William M. White - Geochemistry

The simplest form of the chemical equation for the reduction of ferric iron would be:

(3.102)

Figure 3.18 Electrode reactions in the Daniell cell.

where the subscript aq denotes the aqueous species. This form suggests that the energy involved might be most conveniently measured in an electrochemical cell.

The Daniell cell pictured in Figure 3.18can be used to measure the energy involved in the exchange of electrons between elements, for example, zinc and copper:

(3.103)

where the subscript s denotes the solid. Such a cell provides a measure of the relative preference of Zn and Cu for electrons. In practice, such measurements are made by applying a voltage to the system that is just sufficient to halt the flow of electrons from the zinc plate to the copper one. What is actually measured, then, is a potential energy, denoted E, and referred to as the electrode potential , or simply the potential of the reaction.

If we could measure the potential of two separate half-cell reactions:

we could determine the energy gain/loss in the transfer of an electron from an individual element. Unfortunately, such measurements are not possible (nor would these reactions occur in the natural environment: electrons are not given up except to another element or species §). This requires the establishment of an arbitrary reference value. Once such a reference value is established, the potential involved in reactions such as 3.102 can be established.

The established convention is to measure potentials in a standard hydrogen electrode cell (at standard temperature and pressure). The cell consists on one side of a platinum plate coated with fine Pt powder that is surrounded by H 2gas maintained at a partial pressure of 1 atm and immersed in a solution of unit H +activity. The other side consists of the electrode and solution under investigation. A potential of 0 is assigned to the half-cell reaction:

(3.104)

where the subscript g denotes the gas phase. The potential measured for the entire reaction is then assigned to the half-cell reaction of interest. Thus, for example, the potential of the reaction:

is –0.763 V. This value is assigned to the reaction:

(3.105)

Table 3.3 EH° and pε° for some half-cell reactions.

*CH 2O refers to carbohydrate, the basic product of photosynthesis.

and called the hydrogen scale potential , or E H, of this reaction. Thus, the E Hfor the reduction of Zn +2to Zn 0is −0.763 V. The hydrogen scale potentials of a few half-cell reactions are listed in Table 3.3. The sign convention for E His that the sign of the potential is positive when the reaction proceeds from left to right (i.e., from reactants to products). Thus, if a reaction has positive E H, the metal ion will be reduced by hydrogen gas to the metal. If a reaction has negative E H, the metal will be oxidized to the ion and H +reduced. The standard state potentials (298 K, 0.1 MPa) of more complex reactions can be predicted by algebraic combinations of the reactions and potentials in Table 3.3(see Example 3.11).

The half-cell reactions in Table 3.3are arranged in order of increasing . Thus, a species on the product (right) side of a given reaction will reduce (give up electrons to) the species on the reactant side in all reactions listed below it. Thus, in the Daniell cell reaction in Figure 3.18, Zn metal will reduce Cu 2+in solution. Zn may thus be said to be a stronger reducing agent than Cu.

Electrochemical energy is another form of free energy and can be related to the Gibbs free energy of reaction as:

(3.106)