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Modelowanie matematyczne i badania fizykochemiczne równowag kwasowo-zasadowych w układach binarnych rozpuszczalników

Michałowski T., Pilarski B., Dobkowska A., Młodzianowski J.

Wiadomości Chemiczne

2010

[Z] 64, 1-2

123-154

Conductometric titration (CT) is used as a complementary, non-specific technique against potentiometric (pH) titration (PT). The CT + PT procedure is applied to binary-solvent systems: HmL + Z/A + B (or HmL + Z/W + B) formed of a weak acid HmL and a pH-modifying agent Z (e.g. NaOH, NH3 or HCl), and totally miscible organic solvents A and B (or W = H2O and B) chosen as co-solvents, where acid-base equilibria are considered. The solvent composition in such systems is expressed by the mole fraction x of B. Concentrations of solutes: HmL and Z are the same in the solution titrated (titrand, D) and in titrant (T) and changes in pH value resulted only from differences in acid-base properties of solvents applied in D and T. On the basis of results obtained from PT and CT, the functional relationships related to the solutions of weak acids HmL (m = 1, 2, ...) were formulated, namely: (1) pKi = pKi(x) for acidity parameters; (2) Lp = Lp(x) for molar conductivities, related to the species formed by di- and triprotic acids. For this purpose, the Kohlrausch law on the independence of migrating ions has been applied. The pKi = pKi(x) relationships were formulated for diprotic and triprotic acids on the basis of enderson.Hasselbalch functions and modeled with use of polynomial functions. The pKi(1) and Lp(1) values were obtained by extrapolation. The approach suggested is the essential novelty in contemporary literature related to the subject in question. This way, the paper provides a new methodology, a new dimension (x-scale) to the problems known hitherto. In the experimental part, the pK1 = pK1(x) relationships were formulated for results of mutual pH titrations: HmL/B . HmL/W or HmL/B . HmL/A, obtained for the systems not involving Z. The systems were modeled with the use of Redlich.Kister (R.K) and orthogonal (normal, shifted) Legendre polynomials. Asymmetric functions by Myers.Scott (M.S) and by Michałowski were also suggested for this purpose. It was stated that all approximating functions fit the experimental data very well. The asymmetric functions are applicable for modeling of more bended relationships pK1 = pK1(x), particularly when referred to the limiting x-values in the interval < 0, 1 >. A software that enables to formulate the relationships pKi = pKi(x) according to different approximating functions after introducing the experimental data {(Vj, pHj) | j = 1, ..., N} obtained from PT, was also prepared, together with statistical evaluation of pKi(0) and pKi(1) values, obtained by extrapolation. The results thus obtained are presented in tables and figures. Some criteria of validity of the results obtained according to PT for pK1(0) and pK1(1) are also presented. The first criterion testifying about reversibility of indications of the measuring system is a position of the point of intersection of the plots obtained in the mutual titrations. The second criterion stems from comparison of results obtained from three pH titrations: (1) HmL/B Ť HmL/W, (2) HmL/B Ť HmL/A and (3) HmL/A Ť HmL/W. The convergence of the related plots at x = 0 and x = 1, where x = xB in (1) and (2) and x = xA in (3) testifies on account of the calibration procedure applied for glass electrode.