3.5: Half Cells and Standard Reduction Potentials

   Introduction    

All redox reactions can formally be thought of as the sum of half-reactions. Some can also actually be run with the two half-reactions occurring in different locations. When this is possible they can be used to do electrical work by passing the electrons through a wire to exchange them rather than allowing direct exchange between the reactants. These two separate reaction containers are formally referred to as half-cells. A galvanic cell (generically called a battery*) is made of two connected half-cells that produce electrical energy as the two half-reactions proceed. Below is a cartoon (figure \(\PageIndex{1}\)) of a galvanic cell based on the overall reaction \(\ce{Cu + 2Ag+ -> Cu^{2+} + 2Ag}\). The two half-reactions are:

\[\ce{Cu -> Cu^{2+} + 2e-}\,\text{(oxidation)}\quad\text{and}\quad\ce{Ag+ + e- -> Ag}\,\text{(reduction)} \nonumber\]

Figure \(\PageIndex{1}\) : A galvanic cell based on the spontaneous reaction between copper and silver(I) ions. From OpenStax.

*Definition: Battery

Technically a battery is made of multiple galvanic cells hooked together in series to produce a larger voltage or in parallel to produce more current at the same voltage as a single galvanic cell. A standard D battery is more properly called a D cell as it only contains a single galvanic cell. A 9V alkaline battery contains multiple galvanic cells stacked in series to produce the larger voltage. A single alkaline cell only produces about 1.5 V.

Standard Hydrogen Electrode

The voltage produced by a pair of half-cells connected in a galvanic cell is referred to as the cell potential and usually represented by the symbol E. Experimentation shows that the potentials of each half-reaction (half-cell) can be thought of as existing on a number line. Thus, if we choose an arbitrary half-cell as our reference state and set its potential to 0 V, we can define the potential of all other half-reactions relative to the reference electrode and calculate the potential of any galvanic cell as the difference between the potentials of each half-cell: E_cell = E₂ - E₁. The standard hydrogen electrode is this reference electrode.

The standard hydrogen electrode is constructed so that H₂ gas flows over an inert electrode made of platinum, and can interact with an acid solution which provides H⁺ for the half reaction

\[\ce{2 H^+(aq) + 2 e^{-} -> H_2(g)} \nonumber \]

Both H⁺ and H₂ need to have unit activity (or fugacity), which if the solution and gas behave ideally means a concentration of 1 M and a pressure of 1 bar.

Figure \(\PageIndex{2}\): The standard hydrogen electrode (SHE). From OpenStax.

Standard cell potential (E^o_cell) and the spontaneous direction under standard conditions.

Using the Standard Hydrogen Electrode (SHE) as zero the half-cell potentials are usually tabulated for runing the half-reaction as a reduction (e- as reactants). A number of values are shown in Table P1 of the LibreTexts resources. When two half-cells are paired the half-reaction with the higher reduction potential goes spontaneously (as written) and the other runs in reverse.

Example \(\PageIndex{1}\): Cell Potential and Spontaneity

Which pair of reactants will produce a spontaneous reaction if everything is present in its standard state at 25 °C?

• \(\ce{Fe}\) and \(\ce{Cu^{2+}}\) or
• \(\ce{Fe^{2+}}\) and \(\ce{Cu}\)

Solution

The species with the highest standard reduction potential (Table P1) will force the other to oxidize.

From the table,

\[\ce{Cu^{2+} + 2 e^{-} \rightarrow Cu}\quad E^o = 0.377 V\nonumber \]

\[ \ce{Fe^{2+} + 2 e^{-} \rightarrow Fe} \quad E^o = -0.440 V \nonumber \]

So the iron half-reaction will flip (so that iron is oxidizing) and the spontaneous reaction under standard conditions will be

\[Cu^{2+} + Fe \rightarrow Cu + Fe^{2+} \nonumber \]

\(E^{o}_{cell} = E^{o}_{Cu} - E^{o}_{Fe} = 0.377 V - -0.440 V = 0.777\, V\)

Note

Applying a potential larger than the standard potential to the cell will turn the cell into an electrolytic cell running the reaction in the non-spontaneous direction. This is used to recharge batteries and purify many metals including Na. Some examples may be found in the OpenStax general chemistry text.