4. Table of Standard State Electrochemical Potentials

It is possible to measure the standard state electrochemical potential for individual half reactions. Doing so requires setting one particular half reaction as a reference point to which all other potentials are compared. The half reaction used as the reference involves reduction of the hydrogen ion (H⁺). This half reaction is arbitrarily assigned a standard state reduction potential of 0.00 Volts.

\[\mathrm{2H^+(aq) + 2e^- = H_2(g) \hspace{40px} E^o = 0.00\: V}\]

Tables of standard state electrochemical potentials are freely available on the internet. By convention, all of the half reactions are written as reductions. Earlier we mentioned how alkali metals are strong reducing agents as they have a strong driving force to be oxidized. The half reaction and standard state potential for the reduction of Li⁺ is shown below.

\[\mathrm{Li^+(aq) + e^- = Li(s) \hspace{40px} E^o = -3.045\: V}\]

Note that this reaction has a very large negative standard state potential. Remember from earlier that electrochemical reactions that favor the reactants have negative potentials. An examination of the standard state potentials indicates that the reduction of Li⁺ has the highest value in the table. Therefore it should not be surprising that lithium batteries are in common use today. Also, for those readers who are fans of Star Trek, we can now understand when the Enterprise needed more fuel the call from the bridge was for more dilithium crystals.

We also used fluorine as an example of a powerful oxidizing agent meaning that it has a strong driving force to be reduced. The half reaction and standard state potential for the reduction of fluorine gas is shown below.

\[\mathrm{F_2(g) + 2e^- = 2F^-(aq) \hspace{40px} E^o = 2.87\: V}\]

Note that this reaction has a very large positive standard state potential. Remember that electrochemical reactions that favor the products have positive potentials.

Since an overall electrochemical reaction has a reducing and oxidizing half to it, we often work with systems in which two half reactions are paired up. When considering any pair, the one with the more positive E^o value proceeds as a reduction and the one with the less positive value proceeds as an oxidation.

It is worth noting that reactions are usually run under non-standard state conditions. It is possible to take the conditions so far away from the standard state used to generate the values in a table of E^o values that the reaction may actually proceed in the reverse direction from what occurs in the standard state. For example, looking back at the plot of G for a reaction with a large K shown in Figure 1, starting at a very high concentration of B and a very low concentration of A that is to the right of the equilibrium state in the plot would mean that the reaction proceeds toward reactants instead of products. This would be the reverse of the reaction direction predicted by comparing the ΔG^o or E^o values of A and B.

One final thing to note is that E^o values do vary with other conditions of the solution. For example, electrochemical reactions with H⁺ in one of the half reactions are highly influenced by the pH. The standard state will have [H⁺] = 1 M (note, this constitutes a pH of 0) and the measured E^o value will often have slightly different values if different acids (e.g., nitric, hydrochloric, perchloric) are used to make the 1 M solution. Another common condition with electrochemical reactions involves the ionic strength of the solution. The ionic strength (μ) is defined as follows:

\[\mathrm{\mu = \dfrac{1}{2} \sum [C_i]Z_i^2}\]

Where C_i is the concentration of each ion and Z_i is the charge of each ion. Note that both cations and anions are included in the summation term.

In some cases with electrochemical reactions it is desirable to have a concentration of unreactive ions in the solution as a background electrolyte (e.g., alkali cations paired with halide anions might be such a background electrolyte). Measured E^o values often vary slightly at different ionic strengths.

In some cases it is more common to use formal potentials (E^o’). A formal potential is the reduction potential that applies to a half reaction under a specified set of conditions (e.g., pH, ionic strength, concentration of complexing agents). One common example is that the formal potential of important biological electrochemical reactions are often measured at pH 7, which is much closer to physiological pH than the standard state pH of 0.

Because E^o values vary slightly with conditions, calculated values for a system you wanted to study obtained using the Nernst equation are often only close approximations of what you would actually obtain as a measured value.