Skip to main content
SpringerLink
Log in

Mathematical basis of the integral formalism of chemical kinetics. Compact representation of the general solution of the first-order linear differential equation

  • Brief Communication
  • Published:
Journal of Mathematical Chemistry Aims and scope Submit manuscript

Abstract

The standard approach in chemical and photochemical kinetics is to proceed from the kinetic scheme to the corresponding system of first-order differential equations, and then to integrate it, analytically or numerically. An equivalent integral formulation circumventing such system was recently developed on the basis of physical arguments. The mathematical basis of this ansatz is discussed here. A compact representation of the general solution of the linear first-order differential equation is also obtained.

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

References

  1. Laidler K.J.: Chemical Kinetics. Harper & Row, Cambridge (1987)

    Google Scholar 

  2. Érdi P., Tóth J.: Mathematical Models of Chemical Reactions. Princeton University Press, Princeton (1989)

    Google Scholar 

  3. Berberan-Santos M.N.: J. Lumin. 50, 83 (1991)

    Article  CAS  Google Scholar 

  4. Berberan-Santos M.N., Martinho J.M.G.: Chem. Phys. 164, 259 (1992)

    Article  CAS  Google Scholar 

  5. Berberan-Santos M.N., Pogliani L., Martinho J.M.G.: React. Kinet. Catal. Lett. 54, 287 (1995)

    Article  CAS  Google Scholar 

  6. Pogliani L., Berberan-Santos M.N., Martinho J.M.G.: J. Math. Chem. 20, 193 (1996)

    Article  CAS  Google Scholar 

  7. Berberan-Santos M.N., Martinho J.M.G.: J. Phys. Chem. 94, 5847 (1990)

    Article  CAS  Google Scholar 

  8. Berberan-Santos M.N., Martinho J.M.G.: J. Chem. Phys. 95, 1817 (1991)

    Article  CAS  Google Scholar 

  9. Berberan-Santos M.N., Farinha J.P., Martinho J.M.G.: Chem. Phys. 260, 401 (2000)

    Article  CAS  Google Scholar 

  10. Baleizão C., Berberan-Santos M.N.: J. Chem. Phys. 126, 204510 (2007)

    Article  Google Scholar 

  11. M. N. Berberan-Santos, MATCH, submitted

  12. Apostol T.A.: Calculus, 2nd edn., vol. 1. Blaisdell, Waltham (1967)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centro de Química-Física Molecular and IN, Institute of Nanoscience and Nanotechnology, Instituto Superior Técnico, Universidade Técnica de Lisboa, 1049-001, Lisboa, Portugal

    Mário N. Berberan-Santos

Authors
  1. Mário N. Berberan-Santos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mário N. Berberan-Santos.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Berberan-Santos, M.N. Mathematical basis of the integral formalism of chemical kinetics. Compact representation of the general solution of the first-order linear differential equation. J Math Chem 47, 1184–1188 (2010). https://doi.org/10.1007/s10910-009-9631-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10910-009-9631-4

Keywords

Search

Navigation