# The Diffusion Role in Adsorption of Hexavalent Chromium on Solid Olive Mill Waste
## 4 Results and Discussion
### Uptake Measurements  
Figure 3 shows \(q(t)\) (for the sake of simplicity, the subscript A has been omitted) vs. the contact time between the Cr(VI) solution and either the LAPWP or natural adsorbent. Figure 3: Cr(VI) adsorbed on natural biomass (red squares) (WP) and biomass treated with LAP(dark points), (LAPWP). The inspection of Figure 3 reveals that adsorption on LAPWP is faster than on natural adsorbent. Furthermore, the amount of chromium retained by LAPWP biomass is approximately 25% higher than natural adsorbent. Dry biomass immersed into liquid water absorbs about 40% of its mass. Accordingly, one can estimate that the LAPWP sample contains about 0.4% LAP dispersed in the organic matrix. With this in mind, the experimental results displayed in Figure 3 must consider a synergistic effect between the LAP structure and biomass. Indeed, LAP particles are disk-shaped with a thickness of 1 nm and a diameter of 25 nm. In aqueous medium, at pH 7.6, the faces of the disks assume a negative charge, while the edges exhibit a positive charge [24]. Furthermore, at pH = 7.6, the biomass surface is slightly negative. Thus LAP-platelets orient their edges to bond with the biomass surface, causing a very extensive perturbation in its three-dimensional structure. This molecular rearrangement of biomass makes many more binding sites accessible for \(\text{CrO}_{4}{}^{2-}\), \(\text{HC}_{\text{rO}}{}_{4}{}^{-}\) ions. In other words, the synergistic interaction between LAP-platelets and the biomass surface produces a greater number of adsorption sites to the Cr(VI) species. Obviously, the individual molecules diffuse into the material before binding to the adsorption sites. Namely, the diffusion process plays a key role in understanding the synergic interaction between LAP and the organic matrix of the biomass. To gather information in this direction, uptake measurements were performed in the presence of 1.5, 2.5, 5 and 10 g of LAPWP adsorbent, while the Cr(VI) concentration (48.1 uM) and the dispersion volume (0.250 dm\({}^{3}\)) were kept constant. All of experimental results are presented in Figure 4 where \(q(t)\) as a function of the contact time, \(t\), is plotted, for each amount of LAPWP used. It is evident that increasing the LAPWP mass increases the corresponding uptake curve. Such a trend is mostly attributed to an increase in the adsorbent surface area and the availability of more active binding sites on the surface of the adsorbent. Of course, to evaluate the role of diffusion, the term \(q_{\infty}\) has to be determined. Here, we apply the procedure developed to extract the sedimentation limiting height from the experimental data [25]. It is empirically verified that a plot \(q(t)\) vs. \(t^{-1}\) exhibits a linear trend whereby \(q_{\infty}\) was evaluated by a linear best-fit, as shown in Figure 5. Having obtained \(q_{\infty}\), the dimensionless ratio \(q(t)/q_{\infty}\) is plotted as function of \(t\), as shown in Figure 6a. Figure 4: Cr(VI) amount adsorbed on biomass LAPWP as a function of the contact time. The number on each curve indicates the grams of LAPWP dispersed in 0.25 dm\({}^{3}\) of Cr(VI) solution at 48.1 uM. Each measurement was in duplicate and the root-mean-square error of the measurements was estimated to be 10–15%. The curves are well fitted to Equation (19), that is to say the experimental values are in good agreement with what would be predicted by the diffusion-binding model. However, if the adsorption process is actually governed by diffusion, the ratio \(q(t)/q_{\infty}\) has to verify the _parabolic_ law of diffusion [17]. For this reason, the experimental values of Figure 6a are also plotted as a function of \(\sqrt{(}t)\) in Figure 6b. The straight line obtained confirms the prediction based on Equation (19), in other words,the diffusion-binding model explains the experimental results of Cr(VI) adsorption on LAPWP. According to Equation (18), by the slope of lines in Figure 6b, one can calculate the lifetime \(\tau_{D}\).