Page - 156 - in Advanced Chemical Kinetics

The linearity obtained in the plot of t/qt versus t results in k2 value (as the intercept) and qe valueas theequilibriumadsorptioncapacity (fromtheslope).Similar to thepseudo-firstorder kinetics, k2decreasesas the concentrationof initialMOincreases forbothprocesses (Table3). Althoughhigh correlation coefficients are obtained, calculated qe values are not closer to the experimental values.Moreover, thepredicted chemical adsorption cannot be applicable since onlyphysical interactionsaresuggestedbetweenMOmoleculesandthesupportedcatalystvia D-Rmodel. Elovich equation:The Elovich equation is based on the adsorption capacity and expressed as follows [46–48]: dqt dt ¼αexp �βqt (14) whereβ is the initialadsorptionrate (mgg�1min�1)andα is thedesorptionconstant (gmg�1). The linearizedformofEq. (14)withboundaryconditionsofqt=0at t=0andqt=qtat t= t isas follows qt¼ 1=β ln αβ � 1=β lnt (15) Elovichparameters are given inTable 3. Theplot of qt versus ln t yields a linear relationship with a slope of 1/ β and an intercept of (1/β) ln (α β). The high correlation coefficients indicate suitability of the model for the evaluation of the adsorption process. The limited number of vacant-available sites on the supported catalyst may decrease the possibility of chemical adsorptionprocess through increments inMOconcentration.This eventually results insmallerβvalues inbothdecolorizationanddegradationprocesses. Simultaneously,desorp- tions from the surfacemay be enhanced via less strong physical attractions and increase α values. Interparticlediffusionmodel:Theadsorbatespeciesareprobablytransportedfromthebulkof the solution into the solid phase through intraparticle diffusion/transport process. Themodel is expressedby the followingequation: qt¼Kdifft1=2þC (16) where C (mg g�1) is the intercept and Kdiff is the intraparticle diffusion rate constant (in mgg�1min1/2).Kdiff canbeevaluatedby the linear correlationofqt versus t 1/2 (Table3).Asa general trend,Kdiffvalues increasewith increaseof initialMOconcentrationbutfor thehighest concentrations there seems to be a constancy. Thismay point out the existence of restricted diffusion for theexternalmass.AlthoughCvaluessupplies informationabout the thicknessof the boundary layer, experimental data do not exhibit neither an increasing nor a decreasing trend.Thus, theadsorptionmechanismcannotbeexplainedbyusing thismodelowing to the complexstructureof thesupportedcatalyst. Advanced Chemical Kinetics156