**Acknowledgements**

*Advanced Sorption Process Applications*

*qt* = *qe*

called pseudo-second-order rate model (Eq. 12) [38]:

*qe* <sup>=</sup> *qe*

*qt* = kid t

intra-particle diffusion is the only rate-controlling step.

\_\_*<sup>t</sup>*

slope and the intercept.

**3. Conclusion**

represented in Eq. (14) [41]:

is Lagergren model (pseudo-first-order). The nonlinear and linear forms of the

(1 + *e*<sup>−</sup>*k*1*<sup>t</sup>*

ln(*qe* − *qt*) = ln(*qe*) − *k*<sup>1</sup> *t* (11)

where *qt* and *qe* (mg/g), respectively, are the adsorption capacity at any time (*t*)

2 (*k*<sup>2</sup> *<sup>t</sup>*) \_\_\_\_\_\_\_\_\_ (1 + (*k*<sup>2</sup> *qet*))

The kinetic model that has the correlation between the adsorption of metal ions and the square of active vacant adsorption sites on the surface of adsorbents is

) (10)

*qe* (13)

0.5 + C (14)

(12)

model are represented in Eqs. (10) and (11), respectively [40]:

and at equilibrium. *k1* (1/min) is the pseudo-first-order rate constant.

Eq. (8) can be rearranged to be in the following linear form (Eq. 13):

and at equilibrium. *k2* (g/mg min) is the pseudo-second-order rate constant.

*<sup>q</sup><sup>t</sup>* <sup>=</sup> \_\_\_\_ <sup>1</sup> *qe* 2*k*2 + \_\_*<sup>t</sup>*

where *qt* and *qe* (mg/g), respectively, are the adsorption capacity at any time (*t*)

By plotting ln*(qe−qt)* versus *t* and *t/qt* versus *t* in the previous equations (Eqs. (11) and (13)), all the adsorption kinetic parameters can be determined from the

The influence of mass transfer resistance on binding metal ions on adsorbents was tested using the intra-particle diffusion model (Weber and Morris model)

where *qt* (mg/g) is the adsorption capacity at any time (*t*), *kid* (mg/g min0.5) is the intra-particle diffusion rate constant, and C (mg/g) is a constant related to the thickness of the boundary layer. From plotting of *qt* versus the square root of *t,* the diffusion constant kid can be calculated. If this plot passes through the origin, then

Removal of heavy metals from wastewater would provide an exceptional alternative water resource. Algae biomass adsorbents, which utilized for adsorptive removal of heavy metal pollutants from wastewater, show a promising alternative. Different empirical isotherm models for single analyte have been discussed (i.e., Freundlich, Langmuir, Temkin, Sips, and Redlich-Peterson). In a large number of studies, the Freundlich and Langmuir models are the most commonly and widely used isotherm models. The two kinetic models, which are still in a wide use for studying the rate uptake of heavy metals and their bioadsorption from aqueous solutions, are pseudofirst- and pseudo-second-order kinetic models. In chemisorption process, the pseudosecond-order kinetic model is superior to pseudo-first-order model as it takes into account the interaction of adsorbent-adsorbate through their valency forces.

**160**

The support of the Center for Environment and Water in the research institute of King Fahd University of Petroleum and Minerals King Fahd University of Petroleum and Minerals is highly acknowledged.
