Equilibrium parameters Langmuir kinetic model

The adsorption of methylene blue by coir pith carbon was carried out by varying the parameters such as agitation time, dye concentration, adsorbent dose, pH and temperature. Equilibrium adsorption data obeyed Langmuir isotherm. Adsorption kinetics followed a second order rate kinetic model. The adsorption capacity was found to be 5.87 mg dye per g of the adsorbent. There was no significant change in the per cent removal with pH. The pH effect and desorption studies suggest that chemisorption might be the major mode of the adsorption process. 

Ion exchange isotherms for PAN-KCoFC/Cs, KCoFC/Cs systems and PAN-zeolite 4A/Sr, zeolite 4A/Sr systems were obtained to evaluate the equilibrium parameters such as ion exchange capacity and equilibrium constant for kinetic calculations. The experimental data were modeled by Langmuir equation given by... 

The Langmuir Hinshelwood kinetic model based on this reaction scheme is formulated assuming that all reactions are in equilibrium except for reaction steps (2), (4), (7) and (11). Reaction steps (2), (4) and (7) are all steps which may be slow during the shift reaction [5,6], whereas reaction step (11) represents the slow step for methanol synthesis [8], The kinetic and thermodynamic parameters are taken from available Cu single crystal experiments. We call this type of model a static microkinetic model since the number of active sites are assumed constant (i.e., independent of reaction conditions) [21]. 

Another problem which can appear in the search for the minimum is intercorrelation of some model parameters. For example, such a correlation usually exists between the frequency factor (pre-exponential factor) and the activation energy (argument in the exponent) in the Arrhenius equation or between rate constant (appears in the numerator) and adsorption equilibrium constants (appear in the denominator) in Langmuir-Hinshelwood kinetic expressions. 

For all investigated systems, the correlation coefficients were estimated. The values of the correlation coefficients were very high, near to 1. The best fit gives combined Langmuir-Freundlich isotherm for the most of equilibrium isotherms, but it contents three parameters. The lowest correlation coefficient has Freundlich isotherm. The investigator decides which of the proposed models will be chosen for further mathematical modeling of the adsorption process that is in accordance with the subsequent application in kinetic and dynamic studies. 

The parameter values have been determined based either on the independent experiments or on available correlations as outlined in Table 1. In addition to equilibrium data, which are fitted to the Langmuir isotherm, knowledge of the values of the kinetic parameters and the sohd-phase ratio is necessary in order to accurately describe the performance of adsorbers. The intensity functions, 43 and and the solid phase ratios, and y j, are then found by minimizing the difference between data and model output. This minimization procedure is done by intuitively varying the parameters in the mathematical model until the experimental data and model results agree satisfactorily. 

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