General Equation for the Relation Between the Polarographic Half-Wave Potential and Substituent Effects

  • Petr Zuman


For a reversible oxidation-reduction process, the half-wave potential (corrected for the quotient of the diffusion coefficients of the oxidized and reduced forms) is proportional to the equilibrium constant K of the reaction
$$Ox+ne\rightleftharpoons \operatorname{R}ed$$
$$K=\frac{\left[ Red \right]}{\left[ Ox \right]}$$
$$-E_{{1}/{2}\;}^{0}=\frac{RT}{nF}\ln K$$
$$RT\ln K=\Delta {{F}^{\circ }}$$
where ΔF°is the change in the standard free energy, it follows that
$$-nFE_{{1}/{2}\;}^{0}=\Delta {{F}^{\circ }}$$
For half-wave potentials of irreversible systems, the relationship(4) has been derived:1–5
$${{E}_{{1}/{2}\;}}=\frac{RT}{\alpha nF}\ln 0.87k_{\int }^{0}\sqrt{\frac{{{t}_{1}}}{D}}$$
where R is the gas constant, T is the absolute temperature, α is the transfer coefficient, n is the number of electrons transferred in the electrode process, F is the faraday (96,500 coulombs), k 0 f is the rate constant of the heterogeneous electrode process, t 1 is the drop time, and D is the diffusion coefficient.


Reactive Group Polar Effect Steric Effect Reaction Series Substituent Effect 
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  1. 1.
    N. Mejman, Zh. Fiz. Khim. 22: 1454 (1948).Google Scholar
  2. 2.
    J.Kouteckÿ, Chem. Listy 47: 323 (1953); Google Scholar
  3. J. Kouteckÿ, Collection Czech. Chem. Commun. 18: 597 (1953).Google Scholar
  4. 3.
    P. Delahay, J. Am. Chem. Soc. 75: 1480 (1953); 76: 5417 (1954).Google Scholar
  5. 4.
    P. Delahay, “New Instrumental Methods in Electrochemistry,” p. 82, Interscience Publ., John Wiley & Sons, New York, 1954.Google Scholar
  6. R. Brdicka, Collection Czech. Chem. Commun. 19: S 41 0954).Google Scholar
  7. 6.
    R. W. Taft, Jr., Separation of Polar, Steric and Resonance Effects in Reactivity in “Steric Effects in Organic Chemistry,” (ed. by M. S. Newman) John Wiley & Sons, N’ew York, 1956.Google Scholar
  8. 7.
    J. E. Leffler, J. Org. Chem. 20: 1202 (1955).CrossRefGoogle Scholar
  9. 8.
    P. Zuman, Collection Czech. Chem. Commun. 25: 3225 (1960).Google Scholar
  10. 9.
    P. Zuman, Ricerca Sci. 30: Contributi teor. sper. polarografia 5, S 229 (1960).Google Scholar
  11. 10.
    J. D. Roberts, and W. T. Moreland, Jr., J. Am. Chem. Soc. 75: 2167 (1953).CrossRefGoogle Scholar
  12. 11.
    L. P. Hammett, Chem. Rev. 17: 125 (1935).CrossRefGoogle Scholar
  13. 12.
    L. P. Hammett, “Physical Organic Chemistry,” p. 184, McGraw-Hill, New York, 1940.Google Scholar
  14. 13.
    H. H. Jaffé, Chem. Rev. 53: 191 (1953).CrossRefGoogle Scholar
  15. 14.
    H. C. Brown, and Y. Okamoto, J. Am. Chem. Soc. 80, 4979 (1958).CrossRefGoogle Scholar
  16. 15.
    P. Zuman, and D. J. Voaden, Tetrahedron 16: 130 (1961).CrossRefGoogle Scholar
  17. 16.
    P Zuman, Collection Czech. Chem. Commun. 27: 648 (1962).Google Scholar

Copyright information

© Plenum Press 1967

Authors and Affiliations

  • Petr Zuman
    • 1
  1. 1.Heyrovský Institute of PolarographyCzechoslovak Academy of SciencesPragueCzechoslovakia

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