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Plotting Qt vs. t1/2 give straight line did not pass through the origin with Ki (intraparticle diffusion constant) =0.74, 0.85 and 0.57 mg/g min0.5, (R2 = 0.53, 0.59, 0.73) as shown in fig.1b. The intercept values (film thickness) were 1.01, 0.71 and 1.03 for the sorption of Br.G, To.B and Tr.B. the boundary layer effect is high for Tr.B as a great value of C. The deviation exist in linear consists of two level (Moawed et el., 2014), the first level, the diffusion rate is high then, decreased with the time pass in the second level. The values of ki (1), ki (2) of these steps are (2.74, 0.089 mg g-1 min1/2) for Br.G, (2.65, 0.032 mg/g min1/2) for To.B and (1.35, 0.2 mg/g min1/2) for Tr.B. ki (2) always lower as active centers were blocked by adsorbed dye molecules. The first level is a transport step one after transfer the adsorbed solution into adsorbent, it is too fast step. The second level is equilibrium step which represents diffusion of adsorbate molecules from the external of the adsorbent into the pores of adsorbent molecules (Tran et el., 2017), proving adsorption process controlled by double steps. Rate of diffusion of To.B > Br.G >Tr.B which mean ki dependent on the molecular size of dyes. The lighter molecule’s weight as To.B will diffuse faster in contract Tr.B which has heavier molecule’s weight. Larger ki, better adsorption mechanism which related to improved bonding between adsorbate molecules with adsorbent particles.
(?) the slowness of adsorption step was studied by Bangham equation (Nowak and Bangham, 1996):
log?log??C?/(C?-Q_(t ) m)? = log??(K? m)/(2.303 V) +? log?t ? (5)
The double logarithmic plots against time doesn’t give perfect line with a correlation coefficient (R2= 0.69, 0.74 and 0.77) for sorption of Br.G, To.B and Tr.B dyes onto [email protected], respectively (Fig.1CS). This means that the film diffusion is not the sole rate-controlling step. The values of ? (Table 3) are 0.47, 0.55 and 0.40 for Br.G, To.B and Tr.B dyes which means ? value independent of the dye size.

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