Adsorption thermodynamic equilibrium

In contrast to the ionizing electrode method, the dynamic condenser method is based on a well-understood theory and fulfills the condition of thermodynamic equilibrium. Its practical precision is limited by noise, stray capacitances, and variation of surface potential of the air-electrode surface, i.e., the vibrating plate. At present, the precision of the dynamic condenser method may be limited severely by the nature of the surfaces of the electrode and investigated system. In common use are adsorption-... 

Consequences of the Snyder and Soczewinski model are manifold, and their praetieal importance is very signifieant. The most speetaeular conclusions of this model are (1) a possibility to quantify adsorbents ehromatographic activity and (2) a possibility to dehne and quantify chromatographic polarity of solvents (known as the solvents elution strength). These two conclusions could only be drawn on the assumption as to the displacement mechanism of solute retention. An obvious necessity was to quantify the effect of displacement, which resulted in the following relationship for the thermodynamic equilibrium constant of adsorption, K,, in the case of an active chromatographic adsorbent and of the monocomponent eluent ... 

Monolayers of distearoylphosphatidylcholine spread on the water-1,2-dichloro-ethane interface were studied by Grandell et al. [52] in a novel type of Langmuir trough [53]. Isotherms of the lipid were measured at controlled potential difference across the interface. Electrocapillary curves derived from the isotherms agreed with those measured under the true thermodynamic equilibrium. Weak adsorption or a stable monolayer was found to be formed, when the potential of the aqueous phase was positive or negative respectively, with respect to the potential of the 1,2-dichloroethane phase [52]. This result... 

The classical method to study adsorption deals with establishing a correspondence between thermodynamically equilibrium amount of absorbed gas, the temperature and the partial pressure of the gas in space surrounding adsorbent. Usually, a constant temperature is maintained throughout an adsorption experiment. The shape of isotherms obtained gives information on the character of adsorption. 

The two main assumptions underlying the derivation of Eq. (5) are (1) thermodynamic equilibrium and (2) conditions of constant temperature and pressure. These assumptions, especially assumption number 1, however, are often violated in food systems. Most foods are nonequilibrium systems. The complex nature of food systems (i.e., multicomponent and multiphase) lends itself readily to conditions of nonequilibrium. Many food systems, such as baked products, are not in equilibrium because they experience various physical, chemical, and microbiological changes over time. Other food products, such as butter (a water-in-oil emulsion) and mayonnaise (an oil-in-water emulsion), are produced as nonequilibrium systems, stabilized by the use of emulsifying agents. Some food products violate the assumption of equilibrium because they exhibit hysteresis (the final c/w value is dependent on the path taken, e.g., desorption or adsorption) or delayed crystallization (i.e., lactose crystallization in ice cream and powdered milk). In the case of hysteresis, the final c/w value should be independent of the path taken and should only be dependent on temperature, pressure, and composition (i.e.,... 

The principle we have applied here is called microscopic reversibility or principle of detailed balancing. It shows that there is a link between kinetic rate constants and thermodynamic equilibrium constants. Obviously, equilibrium is not characterized by the cessation of processes at equilibrium the rates of forward and reverse microscopic processes are equal for every elementary reaction step. The microscopic reversibility (which is routinely used in homogeneous solution kinetics) applies also to heterogeneous reactions (adsorption, desorption dissolution, precipitation). 

Thermodynamic equilibrium constant for over-all reaction Adsorption equilibrium constant for species /, or product of absorption constant and initial mole fraction of species i... 

This is called a Langmuir adsorption isotherm for a species A, and the function 9a( Pa) isi shown in Figure 7-23. The KjS are the adsorption-desorption equilibrium constants for species A and B. By historical convention we call these the adsorption isotherms. Before i we proceed let us note that this is a true thermodynamic equilibrium relation so that... 

The duration of each dosing experiment is about 15-50 minutes (depending on the sample and of the time constant of the calorimeter), which was long enough to yield well-resolved heat-flow peaks and a stable horizontal baseline of the microcalorimeter. For all catalysts presented here, adsorption always reached thermodynamic equilibrium. Prior to adsorption measurements, the samples were pretreated in the calorimetric cell by heating overnight under vacuum. 

We extend our description to adsorption at the solid-liquid interface. For many systems we can use the same models as for gas adsorption on a solid surface, we only have to replace the pressure P by the concentration c. The adsorption of macromolecules to surfaces is briefly discussed in Section 10.3.2. For macromolecules desorption is often negligible and thermodynamic equilibrium is only reached after a very long time, if at all. 

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