, we obtain correspondingly ... 

When a set of rate data is obtained, the first step in the analysis is to ascertain which regime of mass transfer applies to the data. The quantity which is measured is the total mass transfer rate V the chemical mass transfer coefficient can be extracted from the data provided the driving force and the interface area are known. The key to the identification of the regime is the dependency of V on the operating variables. The latter are the degree of mixing as represented by k the interface area A the liquid volume V temperature and the physical driving force a -a. ... 

Conversely, the correct approach to formulate the diffusion of a single component in a zeolite membrane is to use the MaxweU-Stefan (M-S) framework for diffusion in a nonideal binary fluid mixture made up of species 1 and 2 where 1 and 2 stands for the gas and the zeohtic material, respectively. In the M-S theory it is recognized that to effect relative motions between the species 1 and 2 in a fluid mixture, a force must be exerted on each species. This driving force is the chemical potential gradient, determined at constant temperature and pressure conditions [68]. The M-S diffiisivity depends on coverage and fugacity, and, therefore, is referred to as the corrected diffiisivity because the coefficient is corrected by a thermodynamic correction factor, which can be determined from the sorption isotherm. 

The three main driving forces which have been used within diffusion models (moisture content, partial pressure of water vapor, and chemical potential) will now be discussed. Attempts to predict diffusion coefficients theoretically will also be reviewed, together with experimental data for fitted diffusion coefficients and their dependence on temperature and moisture content. 

Performances of PV membranes are represented by parameters such as separation factor, flux of permeates, and service life. The separation factor of a membrane is a measure of its permeation selectivity (permselectivity) and is defined as the ratio of the concentration of components in the permeate mixture to that in the feed mixture. The component flux is the amount of a component permeating per unit time and unit area, and is given by the product of the permeability coefficient of the membrane and the driving force. The driving force is the gradient in the chemical potential of the components between the feed and the permeate side of the membrane. These values are influenced by operating variables such as temperature, composition of each component in the feed mixture, and permeate side pressures (see Fig. 107). 

The chemical potential // and drive (afhnity) X are not considered independent concepts in the conventional thermodynamic formalism. Therefore, one does not directly define the temperature and pressure coefficients a and f), as well as oc and Ji, rather, they are always expressed in terms of different quantities ... 

To make comparisons with the above salt effects, however, accurate values of An from acid-base titrations and correction of concentrations to activities should be considered. At this time, however, several different graphical representations of relative efficiencies are possible. These include comparison of the relative effectiveness of changes in chemical potential, Ap, to drive T, from just above to below the operating temperature, comparison of the relative ApAn areas determined from acid-base titration curves, and comparison of the significance of different degrees of positive cooperativity, that is, the impact of changes in the Hill coefficient. 

Most of the multicomponent systems are non-ideal. From thermodynamic viewpoint, the transfer of mass species i at constant temperature and pressure from one phase to the other in a two-phase system is due to existing the difference of chemical potential 7t, x p between phases, in which /t,- p =p + T Fln where y, is the activity coefficient of component i is p at standard state. In other words, for a gas (vapor)-liquid system, the driving force of component i transferred from gas phase to the adjacent liquid phase along direction z is the... 

Mass transport by diffusion can be regarded as the last resort. When movement of the electroactive species is not promoted by the input of external energy, either electrical (migration) or mechanical (convection), diffusion takes over. The driving force in this case is the gradient in chemical potential caused by the gradient in concentration. It is a relatively slow process, with diffusion coefficients for small molecules in dilute aqueous solutions at room temperature, in the range of 2 X 10" -8 X 10 cm s- ... 

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