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Sorption of lead, copper, and cadmium by calcium alginate. Metal binding stoichiometry and the pH effect

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Abstract

Binding of heavy metal ions by calcium alginate has been described in the literature with many different models. In the present study, two most basic models were used to systematically compare their simultaneous description of metal uptake dependence on pH and metal ion concentration in the bulk solution. The experimental datasets corresponding to the binary sorption systems containing protons and heavy metal ion (cadmium, lead, or copper) were taken from the literature. The applicability and limitations of both models are discussed. Neither of the models gave a completely satisfactory description of all data. The two-site occupancy model yielded better results compared to the one-site occupancy model when considering the coherence of the parameters (e.g., affinity constants) but the quality of the obtained fits is similar in both cases.

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Acknowledgments

The author acknowledges the financial supports of the Foundation for Polish Science (START program, 2010) and of the Polish Ministry of Science and Higher Education (contract financed in 2010–2012 under project no. N N204 271238).

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Authors and Affiliations

  1. Institute of Catalysis and Surface Chemistry, Polish Academy of Sciences, ul. Niezapominajek 8, 30-239, Cracow, Poland

    Wojciech Plazinski

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Correspondence to Wojciech Plazinski.

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Appendix

Appendix

Let us consider the reaction of calcium ions binding by alginate and the corresponding equilibrium constant:

$$ \matrix{ {{\text{C}}{{\text{a}}^{{{2} + }}} + 2{{\text{X}}^{ - }}\overset{{{K_{\text{Ca}}}}}{\longleftrightarrow} {\text{Ca}}{{\text{X}}_{{2}}}} \hfill &{{K_{\text{Ca}}} = \frac{{\left[ {{\text{Ca}}{{\text{X}}_{{2}}}} \right]}}{{\left[ {{\text{C}}{{\text{a}}^{{2 + }}}} \right]{{\left[ {{{\text{X}}^{ - }}} \right]}^{{2}}}}}.} \hfill \\ }<!end array> $$
(A1)

This reaction, combining with Eqs. (1), (2), (3), and (4), describes the ternary system, containing heavy metal ions, calcium ions and protons. Each of these species can be present both in the bulk solution and in the complex with alginate (bound). The two-site occupancy mechanism of calcium binding is justified in the context of “egg-box” model describing the interactions between Ca2+ ions and alginate chains (Braccini and Pérez 2001; Grant et al. 1973). Equation (A1) can be combined with Eqs. (1), (2), (3), and (4) and the modified mass–balance relation (now, the presence of bound calcium ions must be included) in order to obtain the mathematical expressions describing the heavy metal (q Me) and calcium (q Ca) uptakes in the function of pH. The exact form of mathematical description (for 2-SO model) is given by the following system of Eqs. (A2) and (A3):

$$ {q_{\text{Ca}}} = {K_{\text{Ca}}}{C_{\text{Ca}}}{\left( {\frac{{{N_s} - 2{q_{\text{Ca}}} - 2{q_{\text{Me}}}}}{{1 + {{10}^{{ - {\text{pH}}}}}/{K_a}}}} \right)^2} $$
(A2)
$$ {q_{\text{M}}} = {K_{\text{Me}}}{C_{\text{Me}}}{\left( {\frac{{{N_s} - 2{q_{\text{Ca}}} - 2{q_{\text{Me}}}}}{{1 + {{10}^{{ - {\text{pH}}}}}/{K_a}}}} \right)^2} $$
(A3)

Some part of the results is presented in Fig. 5. It appeared that the influence of Ca2+ ions on the pH-dependent binding of heavy metals can be (mathematically precisely) described in terms of the r = (K Me C)/(K Ca C Ca) ratio, where K can be either K M,1 or K M,2, depending on the accepted model. When r > 10, the presence of calcium ions does not play a significant role and the system can be treated as a binary one, i.e., only the presence of protons and heavy metal ions should be taken into account. The metals considered in this study (Cu, Pb, Cd) have much higher affinity to alginates in comparison to calcium, according to numerous experimental studies (see, for instance, Haug (1961) and Lim et al. (2008)). Thus, K Ca can be assumed to be at least of an order of magnitude lower than K (the exact value depends on the considered system). The value of the respective concentrations ratio is harder to estimate but in most of the systems the inequality C Ca < C Me is fulfilled (see for instance the data by Khotimchenko et al. (2008)). Thus, the limit of the r > 10 condition corresponds approximately to calcium ion concentration equal to C Me and from Fig. 5 follows that the presence of calcium ions can be neglected only when the value of the (K Me C)/(K Ca C Ca) ratio exceeds (approximately) 10. The values of pK a and N s are not significant for the aforementioned effect.

Fig. 5
figure 5

The q Me/N s and q Ca/N s values plotted in the function of (pH–pK a ) for several values of K Ca C Ca parameter and for the 2-SO model. The fixed value K Me C = 104 g/mol was accepted; the unit of K Ca C Ca is gram per mole. Analogical results can be obtained for the 1-SO model and for other values of K Me C

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Plazinski, W. Sorption of lead, copper, and cadmium by calcium alginate. Metal binding stoichiometry and the pH effect. Environ Sci Pollut Res 19, 3516–3524 (2012). https://doi.org/10.1007/s11356-012-0913-1

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