Читать книгу Geochemistry - William M. White - Страница 147

Consider again the reaction:

(3.102)

If we were to express the equilibrium constant for this reaction, we would write:

Thus, we might find it convenient to define an activity for the electron. For this reason, chemists have defined an analogous parameter to pH, called pε, which is the negative log of the activity of electrons in solution:

(3.112)

The log of the equilibrium constant for eqn. 3.101 may then be written as:

Upon rearranging we have:

(3.113)

When the activities of reactants and products are in their standard states (i.e., a = 1), then:

(3.114)

(where z again is the number of electrons exchanged: 1 in reaction 3.102). pε° values are empirically determined and may be found in various tables. Table 3.3 lists values for some of the more important reactions. For any state other than the standard state, pε is related to the standard state pε° by:

(3.115)

pε and E_H are related by the following equation:

(3.116)

(the factor 2.303 arises from the switch from natural log units to base 10 log units).

In defining electron activity and representing it in log units, there is a clear analogy between pε and pH. However, the analogy is purely mathematical, and not physical. Natural waters do not contain significant concentrations of free electrons. Also, although a system at equilibrium can have only one value for pε, just as it will have only one value of pH, redox equilibrium is often not achieved in natural waters. The pε of a natural system is therefore often difficult to determine. Thus, pε is a hypothetical unit, defined for convenience of incorporating a representation of redox state that fits readily into established thermodynamic constructs such as the equilibrium constant. In this sense, eqn. 3.116 provides a more accurate definition of pε than does eqn. 3.112.

The greater the pε, the greater the tendency of species to lose their transferable, or valence, electrons. In a qualitative way, we can think of the negative of pε as a measure of the availability of electrons. pε can be related in a general way to the relative abundance of electron acceptors. When an electron acceptor, such as oxygen, is abundant relative to the abundance of electron donors, the pε is high and electron donors will be in electron-poor valence states (e.g., Mn⁴⁺ instead of Mn²⁺). pε, and E_H, are particularly useful concepts when combined with pH to produce diagrams representing the stability fields of various species. We will briefly consider how these are constructed.