A Comprehensive Program for the Evaluation of Potentiometric and/or Spectrophotometric Equilibrium Data Using Analytical Derivatives
  • L. Zekany
  • I. Nagypal
Part of the Modern Inorganic Chemistry book series (MICE)


Potentiometry and spectrophotometry are the most frequently used experimental methods to study equilibrium systems in solutions; these methods may be used in many different types of experimental arrangements. The equilibrium system can be described through the mass-balance equations as
$$ {C_{1}} = \sum\limits_{{j = 1}}^{n} {{\alpha _{{jk}}}\left[ {{S_{j}}} \right] = \quad \sum\limits_{{j - 1}}^{n} {{\alpha _{{jk}}}{\beta _{j}}\prod\limits_{{i = 1}}^{k} {{{\left[ {{c_{i}}} \right]}^{{\alpha ji}}}} } } $$
where n is the number of species in the system, including the components; S j is the jth species present in the system; k is the number of components in the system; [c1] ... [c k ] is the equilibrium (free) concentration of the components; \( {\beta _j} = \left[ {{S_j}} \right]/\left( {\prod\nolimits_{i = 1}^k {{{\left[ {{c_i}} \right]}^{\alpha ji}}} } \right) \), the formation constant of the species, (the formation constants of the components are unity); α ji are stoichiometric numbers, giving the number of the ith component in the jth species.


Titration Curve Molar Absorptivity Formation Constant Equilibrium Data Analytical Derivative 
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  1. 1.
    G. E. Forsythe and C. B. Moler, Computer Solution of Linear Algebraic Systems, Prentice-Hall, Englewood Cliffs, New Jersey [Hungarian translation, Müszaki Könyvkiadö, Budapest, (1976)].Google Scholar
  2. 2.
    W. R. Smith, The Computation of Chemical Equilibria in Complex System, Ind. Eng. Chem. Fundam. 19, 1–10 (1980).CrossRefGoogle Scholar
  3. 3.
    A. A. Bugaevsky and B. A. Dunai, Calculation of the Equilibrium Composition and Buffer Properties of Solutions with the Use of Computers (in Russian), Zh. Anal. Khim. 26, 205–209 (1971).Google Scholar
  4. 4.
    A. A. Bugaevsky, L. E. Rudnaya, and T. P. Mukhina, Calculation of Equilibria in Complex Systems (in Russian), Zh. Anal. Khim. 27, 1675–1679 (1972).Google Scholar
  5. 5.
    A. A. Bugaevsky and L. E. Nikishina, On the Analytical Method of Calculating the Derivatives of Equilibrium Concentrations, Talanta 28, 977 (1981).CrossRefGoogle Scholar
  6. 6.
    I. Nagypál, I. Páka, and L. Zékány, Analytical Evaluation of the Derivatives Used in Equilibrium Calculations, Talanta 25, 549–550 (1978).CrossRefGoogle Scholar
  7. 7.
    J. M. Ortega and W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York (1970).Google Scholar
  8. 8.
    Yu. V. Linnik, Method of Least Squares and Principles of the Theory of Observations, Pergamon Press, Oxford (1961).Google Scholar
  9. 9.
    L. G. Sillén and B. Warnqvist, High-speed Computers as a Supplement to Graphical Methods. 6. A Strategy for Two-level LETAGROP Adjustment of Common and “Group” Parameters. Some features that avoid divergence. Ark. Kemi 31, 315–339 (1969).Google Scholar
  10. 10.
    R. H. Barham and W. Drane, An Algorithm for Least Squares Estimation of Nonlinear Parameters When Some of the Parameters are Linear, Technometrics 14, 757–766 (1972).CrossRefGoogle Scholar
  11. 11.
    A. D. Zuberbuhler and Th. A. Kaden, TITFIT, A Comprehensive Program for Numerical Treatment of Potentiometric Data using Analytical Derivatives and Automatically Optimized Subroutines with the Gauss-Newton-Marquardt Algorithm, Talanta 29, 201–206 (1982).CrossRefGoogle Scholar
  12. 12.
    A. Sabatini, A. Vacca, and P. Gans, MINIQUAD—A General Computer Programme for the Computation of Formation Constants from Potentiometric Data, Talanta 21, 53–77 (1974).CrossRefGoogle Scholar
  13. 13.
    H. M. Irving, M. G. Miles, and L. D. Pettit, A Study of Some Problems in Determining the Stoicheiometric Proton Dissociation Constants of Complexes By Potentiometric Titrations Using a Glass Electrode, Anal. Chim. Acta 38, 475–488 (1967).CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1985

Authors and Affiliations

  • L. Zekany
    • 1
  • I. Nagypal
    • 1
  1. 1.Computer Center, Institute of Inorganic and Analytical ChemistryLajos Kossuth UniversityDebrecenHungary

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