# Adsorption of Ni2+ and Cd2+ from Water by Calcium Alginate/Spent Coffee Grounds Composite Beads
## 3 Results and Discussion
### Kinetic Experiments  
The effect of contact time during the adsorption of Cd\({}^{2+}\) and Ni\({}^{2+}\) ions by 0.5g of adsorbent in 100 mL of solution was investigated with initial concentrations 10 ppm and 100 ppm of metal. The percentages of removal by time can be seen in Figure 12. The pseudo-second-order linear equation was used to evaluate the kinetic data because it showed the best fit with the results (R\({}^{2}>\) 0.995). The pseudo-second order model assumes that the rate-limiting step may be chemical sorption or chemisorption involving valency forces through sharing or exchange of electrons between adsorbent and adsorbate. Intraparticle diffusion was found to be rate-limiting following the pseudo-first order sorption rate expression of Lagergren [44] but that is not the case in this study. Therefore, the kinetics of adsorption in this study is mainly due to chemisorption, not diffusion. The linear pseudo-second-order equation is described by Equation (9) [45]:  
\[t/q_{t}=1/(k_{2}q_{e}{}^{2})+t/q_{e} \tag{9}\]  
where \(k_{2}\) (g/mg-min) is the rate constant of pseudo-second-order adsorption, \(q_{e}\) (mg/g) is the amount of Cd\({}^{2+}\) or Ni\({}^{2+}\) ions at equilibrium, and \(q_{t}\) (mg/g) is the amount of Cd\({}^{2+}\) or Ni\({}^{2+}\) ions adsorbed at time \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sorbents** & **pH** & \
\begin{tabular}{c} **Sorption Capacity** \\ **Cd\({}^{2+}\) (mg/g)** \\ \end{tabular} &
\begin{tabular}{c} **Sorption Capacity** \\ **Ni\({}^{2+}\) (mg/g)** \\ \end{tabular} & **References** \\ \hline Free dead algal cells & - & - & 13.90 (L) & - \\ Blank alginate beads & - & - & 25.60 (L) & - \\ Immobilized dead algal cells & 5.0 & - & 31.30 (L) & [36] \\ Composite Based on & 4.0 & - & 44.36 (L) and 47.73 (S) & [37] \\ Alginate and Magadiite & 5.0 & - & 97.93 (L) & [38] \\ Alginate beads & 6.0–7.0 & 39.32 (L) & - & [39] \\ Alginate–calcium & 6.0 & 10.20 (L) & - & [40] \\ carbonate composite beads & & 5.0 & 68.90 (L) & - & [41] \\ Alginate-immobilized & & & 164.50 (L) & 86.49 (L) & [42] \\ _Chlorella sorchiiana_ & & & & \\ Alginate beads & 5.0–6.0 & 31.40 (L) & - & - \\ Alginate-immobilized & 5.0–6.0 & 88.60 (L) & - & [43] \\ _Chlamydomonas reinhardtii_ & & & & \\ Alginate beads from & 4.5 & 130.77 (L) and & - & [15] \\ Laminaria digitata & & 198.43(S) & - & [15] \\ Spent Coffee Grounds & - & 4.48 (L) & - & [35] \\ Spent Coffee Grounds & 5.0 & 11.60 (L) & & [18] \\ Spent Coffee Grounds & 6.0 & 10.67 (L) and 12.75 (S) & 5.61(L) and 7.81 (S) & [This work] \\ Alginate beads & 6.0 & 38.05 (L) and 38.65 (S) & 14.67 (L) and 14.22 (S) & [This work] \\ Alginate-Spent Coffee & & & & \\ Grounds & 6.0 & 25.50 (L) and 91.18 (S) & 12.32 (L) and 20.96 (S) & [This work] \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Maximum adsorption capacities (mg/g) of different alginate, algal-based, or spent coffee adsorbents from [PERSON] model (L) and Sips model (S). (min). The slope and the intercept of graph \(t\)/\(qt\) versus \(t\), give the values of \(k_{2}\) and the \(q_{e}\) calculated during the adsorption of metal ions at a specific initial concentration of Cd\({}^{2+}\) or Ni\({}^{2+}\). The kinetic parameter \(h\) (mg g\({}^{-1}\)min\({}^{-1}\)) is the initial adsorption rate when \(t\)\(\rightarrow\)0. This parameter can be calculated by using Equation (10) [45]:  
\[h=k_{2}{q_{e}}^{2} \tag{10}\]  
Figure 13 shows the plots of pseudo-second-order linear equations and the results obtained from these plots are summarized in Table 5. The initial adsorption rate parameter (h) is greater for CA-SCGs beads in the adsorption of Ni\({}^{2+}\) and Cd\({}^{2+}\) at both initial concentrations. The rate constant of pseudo-second-order adsorption (k\({}_{2}\)) is greater for CA-SCGs in the adsorption of Cd\({}^{2+}\) but not in the adsorption of Ni\({}^{2+}\). Our previous study on the adsorption of Cu\({}^{2+}\) by CA-SCGs at pH 4 showed a much larger difference between the kinetics of adsorption by the CA-SCGs beads and the kinetics of adsorption by the CA beads [10].