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## Journal of the Chilean Chemical Society

##
*versión On-line* ISSN 0717-9707

### J. Chil. Chem. Soc. v.49 n.4 Concepción dic. 2004

#### http://dx.doi.org/10.4067/S0717-97072004000400014

Chil. Chem. Soc., 49, N 4 (2004): págs: 345-350
BENRABÉ L. RIVAS,^{*1} L. NICOLÁS SCHIAPPACASSE,^{1} EDUARDO PEREIRAU.,^{1} IGNACIO MORENO-VILLOSLADA ^{2}
The total retention coefficient a (e_{a}) has been searched and it was found that its influence is higher as a increases, so that its measurement must be performed with higher precision. In addition, e_{a} is higher for high a values due to the stronger influence of errors in the measurements of the different magnitudes that allow its calculation. In order to achieve a measurement of K_{f} with a relative error lower than 7 %, the experimental a found should not exceed the value 0.4 when relative errors for the independent variables ranging between 2 % and 5 % are considered.
Water-soluble polymers have been extensively studied during the last two decades, due to their ability to form complexes or exchange metal ions. These properties allow their use in industrial scale, in the treatment of residual waters, and in quantitative procedures at laboratory scale. When a PMC is formed in aqueous medium, an equilibrium is achieved, which is described in Scheme 1 (the charges are not included to simplify the notation):
Scheme 1
where (p) emphasizes that the L functional groups (ligands or ion exchange groups) are linked to a polymeric backbone. The constant that determines the equilibrium is called the
where [ML _{c} is the free metal ion concentration (non-complexed), [L] is the polymer concentration expressed in terms of repeat units, and m is a factor. Yet, there is controversy about the validity of this definition due to that for a polychelatogen solution, the L groups are not uniformly distributed in the system. Thus, it has been postulated that the exponent m may become different from the stoichiometric coefficient n.^{11-12)} Different techniques have been used to determine formation constants of PMCs. Among the most used are potentiometry and electronic spectroscopy. By the washing method of the LPR technique (see experimental) a The aim of this paper is to establish the relation between errors in the measurement of the variables involved in the ultrafiltration experiment and the variations that are produced either in the pattern of the retention profile and the formation constant of the PMC. This will allow determining which experimental measurement produces the highest impact on the accuracy of ultrafiltration measurements.
Poly(acrylic acid), PAA,
The ultrafiltration equipment has been previously described.
50.0 mL of a solution containing 5.0·10
A retention profile is a plot of the fraction of the initial metal ion retained in the ultrafiltration cell (R) versus the
where V
RESULTS AND DISCUSSION
Geckeler and col.
where a, the fit parameter, is the
where
and
with
In Equation (6) [M] Combining Equations (1) and (8), an expression that relates the association constant with the formation constant of the PMC is obtained:
It has been previously demonstrated that, independently of the coordination sphere composition of the complexed metal-ion,
The relative error involved in the determination of the formation constant of the PMC ( _{a}). Taking in account that, and neglecting errors in the measurment of [L], from Equation (10) it is obtained that:^{23}^{)}
Therefore, if one wishes to minimize the error in the formation constant, it is necessary to diminish e_{a}. If a maximum error of 5% in the calculation of K_{f} is accepted, the higher the value of a is, the higher precision is necessary for its determination: if a = 0.8, the maximum permitted value for e_{a} is 1%; if a = 0.4, the maximum permitted value for e_{a} is 3%; if a = 0.1, e_{a} can be as high as 4.5% without e reaching higher values than the accepted 5%. _{K}
Now that the relation between e_{a} is known, we face the following questions: (i) how does e_{a} depend on errors produced in the measurements of the variables to determine a?; (ii) for a values close to 1, is it possible to reduce e_{a} so that K_{f} can be obtained with an acceptable relative error?; (iii) which is the maximum value of a that allows calculating K_{f} with an acceptable relative error?
Error simulations have been done based on possible errors produced in the measurement of the variables involved in the calculations of F and R (see Equations (2) and (3)). Table 1 summarizes the descriptions of the variables whose error have been simulated, were [M]
Table 2 shows that, for Experiment 1, high errors in V
Systematic errors produced in the measurements of every V
Then, we observe that in order to obtain In order to obtain the maximum value for a that allows obtaining ^{ }
Combining Equations (2), (3), (12), and (13), and assuming that the relative errors in V
^{2} represents the relative error in x (given by: e_{x}^{2} = s_{x}^{2}/x^{2} ) and:
In Equations (16) and (17), F From Equation (14) it is directly concluded that the contribution of _{0} becomes the most important variable influencing e_{a}. On the contrary, h(a) always adopts a low value, so errors in every V_{i} produce less impact in the measure of e_{a}. Equation (14) was derived considering aleatory errors in the variables, and then, it will not predict the results obtained considering systematic errors in every V_{i} and [M]_{i}. Nevertheless, the results in Table 4 are qualitatively consistent with those in Tables 2 and 3. Finally, the plot of e_{a} vs a is shown in Figure 5. It has been constructed evaluating Equation (14) from the different values of a corresponding to the F_{i} given, calculated assuming relative errors in the independent variables listed above. It is also shown the curve e vs a, obtained by substitution of every (a, _{K}e_{a}) in Equation (11). Under these conditions, it can be seen that a = 0.4 is the maximum value of a that yields K_{f} values with arbitrary e £ 7%. _{K}
The formation constant of the PMC ( e_{a}). Due to the functional relation between these parameters, when a takes high values, its measurement must be performed with higher precision. Meanwhile, errors in the measurements of the different magnitudes that allow the calculation of a influence the observed value strongly as a increases. In order to achieve a measurement of K_{f} with a relative error lower than 7 %, the experimental a found should not exceed the value 0.4 when relative errors for the independent variables (2% for V_{0}, 2% for M_{0}, 2% for every [M]_{i}, and 5% for every V_{i}) are considered.
The authors thank to FONDECYT the financial support (Grants No 1030669, No 1020198, and No 2000123). L. N. Sch. thanks to CONICYT the Ph.D fellowship.
1. P. Molyneaux in: 2. B. L. Rivas, K. E. Geckeler, 3. A. von Zelewsky, L. Barbosa, C. N. Schläpfer, 4. T. Siyam, E. Hanna, 5. B. Ya. Spivakov, K. Geckeler, E. Bayer, 6. E. Osipova, V. Sladkov, A. Kamevev, V. Shkinev, K. Geckeler, 7. E. Tsuchida, H. Nishide, 8. P. Gregor, L. B. Luttinger, E. M. Loebl, 9. H. Nishikawa, E. Tsuchida, 10. H. Nishide, N. Oki, E. Tsuchida, 11. M. Kotliar, H. Morawetz, 12. J. A. Marinsky, 13. C. Travers, J. A. Marinsky, 14. T. Miyajima, H. Nishimura, H. Kodama, S. Ishiguro, 15. Yu. Kirsh, V. Kovner, A. Kokorin, K. Zamaraev, V. Chernyak, V. Kabanov, 16. K. Seki, M. Isobe, L. Yamagita, T. Abe, Y. Kurimura, T. Kimijima, 17. B. Ya. Spivakov, V. Shkinev, V. Golovanov, E. Bayer, K. Geckeler, 18. B. L. Rivas, I. Moreno-Villoslada, 19. B. L. Rivas, I. Moreno-Villoslada, 20. B. L. Rivas, I. Moreno-Villoslada, 21. B. L. Rivas, S. A. Pooley, M. Luna, 22. B. L. Rivas, I. Moreno-Villoslada, 23. J. C. Miller, J. N. Miller, " P. L. Meyer, "
(Received: March 3, 2004 - Accepted: October 8, 2004) |