Page - 155 - in Advanced Chemical Kinetics

arecalculatedas0.79kJmol�1 fordecolorizationand0.91kJmol�1 fordegradationprocesses, only physical interactions are probable amongMOmoiety and the supported catalyst. The lower correlation coefficients (R2 = 0.826 for decolorization and R2 = 0.667 for degradation) again represents thepoorer fit of theexperimentaldata. The kinetics ofMOadsorption onto 0.5MZnO-FA-Sep are studied in terms of pseudo-first order [39], pseudo-second order [40], Elovich [41–43] and intraparticle diffusion [44, 45] models. Pseudo-first order model: Pseudo-first ordermodel describes the adsorption rate based on the adsorptioncapacity [39]. Thedifferential equationof themodel is expressedas follows: dqt dt ¼k1 qe�qt (10) wherek1 is thepseudo-first order rate constant (min), qe is theadsorption capacityat equilib- riumandqt is theadsorptioncapacityat time t. IntegratingEq. (10) for theboundaryconditionsofqt =0at t =0andqt=qtat t = tgives ln qe�qt ¼ lnqe�k1t (11) Accordingly, thevaluesof ln(qe�qt)are linearlycorrelatedwith tbyplotof ln (qe�qt)versus t. The rate constant (k1) and qe can be determined from the slope and intercept of the plot, respectively. The pseudo-first order equation fits well for the first 30 min data and then deviationsarenoticed.Althoughrate shouldbeproportional to the firstpowerofMOconcen- tration, the linearity is lost for thehigher initialMOconcentrations. Thismaybeattributed to thelimitingeffectofporediffusionthroughtheadsorptionprocess.Fortherapidadsorptionof the initial stages, the first order rate constants, k1, decreasewith increments inMOconcentra- tions for both decolorization and degradation processes (Table 3). It is also noticed that calculated qe values agreewellwith the experimental data. The high correlation coefficients show the applicability of pseudo-first order kinetics to the adsorption of MO onto the supportedcatalyst. Pseudo-second-order equation: The adsorption kinetics may also be described by the pseudo- secondordermodel [40].Thedifferential equation isgivenas follows: dqt dt ¼k2 qe�qt 2 (12) wherek2 is thesecond-order rateconstantofadsorption. IntegratingEq. (12) for theboundary conditionsofqt=0at t =0andqt=qtat t = tgives t qt ¼ 1 k2q2e þ t qe (13) Adsorption, Kinetics and Photoactivity of ZnO-Supported Fly Ash-Sepiolite Ternary Catalyst http://dx.doi.org/10.5772/intechopen.70504 155