Skip to main content
SpringerLink
Log in

Expressions for Enthalpies of Concurrent Polynuclear Complex Formation Reactions in Two-Phase Aqueous Systems

  • Published:
Journal of Solution Chemistry Aims and scope Submit manuscript

Abstract

The paper presents a new thermodynamic approach to studying polynuclear complex formation reactions in multicomponent two-phase systems, solid phase plus saturated aqueous solution, under real conditions. The quintessence of this developed approach consists in the thermodynamic analysis of concurrent reactions on the basis of the introduced notion of a generalized reaction equation. The formation of complex polynuclear species is characterized by certain peculiarities in the behavior of studied two-phase heterogeneous systems. The formation of polynuclear complexes of the metal ion with a complexing agent leads to expressions for the enthalpy ∆H and heat capacity ∆Cp as certain concentration functions, which are normative multipliers, referring these thermochemical quantities to one mole of the metal ion. It is shown that one of these functions, Φ, characterizes the degree of formation of polynuclear complexes. In the case of concurrent formation of mono- and polynuclear complexes, the derived expressions are useful in distinguishing separate contributions of individual complex formation reactions to the ∆H and ∆Cp of the overall process.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

Abbreviations

GRE:

Generalized reaction equation

MB:

Mass balance

Φ, F and φ :

Concentration functions, defined in this paper

C i :

Total (analytical) concentration of the component “i” (mol·L−1)

α i :

Coefficient of the side reactions of the component “i”

K i , β i :

Equilibrium constants of the component “i”

∆G r :

Total variation of the Gibbs energy (J·mol−1)

∆H r :

Total enthalpy variation (J·mol−1)

∆C p(i) :

Molar heat capacity of the component “i” (J·mol−1·K−1)

References

  1. Gans, P., Sabatini, A., Vacca, A.: Simultaneous calculation of equilibrium constants and standard formation enthalpies from calorimetric data for systems with multiple equilibria in solution. J. Solution Chem. 37, 467–476 (2008)

    Article  CAS  Google Scholar 

  2. Hansen, L.D., Fellingham, G.W., Russell, D.J.: Simultaneous determination of equilibrium constants and enthalpy changes by titration calorimetry: methods, instruments, and uncertainties. Anal. Biochem. 409, 220–229 (2011)

    Article  CAS  Google Scholar 

  3. Arena, G., Gans, P., Sgarlata, C.: HypCal, a general-purpose computer program for the determination of standard reaction enthalpy and binding constant values by means of calorimetry. Anal. Bioanal. Chem. 408, 6413–6422 (2016)

    Article  CAS  Google Scholar 

  4. Arena, G., Cali, R., Maccarrone, G., Purrello, R.: Critical review of the calorimetric method for equilibrium constant determination. Thermochim. Acta 155, 353–376 (1989)

    Article  CAS  Google Scholar 

  5. Peters, D., Sabatini, A., Vacca, A.: Hyperquad Simulation and Speciation (HySS): a utility program for the investigation of equilibria involving soluble and partially soluble species. Coord. Chem. Rev. 184, 311–318 (1999)

    Article  Google Scholar 

  6. Eriksson, G., Königsberger, E.: FactSage and ChemApp: two tools for the prediction of multiphase chemical equilibria in solutions. Pure Appl. Chem. 80, 1293–1302 (2008)

    Article  CAS  Google Scholar 

  7. Smith, D.S., Adams, N.W.H., Kramer, J.R.: Resolving uncertainty in chemical speciation determinations. Geochim. Cosmochim. Acta 63, 3337–3347 (1999)

    Article  CAS  Google Scholar 

  8. Rigano, C., Rizzarelli, E., Sammartano, S.: A computer method for the calculation of enthalpy changes for ion association in solution from calorimetric data. Thermochim. Acta 33, 211–216 (1979)

    Article  CAS  Google Scholar 

  9. De Robertis, A., De Stetefano, C., Rigano, C.: Computer analysis of equilibrium data in solution. ES5CM Fortran and Basic programs for computing formation enthalpies from calorimetric measurements. Thermochim. Acta 138, 141–146 (1989)

    Article  Google Scholar 

  10. Horn, J.R., Brandts, J.F., Murphy, K.P.: Van’t Hoff and calorimetric enthalpies II: effects of linked equilibria. Biochemistry 41, 7501–7507 (2002)

    Article  CAS  Google Scholar 

  11. Tellinghuisen, J.: Optimizing experimental parameters in isothermal titration calorimetry. J. Phys. Chem. B 109, 20027–20035 (2005)

    Article  CAS  Google Scholar 

  12. Povar, I., Spinu, O.: Correlation between global thermodynamic functions and experimental data in multicomponent heterogeneous systems. Can. J. Chem. 94, 113–119 (2016)

    Article  CAS  Google Scholar 

  13. Povar, I., Spinu, O.: The role of hydroxy aluminium sulfate minerals in controlling Al3+ concentration and speciation in acidic soils. Cent. Eur. J. Chem. 12, 877–885 (2014)

    Article  CAS  Google Scholar 

  14. Povar, I., Rusu, V.: Aluminium heterogeneous speciation in natural waters. Can. J. Chem. 90, 326–332 (2012)

    Article  CAS  Google Scholar 

  15. Povar, I., Spinu, O.: Thermodynamics of Complex Chemical Equilibria in Heterogeneous Multicomponent Systems. Printing House of the Academy of Sciences of Moldova, Chisinau (2014)

    Google Scholar 

  16. Pettersson, L., Hedman, B., Andersson, I., Ingri, N.: Formation of metal complexes: a critical survey of equilibrium constants. Chem. Scr. 22, 254–264 (1983)

    CAS  Google Scholar 

  17. Smith, R.M., Motekaitis, R.J., Martell, A.E.: New multidentate ligands. 23. Chelating tendencies of octadentate diamido diamino tetraacetic acids. Inorg. Chem. 24, 1132–1142 (1985)

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Chemistry, 3 Academiei str., MD 2028, Chișinău, Republic of Moldova

    Igor Povar, Oxana Spinu & Boris Pintilie

Authors
  1. Igor Povar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Oxana Spinu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Boris Pintilie
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Igor Povar.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Povar, I., Spinu, O. & Pintilie, B. Expressions for Enthalpies of Concurrent Polynuclear Complex Formation Reactions in Two-Phase Aqueous Systems. J Solution Chem 47, 1725–1739 (2018). https://doi.org/10.1007/s10953-018-0802-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10953-018-0802-4

Keywords

Search

Navigation