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

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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.

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Abbreviations

a α i :

Activity of the compound i in phase α

A :

Debye Huckel constant

a Cu :

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

a Cu–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

B 0 :

Total number of available sites

B ji :

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)

F i :

Sum of interaction parameters

F obj :

Objective function

I :

Ionic length (molal)

K Ca Cu :

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

K d :

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

K Ca :

Langmuir model competition

K Ca–Cu :

Langmuir competition model

K Cu :

Langmuir competition model

K Cu–Ca :

Langmuir competition model

k Cu :

Langmuir power and Lang–Freundlich models

k Ca :

Langmuir power and Lang–Freundlich models

L :

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

m i :

Molality of component i (molal)

n :

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

n i :

Freundlich constant of component i considering a binary mixture

q :

Amount adsorbed (meq/g)

q max :

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)

y i :

Fraction of component i in solid phase

Z :

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

z i :

Ionic charge of component i

z ji :

Arithmetic average between cation i and anion j

α′ 11 :

Parameter of Freundlich model for Copper ion

α′ 12 :

Parameter of Freundlich model for Calcium ion

γ (α) i :

Coefficient of fugacity

γ α i :

Activity coefficient of component i in phase α

θ :

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

Λ ij :

Wilson parameter involving cation i and anion j

A :

Solid phase—alginate

α :

Phase

R :

Solid phase—resin (alginate)

S :

Aqueous phase—solution

* :

Equilibrium

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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Acknowledgments

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

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Authors and Affiliations

  1. Department of Processes and Product Design, School of Chemical Engineering, University of Campinas, UNICAMP, Av. Albert Einstein, 500, Cidade Universitária “Zeferino Vaz”, Campinas, SP, 13083-852, Brazil

    M. G. C. da Silva, R. A. Welter & M. G. A. Vieira

  2. State University of West Paraná, Rua da Faculdade 645, Jardim La Salle, Toledo, PR, 85903-000, Brazil

    R. L. S. Canevesi & E. A. da Silva

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  1. M. G. C. da Silva
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  2. R. L. S. Canevesi
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  3. R. A. Welter
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  4. M. G. A. Vieira
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  5. E. A. da Silva
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Correspondence to M. G. A. Vieira.

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da Silva, M.G.C., Canevesi, R.L.S., Welter, R.A. et al. Chemical equilibrium of ion exchange in the binary mixture Cu2+ and Ca2+ in calcium alginate. Adsorption 21, 445–458 (2015). https://doi.org/10.1007/s10450-015-9682-8

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