Mechanism of mass transport and calculation of free energy for the adsorption of PB(II) Ion by adsorbent made from solid tofu waste immobilized on silica surface

From the perspective of the kinetic adsorption in solution system, generaly there are two model of mechanisms for the mass transport model of transporting the adsorbate mass to the surface of the adsorbent, namely: the intraparticle diffusion and intraparticulate diffusivity. In this research, the rate of intraparticle diffusion constant or diffusion coefficient based on the Weber and Morris, k_id was of 0.4478 mg.g^-1.minute^-1/2 with an initial concentration of Pb (II) ions of approximately 50 ppm. While according to Equation of Erhan obtained k_id was of 0.720 mg.g^-1.minute^-1/2 (this is taken as a rate factor is the percentage of sorbate adsorbed per unit time). For the study of intraparticle diffusivity using α_e (fractional attainment at equilibrium) obtained rate coefficient or rate constant for particle diffusion controlled process (kp) of 0.0627 minutes^-1 (it is taken as rate factor i.e. percent of sorbate adsorbed per unit time (mg.g^-1min^-1(1/2)) at the same initial concentration of Pb (II) ion with intraparticle diffusion. While based on calculations of free energy of adsorption in the range of variations in the initial concentration from 5 to 50 ppm at 27ºC, with rate of stirring about 120 rpm, using Dubinin-Radushkevich equation, was 0.5 Kjoule.mol^-1 which is classified as a type of physical sorption.