Redox equilibria

1. Redox equilibria

2. Electrochemical thermodynamics For reaction to be in equilibrium at the electrode surface, the electrochemical potentials of reactants and products must be equal: Since is equal to it follows that the second term on the left side is the electrochemical potential of the electrons in the inert metal electrode. The electrochemical potentials are connected with the chemical potentials as follows: ( is the inner electric potential of the phase a in which the species i are present )

3. Electrochemical thermodynamics The chemical potential of i is: Thus it follows: Rearrangement and considering yields:

4. Electrochemical thermodynamics The activity of electrons in the metal phase is 1 because they are in their standard state and . So the Nernst equation follows in the form: Inner electric potentials Galvani potential difference(this is ONE term; it is NOT the difference of Galvani potentials, a term which does not exist anymore!!) Whereas a direct measurement of the inner electric potential of a single phase is impossible, the difference, i.e., the Galvani potential difference of two phases having identical composition or its variation for two phases having a common interface, is accessible when a proper reference electrode is used, i.e., a metal/electrolyte system, which should guarantee that the chemical potential of the species i is the same in both electrolytes, i.e., the two electrolytes contacting the metal phases I and II.

5. Electrochemical thermodynamics Using the standard hydrogen electrode as reference system, and setting the potential of that electrode to zero (at all temperatures) one can define standard potentials of redox systems, e.g.: This equation relates to the following electrochemical equilibria: Reduction: Oxidation: reduced form + hydronium ions oxidised form + hydrogen

6. The Plimsoll symbol Samuel Plimsoll (10 February 1824 – 3 June 1898) was a British coal merchant, shipping expert and politician . He introduced the symbol to indicate on the ship's hull the maximum safe draft, and therefore the minimum freeboard. That symbol is now used in physical chemistry to indicate standard values. It is an ideal circle with a horizontal line crossing the circle (it is no zero (0), and no letter O). In 1873 P. published a book entitled “Our Seamen” with case studies of overloaded ships. At that time, about 1,000 sailors a year were being drowned on ships around British shores because of unsafe ships! Plimsoll’s book prompted the Parliament in 1875 to pass a bill giving the mandatory load line painted on the ship’ side! ship water level

7. Standard potentials always refer to the reaction: Oxidised form + hydrogen reduced form + hydronium ions All these data relate to equilibria in which these reductions are coupled to the oxidation of hydrogen: Ox + ne- Red

8. The strength of an oxidant can only be determined in relation to a reductant, and hydrogen is serving as the standard compound for that purpose! Note the similarity to acid-base equilibria: There the strength of an acid is always determined in relation to a base, and water is serving there as the standard compound for that purpose (for all aqueous systems). That similarity between standard potentials and acidity constants is the result of the fact that neither electrons nor protons can exist in chemical systems without strong interactions! There are no really free protons and electrons in chemical systems (they exist as free species only in vacuum).

9. Similarities between proton and electron transfer reactions The radius of a proton (H+ or p+): ~1.6×10-15 m (~1.6fm) The radius of an electron (e-): 2.8×10-15 m The radius of common ions: Li+: 0.9×10-10 m Cl-: 1.67×10-10 m __________________________________________________________ Protons and electrons are of similar size, and about 100.000-times smaller than all other ions! They are always bond to other particles. H+ e- e- H+

10. Biochemical standard potentials: • most electrochemical systems of biochemical relevance involve the coupled transfer of electrons and protons • pH 7 is a more relevant pH than pH 0 (to which the standard potentials refer) • For these reasons one defines a so-called biochemical standard potential:

11. Biochemical standard potentials E’ refer to pH = 7.0 and can be calculated for pH-dependend redox systems as follows:

12. Formal potentials can be defined on various levels:

13. Electrochemical thermodynamics With the activities being and follows: First possibility to define a formal potential:

14. Electrochemical thermodynamics Second possibility to define a formal potential:

15. Formal potentials are conditional constants. They have to be used for all REAL systems. In principal, they can be calculated, provided that all chemical species and their concentrations are known, as well as all equilibrium constants responsible for the side reactions are known. Since the latter is usually NOT the case, formal potentials are normally determined in experiments!

16. Pourbaix Diagram = Potential-pH Diagram Marcel Pourbaix (September 16,1904, in Myshega (Russia) - September 28, 1998, Uccle (Brussels), Belgium) Predominant ion boundaries are represented by lines. They can be calculated from the equilibrium equations for the condition of equal concentrations of neighboring species. E c(Fe) = 1 mol/l, T = 25 °C How to calculate Poubaix diagrams: Kotrlý S, Šůcha L (1985) Handbook of chemical equilibria in analytical chemistry. Ellis Horwood, Chichester

17. Pourbaix Diagram: Must be calculated for certain given concentrations of the involved (soluble) species.

18. Potentiometric Redox Titrations