Equilibrium adsoiption process

In the above-mentioned cases of polymerization of lower alkyf acrylates, because of the high rate of the process = 1260 dm mol sec for MA (Bagdasar yan, 1966) and the high monomer concentration in particles (Gerrens, 1964), the surface of the monomer-polymer phase increases at a rate that may exceed the rate of attainment of equilibrium adsoiption. 

Adsoiption is a widely used separation process in the chemical process industry. Selectivity is a key property that determines the ease and efficiency of any separation. Although, selectivity is a function of both composition and pressure, most of the design calculations are carried out using a Langmuirian approach with constant selectivity, using only pure component data. The conventional techniques to characterize the selectivity behavior by measuring mixture equilibrium data require a large investment of time and elaborate experimental setup. Moreover selectivity is very sensitive to experimental errors. 

Here, 2m represents the REC per unit mass of solid. Helfferich uses the total concentration of ions in equivalents for both phases. Tliis difference is due to the different nature of adsoiption and ion exchange. In ion exchange, the concentration in equivalents in both phases is constant tliroughout the process (stoichiometric phenomenon). On the other hand, in adsoiption this is not the case. Tliis is why in ion exchange, the total amount in equivalents in tlie solid phase is used, whereas in adsoiption the equilibrium uptake q is used. 

In this expression, U(t) is relative rate of uptake and C is relative to equilibrium, i.e. the sites available for ion exchange or adsoiption for the specified ratio V/m. Thus, the absolute rate is a coupled result of kinetics and equilibrium. Note that in a solid diffusion-controlled process, U(t) is relative to the ease of movement of the incoming species in the solid phase (through D ). 

Equilibrium Tlie physical process (reaction) of adsoiption or ion exchange is considered to be so fast relative to diffusion steps tliat in and neai the solid paiticles, a local equilibrium exists. Tlien, tlie so-called adsoiption isotlierm of the form q = f(Cff relates the stationaiy and mobile-phase concentrations at equilibrium. Tlie smface equilibrium relationship between tlie solute in solution and on tlie solid smface can be described by simple analytical equations (see Section 4.1.4). Tlie material balance, rate, and equilibrium equations should be solved simultaneously using tlie appropriate initial and boundary conditions. Tliis system consists of foiu equations and four unknown paianieters (C, q, q, and Q). 

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