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Adsorption

, Volume 21, Issue 6–7, pp 445–458 | Cite as

Chemical equilibrium of ion exchange in the binary mixture Cu2+ and Ca2+ in calcium alginate

  • M. G. C. da Silva
  • R. L. S. Canevesi
  • R. A. Welter
  • M. G. A. VieiraEmail author
  • E. A. da Silva
Article
First Online:

Abstract

Biopolymer alginate is capable of triggering interchain interactions in the presence of divalent and trivalent cations. Calcium alginate particles obtained by the emulsification method have been used in ion-exchange packed bed tests to remove synthetic copper effluents. Adsorption equilibrium data were obtained from single and binary component systems, which were subsequently subject to mathematical modeling. In the case of the modeling system with binary components, where the calcium was considered as a second ion, there was no significant improvement for the models analyzed, in counterpoise to the isotherm models applied to the single component system. The ideal law of mass action and the law of mass action which presupposed that both phases were non-ideal showed similar results. This process was found to be effective and feasible for industrial applications used to in heavy metal removal processes.

Keywords

Ion exchange Copper Calcium alginate Modeling 

List of symbols

aiα

Activity of the compound i in phase α

A

Debye Huckel constant

aCu

Freundlich constant considering the presence of copper in the binary mixture (L/meq)

aCu–Ca

Freundlich constant considering the copper and calcium binary mixture (L/meq)

b

Parameter associated with the bioadsorbent adsorption capacity (L/meq)

B

Number of empty sites

B0

Total number of available sites

Bji

Bromley parameter involving the cation i and the anion j

B–Cu

Active sites connected to copper ions

B–Ca

Active sites connected to calcium ions

B–Cu–Ca

Active sites connected to copper and calcium ions

C

Metal solution concentration in equilibrium state (meq/L)

CECavailable

Available cation exchange capacity (meq/g)

CECTotal

Total cation exchange capacity (meq/g)

Fi

Sum of interaction parameters

Fobj

Objective function

I

Ionic length (molal)

KCuCa

Thermodynamic equilibrium constant of the ion exchange reaction between copper and calcium

Kd

Parameter associated with the free energy of biosorption (mg/L)

KCa

Langmuir model competition

KCa–Cu

Langmuir competition model

KCu

Langmuir competition model

KCu–Ca

Langmuir competition model

kCu

Langmuir power and Lang–Freundlich models

kCa

Langmuir power and Lang–Freundlich models

L

Bed height covered by ionic solution (eq. ad. and des.) (cm)

mi

Molality of component i (molal)

n

Parameter associated with the effect of the concentration of metal ions on the adsorption capacity

ni

Freundlich constant of component i considering a binary mixture

q

Amount adsorbed (meq/g)

qmax

Maximum amount adsorbed (meq/g)

qi

Amount of component i adsorbed

r

Ratio between the amount of adsorbed and desorbed ions of alginate particles

t

Time (min)

V

Power flow system in porous bed (mL/min)

yi

Fraction of component i in solid phase

Z

Bed height (equation of ratio between ad. and des.) (cm)

zi

Ionic charge of component i

zji

Arithmetic average between cation i and anion j

Greek

α′11

Parameter of Freundlich model for Copper ion

α′12

Parameter of Freundlich model for Calcium ion

γi(α)

Coefficient of fugacity

γiα

Activity coefficient of component i in phase α

θ

Parameter fitted for each model used according to the objective function Fobj, used

Λij

Wilson parameter involving cation i and anion j

Superscripts

A

Solid phase—alginate

α

Phase

R

Solid phase—resin (alginate)

S

Aqueous phase—solution

*

Equilibrium

Subscripts

i

Cation

j

Anion

n

Number of components

m

Number referring to the total test concentration

f

Copper fraction at a given total concentration

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Notes

Acknowledgments

The authors would like to acknowledge the financial support received from FAPESP and CNPq for this research.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • M. G. C. da Silva
    • 1
  • R. L. S. Canevesi
    • 2
  • R. A. Welter
    • 1
  • M. G. A. Vieira
    • 1
    Email author
  • E. A. da Silva
    • 2
  1. 1.Department of Processes and Product Design, School of Chemical EngineeringUniversity of Campinas, UNICAMPCampinasBrazil
  2. 2.State University of West ParanáToledoBrazil

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