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The mathematical model has been presented in the paper based on biosorption equilibrium and kinetics as well as relevant mass balances of the integrated system.
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The influence of different levels of pH on biosorption equilibrium was studied through changing the pH of the solution in range of 2 7.
Based on the equilibrium biosorption, the pseudo-second-order kinetic equation is expressed by the relation (Hamdaoui et al. 2008): frac{t}{{q_{text{t}} }} = frac{1}{{K_{2} q_{text{e}}^{2} }} + frac{t}{{q_{text{e}}}}, (7 where K 2 is the rate constant (g/mg min): h = K_{2} ;q_{text{e}}^{2}, (8) h is the initial biosorption rate (mg/g min).
The phenomenological mathematical modeling of the kinetics of biosorption was based on binary equilibrium equations, material balances and possible limiting mass transfer steps instead of the empirical models usually applied.
(d) The affinity constant (KD) was calculated from steady state analysis based on R equilibrium values.
and Prism GraphPad version 5. Steady state analysis was performed based on the equilibrium response.
The pseudo-second-order equation based on adsorption equilibrium capacity may be expressed as follows: frac{t}{{q_{t} }} = frac{1}{{K_{2} q_{e}^{2} }} + frac{1}{{q_{e} }}left( t right) (4 where q e is the equilibrium biosorption capacity and K 2 is the pseudo-second-order rate constant (g/mg min).
d) Synthesis of new ceramic oxides based on phase equilibrium diagrams.
CREIM is a computable regional general equilibrium model based on Marshallian equilibrium of outputs (see Takayama 1985).
The process model is based on equilibrium thermodynamics.
These observations were explained based on equilibrium theory.
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