Definitions

# Standard electrode potential

In electrochemistry, the standard electrode potential, abbreviated Eo, E0, or EO (with a superscript plimsoll character, pronounced nought), is the measure of individual potential of a reversible electrode (at equilibrium) at standard state, which is with solutes at an effective concentration of 1 mol/kg, and gases at a pressure of 1 atmosphere / 100 kPa (Kilopascals)). The values are most often tabularized at 25 °C. The basis for an electrochemical cell such as the galvanic cell is always a redox reaction which can be broken down into two half-reactions: oxidation at anode (loss of electron) and reduction at cathode (gain of electron). Electricity is generated due to electric potential difference between two electrodes. This potential difference is created as a result of the difference between individual potentials of the two metal electrodes with respect to the electrolyte.

Although the overall potential of a cell can be measured, there is no simple way to accurately measure the electrode/electrolyte potentials in isolation. The electric potential also varies with temperature, concentration and pressure. Since the oxidation potential of a half-reaction is the negative of the reduction potential in a redox reaction, it is sufficient to calculate either one of the potentials. Therefore, standard electrode potential is commonly written as standard reduction potential.

## Calculation of standard electrode potentials

The electrode potential may not be obtained empirically. The galvanic cell potential results from a pair of electrodes. Thus, only one empirical value is available in a pair of electrodes and it is not possible to determine the value for each electrode in the pair using the empirically obtained galvanic cell potential. A reference electrode, the standard hydrogen electrode (SHE), for which the potential is defined or agreed upon by convention, needed to be established. In this case SHE is set to 0.00 V and any electrode, for which the electrode potential is not yet known, can be paired with SHE -to form a galvanic cell- and the galvanic cell potential gives the unknown electrode's potential. Using this process, any electrode with an unknown potential can be paired with either the SHE or another electrode for which the potential has already been derived and that unknown value can be established.

Since the electrode potentials are conventionally defined as reduction potentials, the sign of the potential for the metal electrode being oxidized must be reversed when calculating the overall cell potential. Note that the electrode potentials are independent of the number of electrons transferred -that is, they are set to one mole of electrons transferred- and so the two electrode potentials can be simply combined to give the overall cell potential even if different numbers of electrons are involved in the two electrode reactions

Since the table of standard electrode potentials is defined for a transfer of one mole of electrons, care must be made in determining an electrode potential using two other electrode potentials. Adjustments have to be made for the number of electrons being transferred.

For example:

(eq1) Fe3+ + 3e- --> Fe(s) is listed as -0.036 V

(eq2) Fe2+ + 2e- --> Fe(s) is listed as -0.44 V

to get a third equation:

(eq3) Fe3+ + e- --> Fe2+ (listed as +0.77 V)

one would need to take eq1 and multiply the voltage by 3, reverse eq2 (changes the sign) and multiply the voltage by 2. Adding those two voltages together gives the standard potential for eq3.

## Standard reduction potential table

Since the values are given in their ability to be reduced, the bigger the standard reduction potentials, the easier they are to be reduced, in other words, they are simply better oxidizing agents. For example, F2 has 2.87 V and Li+ has -3.05 V. F2 reduces easily and is therefore a good oxidizing agent. In contrast, Li(s) would rather undergo oxidation (hence a good reducing agent). Thus Zn2+ whose standard reduction potential is -0.76 V can be oxidized by any other electrode whose standard reduction potential is greater than -0.76 V (eg. H+(0 V), Cu2+(0.16 V), F2(2.87 V)) and can be reduced by any electrode with standard reduction potential less than -0.76 V (eg. H2(-2.23 V), Na+(-2.71 V), Li+(-3.05 V)).

In a galvanic cell, where a spontaneous redox reaction drives the cell to produce an electric potential, Gibbs free energy ΔGo must be negative, in accordance with the following equation:

ΔGocell = -nFEocell
where n is number of moles of electrons per mole of products and F is the Faraday constant, ~96485 C/mol. As such, the following rules apply:

If Eocell> 0, then the process is spontaneous (galvanic cell)

If Eocell< 0, then the process is nonspontaneous (electrolytic cell)

Thus in order to have a spontaneous reaction (-ΔGo), Eocell must be positive, where:

Eocell= Eoanode + Eocathode

where Eoanode is the standard potential at the anode (reverse the sign of the standard reduction potential value for the electrode) and Eocathode is the standard potential at the cathode as given in the table of standard electrode potential.

## Non-standard condition

The standard electrode potentials are given at standard conditions. However, real cells may operate under non-standard conditions. Given the standard potential of the half-cell, its potential at non-standard effective concentrations can be calculated using the Nernst equation:

$E_\left\{text\left\{half-cell\right\}\right\} = E^0 - frac\left\{RT\right\}\left\{nF\right\}lnfrac\left\{\left\{text\left\{red\right\}\right\}\right\}\left\{\left\{text\left\{oxd\right\}\right\}\right\}$

The values of E0 depend on temperature (except for SHE, for which the potential has been, arbitrarily, declared 0 at all temperatures) and are normally referenced to the SHE at the same temperature. For condensed phases, they are also expected to depend somewhat on pressure (see the article on equilibrium constant). For example, the standard electrode potential for Ni/NiO redox couple has been well studied because such a solid has applications in high-temperature pseudo-reference electrodes (when enclosed inside an yttrium-stabilized zirconia ceramic membrane). The standard potential of Ni/NiO has been correlated for temperatures between 0 and 400 °C to be approximately:

E0(T) = -0.0003 T + 0.1414

where E0 is in volts, and T is in degrees Celsius.

In biochemistry, potentials are usually defined for pH 7, with the standard potential under these conditions being Eo' - also referred to as the mid-point potential or Em,7 because it is the potential at which the concentrations of the oxidised and reduced forms of the redox pair are equal.

The actual redox potential for a pair at a given pH of x (Eh, pH = x) is related to the midpoint potential by:

$E_\left\{h,pH=x\right\} = E_\left\{m,pH=x\right\} - frac\left\{2.3RT\right\}\left\{nF\right\}log_\left\{10\right\}frac\left\{\left[text\left\{red\right\}\right]\right\}\left\{\left[text\left\{oxd\right\}\right]\right\}$

## Further reading

• Zumdahl, Steven S., Zumdahl, Susan A (2000) Chemistry (5th ed.), Houghton Mifflin Company. ISBN 0-395-98583-8
• Atkins, Peter, Jones, Loretta (2005) Chemical Principles (3rd ed.), W.H. Freeman and Company. ISBN 0-7167-5701-X
• Zu, Y, Couture, MM, Kolling, DR, Crofts, AR, Eltis, LD, Fee, JA, Hirst, J (2003) Biochemistry, 42, 12400-12408
• Shuttleworth, SJ (1820) Electrochemistry (50th ed.), Harper Collins.

## References

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